*** Pre-print draft of paper forthcoming in The Leibniz Review 26 (2016) *** Leibnizian Bodies: Phenomena, Aggregates of Monads, or Both? Stephen Puryear North Carolina State University Abstract I propose a straightforward reconciliation of Leibniz's conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz's idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in the requisite sense. Accordingly, a phenomenon in one monad can indeed be an aggregate of other monads, in Leibniz's technical sense, just as the latter monads can be constituents of the phenomenon. So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think. 1. Introduction Leibniz notoriously advances what appear to be conflicting accounts of the nature of material bodies. On the one hand, he characterizes them as aggregates, assemblages, collections, or multitudes of substances. In some of these cases the substances he has in mind may well be of the corporeal variety, that is, the composites of substantial form and (secondary) matter of which he believes every body, whether animate or inanimate, is composed ad infinitum. But in many of these texts his point is clearly that bodies are, at least in the final analysis, aggregates of simple substances or monads.1 He therefore affirms what has come to be known as the aggregate 1. See, for example, GP IV, 491-92/AG 146-47; GP VII, 564; GP III, 367; GP III, 622; GP VI, 598/AG 207; GP VI, 607/AG 213; GP II, 504/L 614. Leibniz also expresses this claim by saying that a body is not a substance but substances, as is clear from what he says at A VI, 4, 1670/AG 105; cf. A II, 2, 639; GP II, 262. For further discussion, see Robert M. Adams, Leibniz: Determinist, Theist, Idealist [Leibniz] (New York: Oxford University Press, 1994) 241-44. Note that though in this paper I speak of bodies as aggregates of simple substances, the reconciliation LEIBNIZIAN BODIES 2 thesis, or as I will call it, Aggregation: (Aggregation) A body is an aggregate (assemblage, collection, multitude) of simple substances (monads). In still other texts, Leibniz expresses the same basic view by saying that simple substances are in bodies or matter, or equivalently, that such substances are constituents, ingredients, or elements of bodies.2 So he also endorses Inclusion: (Inclusion) Simple substances (monads) are in bodies as constituents, ingredients, or elements. On the other hand, Leibniz also frequently affirms what I will call Phenomenalism3: (Phenomenalism) A body is a phenomenon or appearance, that is, a being of perception or of the imagination. The problem, as commentators have long recognized, is that Phenomenalism appears to conflict with both Aggregation and Inclusion. Leibniz often speaks of phenomena in terms which imply that they are something like perceptual contents or (merely) intentional objects, that is, I am proposing works equally well on the assumption that bodies are ultimately aggregates of corporeal or composite substances. 2. For the claim that simple substances are in bodies or matter, see, for example, A VI, 4, 1673; GP IV, 492/AG 147; GP IV, 512/AG 163; GP II, 301. For the claim that simple substances are constituents, ingredients, or elements of bodies, see, for example, GP II, 267-68/DeV 301; GP VII, 502; GP II, 483-84/DesB 323; GP VI, 607, 608/AG 214; GP II, 517-19/AG 203-5. 3. Some commentators have wanted to reserve the term 'phenomenalism' for the view that bodies are mere appearances, appearances that neither correspond to nor are grounded in any external reality (see, e.g., Donald Rutherford, "Phenomenalism and the Reality of Body in Leibniz's Later Philosophy" ["Phenomenalism"] Studia Leibnitiana 22:1 (1990) 11-28; Donald Rutherford, "Metaphysics: The Late Period" ["Metaphysics"] in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (New York: Cambridge University Press, 1995) 143-47). As I am characterizing it, however, Phenomenalism remains neutral concerning whether the appearances with which bodies are identified correspond to or are grounded in anything outside the perceiver. LEIBNIZIAN BODIES 3 things which have their being only within the perceiving subject. 4 Throughout the period of his mature metaphysics (ca. 1686-1716), he often describes phenomena as internal to the soul or perceiver, and even more frequently likens them to well-ordered dreams.5 In still other texts he construes them as beings of perception or of the imagination, which he likens to beings of reason (A II, 2, 184-86/AG 85-86; GP VI, 586/AG 263). This is telling because in the schools, an ens rationis had typically been understood, as in Suárez, as "that which has being only objectively in the intellect."6 Leibniz's point would appear to be that phenomena have their being only within the faculties of perception and imagination of mind-like, perceiving substances, that is, monads. But if a body is a phenomenon in this sense, then it is hard to see how it could also be an aggregate of monads. For how could that which has its being only within the mind be in any real sense an aggregate of beings existing outside the mind? Likewise, it is hard to see how that which exists outside the mind, that is, other monads, could be in any real sense ingredients or constituents of a perceptual content subsisting only in the mind. 7 On the most natural 4. Cf. Adams, Leibniz, 219. In describing phenomena as perceptual contents, I do not mean to suggest that they are perceptions or perceptual states. Nor do I mean to rule out the possibility that they can be divided into smaller perceptual contents. Indeed they can be divided, just as a phenomenon such as the centaur in my dream can be divided into parts (the human part, the horse part), which can in turn be divided into still smaller parts, and so forth. Cf. Pauline Phemister, Leibniz and the Natural World: Activity, Passivity and Corporeal Substance in Leibniz's Philosophy [Natural World] (Dordrecht: Springer, 2005) 168. 5. On phenomena as internal, see GP VII, 296/L 232; A VI, 4, 1549-51/AG 46-47; A II, 2, 91/WFN 53; GP VII, 319/L 363; GP IV, 484/WFN 18; GP IV, 476-77/WFN 27; GP VI, 404/H 409-10; GP VI, 589-90/AG 265. On phenomena as like well-ordered dreams, see A VI, 4, 1622/Ar 315; A II, 2, 186/AG 86; A II, 2, 201-2/WFN 55; GP IV, 473/WFN 23; GP IV, 484/WFN 18; GP IV, 476-77/WFN 27; GP IV, 519/WFN 81; GP IV, 569/WFN 123; GP VI, 494/AG 188; NE 374-75; GP VII, 467-68; GP VI, 404/H 409-10; GP VI, 589-90/AG 265; GP III, 567n; GP III, 623; GP II, 435-36/DesB 227; GP II, 504/DesB 351. 6. Disputationes metaphysicae, disp. 54, sec. 1, no. 6, in John Doyle, Francisco Suárez, S. J.: On Beings of Reason, Metaphysical Disputation LIV (Milwaukee: Marquette University Press, 1994) 62. On Leibniz's familiarity with Suárez and his Disputationes, see Roger Ariew, "Descartes and Leibniz as Readers of Suárez: Theory of Distinctions and Principle of Individuation," in The Philosophy of Francisco Suárez, ed. Benjamin Hill and Henrik Lagerlund (New York: Oxford University Press, 2012) 46-54. 7. Glenn A. Hartz, Leibniz's Final System: Monads, Matter, and Animals [Final LEIBNIZIAN BODIES 4 interpretation of Phenomenalism, then, that doctrine seems flatly incompatible with Aggregation and Inclusion. Reactions to this apparent tension have run the gamut. Some commentators, such as Robert Adams and Donald Rutherford, have argued that on a proper understanding of these doctrines, they are in fact compatible.8 I will refer to this general outlook as compatibilism.9 But many Leibniz scholars have been unmoved by these arguments. They have instead tended to favor one form or another of incompatibilism, that is, the view that Phenomenalism does indeed conflict with Aggregation and Inclusion. Perhaps the most straightforward version of this sort of approach involves supposing that Leibniz treats these doctrines as compatible because he simply fails to see any inconsistency in them. But could he really have failed to perceive such a conspicuous tension in views he developed and defended many times over many years? The possibility seems rather remote. In the early days of this debate, some incompatibilists attempted to blunt the perceived tension by downplaying or denying Leibniz's commitment to one or the other of these doctrines. According to some, Leibniz embraced Aggregation but only "toyed" or "flirted" with Phenomenalism.10 According to another, he went through a period of uncertainty and vacillation until around 1704, when he settled on Phenomenalism as his considered view.11 These interpretations failed to System] (Abingdon: Routledge, 2007) 144; Richard T. W. Arthur, "Presupposition, Aggregation, and Leibniz's Argument for a Plurality of Substances" ["Presupposition"] Leibniz Review 21 (2011) 95. 8 . See Adams, Leibniz, 217-61; Rutherford, "Phenomenalism," 18-19; Rutherford, "Aggregation," 69; Rutherford, "Metaphysics," 147-48; Donald Rutherford, "Leibniz as Idealist" ["Idealist"] Oxford Studies in Early Modern Philosophy 4 (2008) 181; Paul Hoffman, "The Being of Leibnizian Phenomena" ["Being"] Studia Leibnitiana 28:1 (1996) 118; Paul Lodge, "Leibniz's Notion of an Aggregate" ["Aggregate"] British Journal for the History of Philosophy 9:3 (2001) 467-86; Lodge, DeV lxxxiv-v. 9. Cf. Hartz, Final System, 13-14. 10. See G. H. R. Parkinson, Logic and Reality in Leibniz's Metaphysics (Oxford: The Clarendon Press, 1965) 166-67, 190-91; Nicholas Jolley, "Leibniz and Phenomenalism," Studia Leibnitiana 18:1 (1986) 38-46. 11. See Louis Loeb, From Descartes to Hume: Continental Metaphysics and the Development of Modern Philosophy (Ithaca, NY: Cornell University Press, 1981) 293-305; cf. Montgomery Furth, "Monadology," The Philosophical Review 76:2 (1967) 184-89. LEIBNIZIAN BODIES 5 gain much traction, however, as commentators increasingly appreciated that Leibniz endorses all three doctrines in writings from the same period, including the last years of his life, and sometimes even in the very same writings. In recognition of this, other incompatibilists have taken up the challenge of explaining why Leibniz would more or less simultaneously affirm doctrines he recognized as incompatible. Thus, to mention just two recent examples, Glenn Hartz speculates that Leibniz intentionally kept both theories in play, exploring, defending, and critizing them without ever picking a winner, 12 while Daniel Garber maintains that Leibniz struggled to decide between the two competing conceptions of body and never arrived at a settled view of the matter.13 In what follows I will argue that there is no need to resort to such incompatibilist hypotheses, because Aggregation and Inclusion can plausibly be reconciled with Phenomenalism. In Section 2, I set the stage by considering and raising doubts about the strategy of revising the usual understanding of Phenomenalism in order to bring it into harmony with Aggregation and Inclusion. I then devote the remainder of the essay to developing and defending a version of the opposite strategy, namely, one which revises the usual understanding of Aggregation and Inclusion in order to bring them into line with Phenomenalism. In Section 3, I argue that when Leibniz affirms Aggregation and Inclusion, he can plausibly be taken to be presupposing the technical conceptions of aggregate, constituent, and ingredient that he articulates in various collections of definitions 12. See Hartz, Final System. Hartz frames his discussion in terms of the "realist theory", of which Aggregation and Inclusion are components, and the "idealist theory", of which Phenomenalism is a part (pp. 27-29). 13. See Daniel Garber, Leibniz: Body, Substance, Monad [Body, Substance, Monad] (New York: Oxford University Press, 2009) 267-388. Garber identifies two strands in Leibniz's thinking about the relation between monads and bodies: the view that bodies are aggregates of monads (p. 356) and the view that they are "the contents of the perceptions of individual monads" (p. 363). Some of his remarks suggest that he understands the latter view to include the idea that these perceptual contents have no foundation in any external reality. For example, he says that on this view bodies are "the common dream of an infinity of monads" (p. 364). Yet there is no reason why the contents of our perceptions of monads could not have a foundation in some external reality, and indeed in describing this view Garber speaks of monads "grounding" the existence of bodies through their perceptions of them (ibid.). The thought appears to be that what I am calling Aggregation and Phenomenalism are conflicting conceptions of body (cf. p. 296, n. 7). LEIBNIZIAN BODIES 6 assembled in the late 1670s and 1680s. According to these definitions, to be a constituent or ingredient of a thing is just be one of its immediate requisites, and an aggregate of Fs is simply a being that has those Fs as constituents, i.e., immediate requisites. Finally, in Section 4, I argue that the monads which serve as the real foundation of a well-founded phenomenon can plausibly be understood as its immediate requisites, even if the phenomenon has its being in another monad. From this it follows that a phenomenon having its being solely in the mind can be, in Leibniz's technical sense, an "aggregate" of things outside the mind, just as things outside the mind can be "constituents" or "ingredients" of things inside the mind. Properly understood, then, Aggregation and Inclusion do in fact cohere with Phenomenalism, and at least with respect to this issue, compatibilism should be preferred to any of the various incompatibilist approaches on offer.14 2. Leibnizian Phenomena Despite their apparent incompatibility, Leibniz writes as if he considers these doctrines perfectly compatible. As I noted above, he affirms all three in writings from the same period and even in the same writings. Even more significantly, there are many texts in which he speaks as if he thinks being an aggregate goes hand-in-hand with being a phenomenon. In a letter to the Electress Sophie dated 31 October 1705, for example, he writes that a mass of matter is only "an aggregate, a collection [amas], a multitude of an infinity of true substances, a well-founded phenomenon" (GP VII, 564).15 Similarly, in the Entretien de Philarète et Ariste, he remarks: 14. The question of compatibility also arises in connection with Leibniz's apparent acceptance of corporeal substances and his belief that the only true substances are simple. For a recent attempt at a compatibilist account of Leibniz's claims about substance, see Jeffrey K. McDonough, "Leibniz's Conciliatory Account of Substance," Philosophers' Imprint 13:6 (2013) 1-23. 15. The parenthetical "setting the understanding aside" which qualifies this remark has been taken by some to imply that the aggregate of simple substances mentioned here exists independently of perception (see Hidé Ishiguro, "Unity Without Simplicity: Leibniz on Organisms," The Monist 81:4 (1998) 549; Lodge, "Aggregate," 484; cf. Rutherford, "Idealist," 179n60). But this conflicts with Leibniz's claim that this aggregate is also a phenomenon, something which is not independent of perception. In my view, Leibniz uses the word 'understanding' here rather than a broader term such as 'perception' or 'mind' because the point of the parenthetical is not to set aside perception or mental activity in general, but to set aside ideal things, particularly mathematical bodies, which, as he points out LEIBNIZIAN BODIES 7 [B]ody is not a true unity; it is only an aggregate, what the schools call one by accident, an assemblage like a flock; its unity arises from our perception. It is a being of reason, or rather of imagination, a phenomenon. (GP VI, 586/AG 263).16 Texts such as these suggest that on Leibniz's view, something can be at once both an aggregate of substances and a phenomenon. On a number of occasions, Leibniz even claims that being an aggregate entails being a phenomenon.17 In a 1715 letter to Nicolas Remond, for instance, he reasons as follows: [S]econdary matter (e.g., the organic body) is not a substance, but a collection [amas] of several substances, like a pond full of fish or a flock of sheep. Consequently it is what we call unum per accidens, and in a word, a phenomenon. (GP III, 657; cf. GP II, 252/DeV 265; GP VII, 344/AG 319) The argument here is rather compressed, but elsewhere Leibniz supplies the missing premises. A collection or aggregate of substances, he tells us, is an unum per accidens rather than an unum per se. As such, it has unity only insofar as the substances are perceived as one, or in other words, only insofar as they appear to some perceiver as a unity (GP II, 517/AG 203; cf. GP VI, 586/AG 263). The unity of an aggregate is therefore phenomenal or apparent, and since on Leibniz's view being and unity are convertible, it follows that the being of an aggregate must also be phenomenal: This unity of the idea of an aggregate is a very genuine one; but at bottom it must be admitted that this unity of collections [collections] is only a respect or relation the foundation of which is in that which we find in each of the individual substances taken alone. Thus these Beings by Aggregation have only a mental unity, and consequently their being is also in a way mental, or phenomenal, like that of a rainbow. (NE 146; cf. A II, 2, 186/AG 86; GP II, 300/DesB 21; earlier in the letter, reside in the understanding and are "not at all composed of points" (GP VII, 561). In effect, the sense of his remark is that if we set aside ideal things, including mathematical bodies, what remains, actual bodies, are composed of indivisible constituents. 16. See also GP III, 69/WFN 129-30; GP II, 261-62/DeV 285-87. Leibniz does not explicitly indicate here what body is an aggregate of, but given his frequently expressed belief that composites must ultimately be aggregates of simples, the clear implication is that body is an aggregate of monads. 17. Cf. Adams, Leibniz, 245-47. LEIBNIZIAN BODIES 8 GP II, 304/DesB 31)18 From the fact that something is an aggregate, then, it follows that it must also be a phenomenon, even if it is an aggregate of substances. But how is this possible? In defending his version of compatibilism, Adams attempts to render Leibniz's position more palatable by offering reasons for thinking that an aggregate need not have the same ontological status as its constituents. For instance, he likens aggregates to sets, which need not have the same ontological status as their members.19 Further, he notes that an aggregate of substances, as "a sort of logical or metaphysical construction out of substances", need not have the same ontological status as those substances.20 In my opinion, however, he fails to make his case. For the observation that an aggregate need not have the same ontological status as its constituents does little to explain how something as different from simple substances as a perceptual content could be nothing but an aggregate of such substances.21 More importantly, it seems to me that any satisfactory case for the compatibility of Leibniz's claims about body must suggest a way in which our understanding of either Phenomenalism, on the one hand, or Aggregation and Inclusion, on the other, can plausibly be revised so as to bring them into harmony with the other(s). Since Adams makes no attempt to offer any such revised understanding, his case remains at best incomplete. One compatibilist who has proposed such a revision is Rutherford. He grants that Leibniz sometimes conceives of phenomena in the "narrower and more usual" sense of an appearance or object of perception,22 or the content of a mental representation, something which has its being only in the mind and which "by itself makes no claim on an extramental existence."23 However, he maintains that Leibniz frequently uses the term 'phenomenon' more broadly to refer to any aggregate or being by aggregation. In this sense of the term, a phenomenon is anything that 18. In his letter to Arnauld from 30 April 1687, Leibniz claims both that beings by aggregation "have their unity only in our mind" and that "one and being are reciprocal" (A II, 2, 186/AG 86). The clear implication is that aggregates also have their being only in the mind, thus are phenomena. 19. Adams, Leibniz, 244-45. 20. Adams, Leibniz, 245. 21. For other, related criticisms of this aspect of Adams' view, see Hoffman, "Being"; Hartz, Final System, 143-46, 149-51. 22. Rutherford, "Aggregation," 69-70. 23. Rutherford, "Idealist," 147, 181. LEIBNIZIAN BODIES 9 depends on perception for its existence.24 As such, it refers not only to those purely mental beings that are phenomena in the narrow sense, but also to aggregates of monads, which are not purely mental but "semi-mental" beings. These aggregates are not purely mental, says Rutherford, because they are constituted from monads in a way that no mental content could be. But they nonetheless depend on perception for their existence, since they do not exist unless some perceiver apprehends their constituents as one. Accordingly, so long as we understand Phenomenalism as the claim that a body is a phenomenon in this broader sense, that doctrine harmonizes perfectly with Aggregation and Inclusion. One problem with this recasting of Phenomenalism is that it does not fit particularly well with Leibniz's characterizations of phenomena. Although a few scattered texts can be found in which he speaks of phenomena as external, the bulk of the evidence, as I noted above, points to the narrow, more usual sense of the term.25 For this reason it seems to me that we would do better, if possible, to reconcile his claims about body without giving this seemingly ancillary use of 'phenomenon' such a prominent role in his thought. Moreover, there are some texts in which Leibniz affirms both Aggregation and Phenomenalism while clearly having the narrow conception of phenomenon in mind. For instance, in the aforementioned remark from the Entretien de Philarète et Ariste, Leibniz asserts in the same breath both that body is an aggregate-presumably of substances-and a phenomenon, which he equates with a being of the imagination. Slightly later in the same discussion he characterizes phenomena as "internal" and "in the soul", as "modifications of our souls", and as differing from dreams only by dint of their interconnections (GP VI, 589-91/AG 265-66). Surely the most natural interpretation of this remark is that a body is both an aggregate of monads and something having its being only within the soul. Another such text appears in an addendum to Leibniz's July 1714 letter to Remond. Within a single paragraph he claims that bodies are assemblages 24. See Rutherford, "Phenomenalism," 18-19; Rutherford, "Aggregation," 69-70; Rutherford, "Idealist," 181. For similar proposals see Phemister, Natural World, 165-69; Garber, Body, Substance, Monad, 292-96; Lodge, DeV lxxxiii-lxxxiv. 25. For descriptions of phenomena as external, see GP III, 465; GP VI, 599/AG 208. Leibniz does draw a distinction in the New Essays between internal and external appearances, but by the latter he means "those consisting in what appears to others" (NE 237). Such appearances need not be external to perceivers in general. For evidence of the narrow conception of phenomena, see §1 above and especially note 5. LEIBNIZIAN BODIES 10 of monads; that they are well-founded phenomena or appearances; that these phenomena are "different in different observers" and "like exact and enduring dreams"; and that material objects are "nothing outside of perceptions" (GP III, 622-23). Once again, the clear implication is that these aggregates of monads are phenomena in the narrow sense of a kind of mental being. Of course, we could suppose that Leibniz vacillates in his understanding of phenomena even within these passages, but if possible, I would prefer to avoid saddling him with that unflattering charge. Besides these textual considerations, there is another reason for doubting whether Leibniz ever conceived of phenomena as having any claim to an extramental being or existence. It is supposed to be of the essence of a phenomenon that it depends on perception for its being. By perceiving or imagining many substances as one, we bring it about that the phenomenon has being. We give it unity, and thus give it being. But if that being is extramental, even in part, then it follows that we have the power to create new beings outside of us just by way of our mental activity-a power of a sort that seems utterly foreign to Leibniz's thought. In contrast, there is nothing untoward in the idea that through our mental activity we create new perceptual contents. Hence, if a phenomenon is something which depends on perception for its being, it seems to follow that its being must be within the mind, not outside it; it must be a phenomenon in the "narrower and more usual" sense. Having expressed my doubts about the prospects of revising Phenomenalism in order to bring it into line with Aggregation and Inclusion, I now want to lobby for a version of the opposite approach. I will argue that Aggregation and Inclusion can plausibly be construed so as to bring them into harmony with Phenomenalism, as that doctrine is most naturally understood. Ironically, I will rely on some important insights from other aspects of Rutherford's interpretation of Leibniz, though not ones he appropriates in addressing this problem. 3. Leibnizian Aggregates During the late 1670s and the 1680s, just as his mature metaphysics was taking shape, Leibniz was hard at work developing definitions of various basic concepts in support of his plan for a scientia generalis or universal method for science. 26 As it happens, we find among these definitions technical characterizations of 'aggregate' and of the related inclusion terms 26. On the idea of a scientia generalis, see Louis Couturat, La Logique de Leibniz d'après des Documents Inédits (Paris: F. Alcan, 1901) chs. 5-6. LEIBNIZIAN BODIES 11 that differ from the ordinary, mereological understanding of these terms.27 My contention in what follows will be that these technical definitions are precisely the ones Leibniz presupposes when he affirms Aggregation and Inclusion, and that once this is recognized, we can see that these doctrines straightforwardly cohere with Phenomenalism. The first of these contentions is not particularly new. In fact, the idea that Leibniz presupposes these technical conceptions in his mature metaphysical writings goes back at least to Rutherford's work in the early 1990s.28 More recently, the idea has been taken up by Stefano Di Bella, Massimo Mugnai, Richard Arthur, and again by Rutherford, though none of them apply the idea to our problem in the way I will be doing.29 As these writers have already analyzed the relevant texts in considerable detail, I will forego a close exposition of that material and instead sketch the general contours of the relevant conceptual terrain. To begin, it will be necessary to consider some background concepts from Leibniz's theory of conditions. Leibniz defines a condition (conditio) as something that must be posited in order for another thing, the conditionatum, to be posited (A VI, 4, 389; A VI, 4, 401; A VI, 4, 563; A VI, 4, 641; A VI, 4, 871; A VI, 4, 932). In essence, one thing is a condition of another just in case the latter is ontologically dependent on the former. He then defines a requisite (requisitum) as a condition that is prior in nature to the corresponding conditionatum (A VI, 4, 308; A VI, 4, 402; A VI, 4, 563; A VI, 4, 627; A VI, 4, 871). The notion of priority in nature is one Leibniz characterizes in a number of ways. In some texts, he describes this kind of priority as a matter of being more easily understood (A VI, 4, 180; A VI, 4, 389; A VI, 4, 563) or more easily shown to be possible (A VI, 4, 180; A VI, 4, 1427). In others, he claims that thing A is prior in nature to thing B just in case A has a simpler concept (notio) than B (A VI, 4, 389; A VI, 4, 872), enters into the concept (conceptum) of B (A VI, 4, 937), or involves the reason for B (A VI, 4, 563; A VI, 4, 940). Without going into the details of how these characterizations are related or whether they are equivalent or even compatible, I will proceed under the 27. Cf. Hartz, Final System, 105. 28. See, especially, Donald Rutherford, "Leibniz's 'Analysis of Multitude and Phenomena into Unities and Reality'," Journal of the History of Philosophy 28:4 (1990) 525-52. 29. See Stefano Di Bella, "Leibniz's Theory of Conditions: A Framework for Ontological Dependence," Leibniz Review 15 (2005) 67-93; Massimo Mugnai, "Leibniz and 'Bradley's Regress'," Leibniz Review 20 (2010) 1-12; Arthur, "Presupposition," 91-115; Rutherford, "Idealist". LEIBNIZIAN BODIES 12 assumption that the central idea has to do with conceptual priority. So I will assume that one thing is prior in nature to another just in case its concept is included in or presupposed by the concept of the other. 30 Accordingly, A will be a requisite of B just in case (i) A is conceptually prior to B and (ii) B cannot be posited without thereby positing A. Within the category of requisites, Leibniz distinguishes the mediate from the immediate. Mediate requisites, he tells us, are those which "must be investigated by reasoning, such as causes" (A VI, 4, 627/Ar 271). Immediate requisites, in contrast, must be "independent of any change or action and passion" (A VI, 4, 650). The distinction is not entirely clear, but his thought appears to be that the dependence of a thing on its mediate requisites is physical or metaphysical, whereas the dependence of a thing on its immediate requisites, if it has them, is conceptual. Thus oxygen would be a mediate requisite of fire, God a mediate requisite of the universe, and so forth. But, to use Leibniz's own favorite illustration, the endpoints of a finite line would be immediate requisites of the line, since it is not just physically or metaphysically but conceptually impossible for there to be such a line in the absence of its endpoints (A VI, 4, 1669/AG 103; A VI, 4, 1673; GM VII, 19/L 667). From this point of view, to say that one thing is an immediate requisite of another is to say that the latter depends on the former with conceptual necessity. In addition to these presupposition relations, Leibniz defines a corresponding system of what may be called entailment relations. If positing B presupposes positing A, then he calls B the conditioned (conditonatum) and A the condition (conditio). But if positing A entails positing B, then in his terminology B is the inferred (illatum) and A the inferential basis (inferens) (A VI, 4, 389; A VI, 4, 401; A VI, 4, 563; A VI, 4, 641; A VI, 4, 864; A VI, 4, 869; A VI, 4, 871; A VI, 4, 940), or B the determined (determinatum) and A the determining (determinans) (6.4:404). If positing B presupposes positing A and A is prior in nature to B, Leibniz calls A the requisite (requisitum) and B the requiring (requirens). Similarly, if positing A entails positing B and A is prior in nature to B, he calls A the predetermining (praedeterminans) and the B the predetermined (praedeterminatum) (A VI, 4, 403; A VI, 4, 564).31 Finally, 30 . On the notion of priority in nature, see Christia Mercer, Leibniz's Metaphysics: Its Origin and Development (New York: Cambridge University Press, 2001) 314-19. 31. Alternatively, Leibniz sometimes refers to an inferens that is prior in nature to the corresponding illatum as the cause or producer (producens), and the illatum as the effect or product (productum) (A VI, 4, 393; A VI, 4, 565; A VI, 4, 872). LEIBNIZIAN BODIES 13 though this is not entirely clear, Leibniz appears to distinguish between predetermination that is mediate, as when a cause produces a distinct effect, and predetermination that is immediate, as when a foundational reality gives rise to a less foundational reality which it grounds. The latter relation he also calls resulting: "I understand that to result [...] which is immediately understood to be posited once we have posited those things from which it results" (A VI, 4, 310; cf. GM VII, 21-22/L 669). With these background concepts in place, we can now introduce Leibniz's technical definitions of 'aggregate' and the related inclusion terms. Since he has more to say about them, I will start with the latter. Here four points are salient. First, in Leibniz's terminology, to be in [inesse] or exist in [inexisto] something is the same as to be an ingredient [ingrediens], constituent [constituens], or content [contentum] of that thing. This is evident both from the fact that he uses these terms interchangeably and from the fact that he defines them the same way. Second, Leibniz frequently and typically defines inclusion in terms of presupposition, and more specifically in terms of the idea of an immediate requisite (A VI, 4, 411; A VI, 4, 650; A VI, 4, 941; A VI, 4, 1001-2; GM VII, 19/L 667). In his idiolect, to say that A is an ingredient of L is just to say that A is an immediate requisite of L. More colloquially, a thing's ingredients are just those things it immediately presupposes. Third, on a few occasions, Leibniz offers an alternative definition of inclusion not in terms of presupposition, but in terms of entailment, that is, not in terms of being an immediate requisite, but, in effect, in terms of being a result or "immediate predeterminatum" (A VI, 4, 998; A VI, 4, 1002; cf. A VI, 4, 627/Ar 271). According to this alternative definition, to say that A is an ingredient of L is just to say that L results either from A itself or from A together with some other entities B, C, ... (but not from B, C, ... alone). Finally, it is important to note that Leibniz appears to consider these definitions not only compatible but (extensionally) equivalent. This is evident from the fact that in two of the texts in which he defines inclusion in terms of resulting, he reiterates that the ingredients are immediate requisites of the thing they predetermine (A VI, 4, 998; A VI, 4, 1002). An interesting consequence of this equivalence is that for Leibniz, A will be an immediate requisite of L just in case L results either from A itself or from A together with B, C, ... (but not from B, C, ... alone). So the endpoints of a finite line will be its immediate requisites. But by that very fact the line will also result from the endpoints, because they cannot be posited as such, that is, as endpoints, without thereby positing the line, it being impossible to have termini without a thing that terminates. At the same time, it will be true that those LEIBNIZIAN BODIES 14 things from which another results are its immediate requisites, since a thing results from its constituents and we cannot posit a thing without thereby positing its constituents, assuming it has them. As for the concept of aggregate, the first thing to note is that if aggregation is just the inverse of inclusion, then we would expect Leibniz to define the notion of an aggregate in keeping with his technical definitions of the inclusion terms. This expectation is not disappointed, as we can see from this text composed around 1689 or 1690: In order to explain what it means to contain [continens] and be contained [contentum] or exist in [inexistentia], the concept of immediate requisite is not needed, for to have an aggregate it suffices that several beings different from it are understood to come together in a way similar to it. Thus if A, B, C are posited in the same way, and by this very fact L is understood to be posited, then A, B, C will be aggregated things [aggreganda] and L the whole arising through aggregation. At the same time, it is true that they are immediate requisites. (A VI, 4, 998; cf. A VI, 4, 627/Ar 271) Here Leibniz begins by making the point that inclusion can be defined without appealing to the notion of an immediate requisite, but then he seamlessly transitions to making the point that an aggregate is just something which must be understood to be posited by the very fact that two or more other things are posited "in the same way".32 In effect, he appears to be defining an aggregate as a thing which results from two or more other things, just as he elsewhere defines the ingredients of a thing as those things from which it results. But he adds that even though the notions of aggregate and ingredient can be defined in this way, it is also true that the constituents of the aggregate will be its immediate requisites. The implication appears to be that an aggregate can also be defined as some L which has A, B, C as its immediate requisites. Many of the texts in which Leibniz propounds these technical definitions of aggregation and inclusion date from the 1680s, around the time his mature metaphysics was taking shape. Yet in none of them does he clearly have that metaphysics in view. One question we must therefore consider is what reason we have to believe that he understands the various 32. When Leibniz speaks of A, B, C being "posited in the same way" and coming together "in a way similar to" L, he may mean that what we posit of A, B, C (e.g., being, existence, reality) must be the same quality that, by that very fact, we posit of L, in order for L to be an aggregate of A, B, C. LEIBNIZIAN BODIES 15 inclusion and aggregation terms in accordance with these definitions when, in other contexts, he discusses the relationship of bodies to monads. Though the evidence concerning this point is far from abundant, there are several texts in which Leibniz clearly alludes to these technical definitions in explicating his theory of body. In some of these, he claims that monads are not parts but requisites, even immediate requisites, of bodies. One relatively late example comes from a 1712 letter to Friedrich Wilhelm Bierling, in which Leibniz notes that monads "are not parts of bodies, but requisites" (GP VII, 503). Even more explicit are a pair of remarks in the Fardella notes, which Leibniz recorded in 1690, around the same time he composed some of the texts in which he articulates the technical definitions of aggregation and inclusion. In the first of these, Leibniz cautions that we must not infer that the indivisible substance enters into the composition of body as a part, but rather as an essential, internal requisite, just as we grant that a point is not a part that makes up a line, but rather something heterogeneous, which is nonetheless necessarily required for the line to be and to be understood. (A VI, 4, 1669/AG 103) By a requisite that is "essential" and "internal", we can plausibly assume that Leibniz means an immediate requisite, as opposed to a mediate one, such as a cause, which would be external and inessential. So the point would be that substances are not parts but immediate requisites of bodies. In the second of the Fardella passages, Leibniz is even more explicit about this: There are infinite simple substances or created things in any particle of matter; and matter is composed [componitur] from these, not as from parts, but as from constitutive principles or immediate requisites, just as points enter into the essence of a continuum and yet not as parts; for nothing is a part unless it is homogeneous with a whole, but substance is not homogeneous with matter or body any more than a point is with a line. (A VI, 4, 1673; cf. GP VII, 503; GP II, 252/DeV 265; GP II, 435/DesB 227; GP II, 451/DesB 255) Once again, monads are said to relate to bodies not as parts but as immediate requisites. A body is therefore not an aggregate of monads in the sense of a mereological whole of monads, but in the technical sense of a being which has monads as its (ultimate) immediate requisites. In all these passages, Leibniz is clearly alluding to his technical conception of aggregate. LEIBNIZIAN BODIES 16 Another significant text appears in Leibniz's correspondence with De Volder, in a letter dated 30 June 1704. Once again he warns that his talk of bodies being composed of monads must be understood with care: Accurately speaking, however, matter is not composed of constitutive unities, but results from them, since matter or extended mass is only a phenomenon grounded [fundatum] in things, like a rainbow or parhelion, and all reality belongs only to unities. Phenomena can therefore always be divided into smaller phenomena which could appear to other more subtle animals, and a smallest phenomenon will never be reached. Substantial unities are not parts but the foundations [fundamenta] of phenomena. (GP II, 268/DeV 303; cf. GP II, 436/DesB 227)33 The parts of phenomena, Leibniz tells us here, are always smaller phenomena, not substantial unities. Unlike before, however, there is no mention here of the idea that monads are immediate requisites of bodies. Instead, he contrasts the idea that bodies are composed of monads as of parts with the idea that bodies result from monads, which he connects in turn with the thought that bodies, as phenomena, are grounded in or founded upon simple substances. As we are now in a position to see, however, the fundamental point is the same. In Leibniz's idiolect, the claim that L results from A, B, and C is equivalent to the claim that A, B, and C are immediate requisites of L, which is in turn equivalent to the claim that L is an aggregate of A, B, and C. Hence, to say that a body is not composed of monads as of parts, but rather results from monads, is once again to suggest that a body is an aggregate of monads not in the ordinary sense of a mereological whole of monads, but in the technical sense of a being 33. An anonymous referee points out that this talk of phenomena being divided into smaller phenomena, which may appear to other, more subtle animals, casts doubt on the view that phenomena have their being only in the soul; for a phenomenon having its being in one soul cannot appear to another soul. I reply that even though strictly speaking a phenomenon has its being in a particular substance, we may suppose that Leibniz sometimes thinks of the phenomenon in one soul as in a sense identical to the corresponding phenomena in other souls. Thus, the expression "the phenomenon of the moon" might refer not just to the moon-appearance in my mind, but collectively to all the moon-appearances in various substances. From this point of view, a phenomenon may be said to appear to other substances, even though it has its being only within the soul (or souls), and even if, strictly speaking, each phenomenon has its being only within a particular soul. LEIBNIZIAN BODIES 17 which has monads as its immediate requisites. The same can be said of other passages in which he speaks of bodies or matter as resulting from monads.34 In addition to these texts, I want to offer one other reason for thinking that Leibniz has these definitions in view when he affirms Aggregation and Inclusion. The reason, which I will develop in the next section, is simply that if we assume he was presupposing these definitions, we can make good sense of an aspect of his view that is otherwise quite puzzling: namely, his belief that an aggregate of monads is also a phenomenon having its being in the perceiving subject. 4. Monads as Immediate Requisites So far I have argued that in Leibniz's terminology, Aggregation and Inclusion amount to nothing more than the claim that a body is a being which has simple substances as its (ultimate) immediate requisites, or equivalently, which results from such substances. That is the sense in which monads are in matter and bodies are aggregates of monads. To say this much, however, is not yet to solve our problem, but only to reframe it. The problem now becomes that of explaining how a phenomenon having its being in one monad could have other monads as its immediate requisites. Recall that in Leibniz's terminology, A is an immediate requisite of B just in case (i) A is prior in nature to B and (ii) the positing of B immediately presupposes the positing of A. As for (i), it can plausibly be argued that on Leibniz's view, a phenomenon's foundational monads are naturally prior to it in the sense that they constitute God's reason for creating that phenomenon rather than another (T 66; Monadology, §§49-52).35 (ii), however, is a different story. In what sense, we might ask, does positing a phenomenon immediately presuppose the positing of those monads which serve as its real foundation, that is, its foundational monads? As I noted in Section 1 above, Leibniz characterizes phenomena as internal to the soul, as like well-ordered dreams, and as beings of perception or of the imagination. As such, they would appear to have their being in the perceiving subject. But if so, then it cannot be the being of a phenomenon which immediately presupposes its foundational monads. For the phenomenon would continue to have its being in the perceiving 34. On the notion of resulting, see Rutherford, "Idealist," 179-84, and the citations therein. 35 . On this aspect of Leibniz's view, see Stephen Puryear, "Monadic Interaction," British Journal for the History of Philosophy 18:5 (2010). LEIBNIZIAN BODIES 18 subject even if its foundation ceased to exist, though of course it would then be an imaginary rather than a real phenomenon. The difficulty therefore remains of explaining how a phenomenon's foundational monads can plausibly be understood as its immediate requisites. Unless and until this can be explained, we have not yet vindicated the idea that a body could be both a phenomenon and an aggregate of monads. In this section, I will attempt just such an explanation. In particular, I want to suggest that there are at least two important respects in which a phenomenon immediately presupposes its foundational monads, and thus two respects in which those monads can be considered immediate requisites of the phenomenon, even though the phenomenon does not depend on those monads for its being. Hence, I will be arguing for the striking thesis that a phenomenon having its being in one monad can be understood to have other monads as its immediate requisites, and thus, in Leibniz's technical sense, to be an aggregate of those monads. To be sure, when Leibniz defines the aggregation and inclusion terms, he sometimes characterizes the dependence of a thing on its immediate requisites as a dependence of being (see, e.g., A VI, 4, 871). However, he sometimes characterizes it as a dependence of existence. For instance, he explains that "If A is an immediate requisite of B, A is said to be in B, that is, A must not be posterior in nature to B, and having posited the nonexistence [non existere] of A, it must follow that B also does not exist [non existere]" (A VI, 4, 650). Similarly, he writes: "If, having posited that A exists [existere], it follows that B exists [existere] (not necessarily at the same time), A will be the inferential basis [inferens], B the inferred [illatum]" (A VI, 4, 563). In yet another passage he appears to characterize the dependence as a dependence of reality: And hence we see that, that is in a subject whose reality is part of the reality of the subject itself. Or, to speak in a way more apt for forming and demonstrating propositions, A is in B, if every thing that is immediately required for A is also immediately required for B. But that which is immediately required for something, such that nothing more is immediately or even mediately required for it, can be called reality. (A VI, 4, 990)36 36. Cf. Rutherford, "Idealist," 173. An anonymous referee notes a potential problem for my view in this text. Leibniz defines reality as "that which is immediately required for something, such that nothing more is immediately or even mediately required for it." On my view, however, the reality of a body, LEIBNIZIAN BODIES 19 Hence, while the relation of a thing to its immediate requisites can be understood as a dependence of being, Leibniz appears to allow for the possibility that the dependence is one of existence or reality. Let us consider, then, whether a phenomenon might be thought to depend immediately on its foundational monads in one of these other senses. Starting with the easier case, it seems clear that a phenomenon's reality does depend immediately on the existence or reality of its foundational monads. Though in themselves imaginary, phenomena can be said to acquire a kind of reality, Leibniz thinks, in virtue of having a foundation in some external, substantial realities. 37 A phenomenon with this sort of reality therefore depends on its foundational monads for this reality. Having posited the reality of a phenomenon, we must thereby be understood to have posited the reality of its foundation. Further, this dependence has just the sort of immediacy which Leibniz requires for aggregation in his technical sense. The reality of the foundation does not cause the reality of the phenomenon; nor is the connection a mere physical or metaphysical one. Rather, the existence of the phenomenon immediately and necessarily presupposes the existence of its foundation-that is, presupposes it with conceptual necessity. For it is conceptually impossible for a phenomenon to be real in this sense without having a foundation in this substantial reality. This provides us with one sense, then, in which a phenomenon's foundational monads can be understood as its immediate requisites, even if the phenomenon does not depend on those monads for its being. Now for the trickier case of existence. The first thing to note here is that, which is the reality of its foundational monads, is not the only thing the body immediately requires; for it evidently also immediately requires the perceiver in which it has its being. I do not know whether this passage can be fully reconciled with my view, but I would note that it is far from clear that the contents of a perceiving substance always immediately require or presuppose that substance in the sense Leibniz has in mind here, since otherwise every substance would be in each of its own contents-a consequence he would presumably reject. 37. In some texts Leibniz acknowledges that a phenomenon can be considered true or real even if it lacks a foundation in some external reality, in virtue of its coherence with other phenomena (see, e.g., A VI, 4, 1502/L 364; DM 14; GP II, 270/DesB 307). I follow Adams in seeing this kind of reality as weaker than phenomenal reality in the fullest sense, which requires an external foundation (Adams, Leibniz, 259-60). My point is that this more robust sort of reality does depend immediately on the existence and reality of the phenomenon's foundation. I thank an anonymous referee for pressing me to clarify this. LEIBNIZIAN BODIES 20 contrary to what is often assumed, existence is not the same as being. If it were, there could be no such dependence of a phenomenon on its foundation, since a phenomenon does not depend on its foundation for its being. On Leibniz's view, however, existence is more than mere being. He makes this clear when he claims, as he does in a number of places, that being is (distinctly) conceivable, whereas existence is (distinctly) perceivable (A VI, 1, 285/L 91; A VI, 4, 869; A VI, 4, 1499, 1500/L 363; A VI, 4, 2739; C 437). In his thought, conceivability concerns possibility, so the contrast here is between the possible and the actual. We conceive the possible, but perceive the actual. This means that existence is something more than just being. A being [ens] is anything that is possible, and to have being [esse] is nothing other than to be possible: "Being is that the concept of which involves something positive or that which can be conceived by us, provided what we conceive is possible and involves no contradiction" (A VI, 4, 1500/L 363). Leibniz also equates possibility with essence [essentia]. So being [esse] is likewise equivalent to essence, something that is all the less surprising given the etymological connection between 'essentia' and 'esse'. In contrast, to exist [existere] is to be not just possible but actual, not just conceivable but perceivable. The difference between being and existence can also be seen in Leibniz's doctrine of the striving possibles, which have their being in the divine understanding (T 201; GP VII, 303-5/AG 150-52). These possibles all strive to exist, but only some succeed. Yet those which fail to exist still have being, namely, in the mind of God. Existence is therefore more than mere being.38 Indeed, on Leibniz's view, even beings that we humans have actually conceived or imagined, and which therefore have their being in our minds as well as the divine mind, can fail to exist. This point emerges from an essay on freedom and contingency in which Leibniz appeals to "those possibles, which neither are, nor were, nor will be" in an interesting (though flawed) argument against necessitarianism (A VI, 4, 1653-54/AG 94). The argument is this: [I]f certain possibles never exist, then certainly existents are not always necessary, for otherwise it would be impossible for others to exist in their place, insofar as everything that 38. Leibniz does occasionally speak of imaginary phenomena existing in the mind (A VI, 4, 1500/L 363; cf. GP II, 517/DesB 371/AG 203). This sort of existence is equivalent to having being in the mind, but should be distinguished from the kind of existence which can only be ascribed to real beings (i.e., existence tout court). LEIBNIZIAN BODIES 21 never exists would be impossible. Nor indeed can we deny that many fables, such as those called Roman, are considered possible, even though they find no place in this universal series, which God chose, unless one imagines that in so great an expanse of space and time there are some poetical regions where King Arthur of Great Britain, Amadis of Gaul, and the illustrious Dietrich von Bern of the German stories can be seen wandering round. (ibid.) In this text Leibniz assigns fictional characters such as King Arthur, whom we have actually imagined and who thus have being in our minds, i.e., are beings of our imagination (or at least of our reason), to the category of possibles that do not exist. So the fact that they having being in our minds does not suffice for their existence. In light of all this, two points seem clear. First, things that have substantial being, that is, actual substances, exist. Second, imaginary phenomena such as King Arthur do not exist, even though they have their being in minds that exist. But now let us add to this the point that in Leibniz's ontology, there is a third type of thing which lies between substances and imaginary phenomena: namely, real or well-founded phenomena. Like imaginary phenomena, these phenomena have their being in the mind: they are beings of perception or of the imagination. But in contrast to imaginary phenomena, well-founded phenomena do have some claim to existence-not, to be sure, an extramental existence, but a kind of existence nonetheless. On Leibniz's view, King Arthur does not exist, nor does the centaur, the golden mountain, or any other fictional or merely possible being. But well-founded phenomena do exist. For instance, the rainbow that I see in the sky after a storm actually exists; unlike King Arthur, it is not a merely possible being. What explains this difference? It can only be that a well-founded phenomenon has a foundation in some external reality, whereas imaginary phenomena do not. Hence, from this point of view, a well-founded phenomenon can be said to exist, and to exist in virtue of having a foundation in some external reality. It therefore depends on this foundation for its existence. And since this dependence is an immediate one, this gives another sense in which a phenomenon's foundational monads can be considered it immediate requisites. My suggestion, then, is that a phenomenon can be understood to depend immediately on its foundational monads for both its reality and its existence, even though it does not depend on those monads for its being.39 39. Others who distinguish being from reality in their interpretations include LEIBNIZIAN BODIES 22 Having posited a phenomenon, or more exactly, having posited its reality or existence, we must by that very fact be understood to have posited its foundation. As such, the monads constituting that foundation can plausibly be viewed as immediate requisites of the phenomenon. Given Leibniz's technical definition of an aggregate of monads as a being which has those monads as immediate requisites, then, it follows that a phenomenon in the mind can be considered an aggregate of monads outside the mind. A cardinal advantage of this reading is that it furnishes a rather straightforward reconciliation of Leibniz's apparently incompatible claims about body. By showing how monads could be immediate requisites of a phenomenon having its being in some other monad, it allows us to see how a body could be both a phenomenon and, in Leibniz's technical sense, an aggregate of monads. Likewise, it allows us to see how those monads could be in, or be ingredients or constituents of, a phenomenon. In short, on this way of understanding things, Aggregation and Inclusion cohere perfectly with Phenomenalism. Against this, one might object that it is rather a stretch to suppose that a phenomenon's foundational monads are its constituents or ingredients, or that they are in or internal to the phenomenon, given that their being is outside of, and not constitutive of, the being of the phenomenon. I reply as follows. On my reading, Leibniz considers an aggregate to be a phenomenon, which is in itself imaginary but can acquire a kind of reality in virtue of having a foundation in certain monads. As he frequently puts it, this aggregate, or phenomenon, "borrows" or "derives" its reality from those substances.40 Indeed, he says of beings by aggregation, "which are Lodge, "Aggregate," 482-83; Kenneth L. Pearce, "Leibniz and the Veridicality of Body Perceptions," Philosophers' Imprint 16:5 (2016) 8. However, their views differ from mine in important respects. Lodge holds that Leibnizian aggregates have a "complex kind of being", part of which is in, and dependent on the mind, and part of which is outside the mind, and dependent upon its constituent substances (p. 483; cf. pp. 472-73)-a strange kind of being! In contrast, I see the being of the phenomenon as wholly within, and wholly dependent on, the mind (or substance) to which it appears, even though it has a reality that can be said to derive from external substances. Pearce assimilates existence to being (p. 8), whereas on my view, existence (tout court) is understood as correlated with reality: only things which are real can be said to exist (tout court), and not all beings are real. For an earlier account on which reality is distinguished from unity, see Glenn A. Hartz, "Leibniz's Phenomenalisms," The Philosophical Review 101:3 (1992) 517. 40. See, for example, A II, 2, 184/AG 85; GP VI, 516; GP II, 261-62/DeV 285-87; LEIBNIZIAN BODIES 23 phenomena rather than substances," that "all their reality consists only in that of simple things" (GP III, 69/WF 129-30). Likewise, in the text quoted above from the 30 June 1704 letter to De Volder, he affirms that matter "is nothing but a phenomenon founded in things," that "there is no reality in anything except the reality of unities," and that "substantial unities are not parts, but the foundations of phenomena." (GP II, 268/DeV 303). His view is therefore that aggregates, which are phenomena, have a reality that consists in the reality of their foundational substances. Of course, this is not to say that the aggregate has reality in the same way or to the same degree as the individual substances: it has only phenomenal reality, not substantial reality. Nonetheless, its reality consists in, or is constituted from, the reality of the substances. In a way, the reality of the substances is in the phenomenon. Hence, this gives us a sense in which, intuitively, these substances can plausibly be considered constituents of the phenomenon. Even though they are not constitutive of the phenomenon's being, they, or rather their reality, is constitutive of the reality of the phenomenon, and thus, in a sense, the substances themselves can be considered constituents of that phenomenon.41 GP II, 267/DeV 301. 41. Here I part company with Samuel Levey, who contends that an aggregate can borrow reality from its constituents only if (roughly) it is nothing more than those constituents (Levey, "On Unity, Borrowed Reality and Multitude in Leibniz," Leibniz Review 22 (2012) 104-5; cf. Rutherford, "Idealist," 148, 160-61, 184). I see no reason why a phenomenon could not be something more than its foundation-have some being over and above the being of its foundation-and yet have a reality that it derives from that foundation. Analogy: If the images on my television screen accurately depict actual events (e.g., a soccer match), then those images could be said to have a kind of reality in virtue of having a real foundation, a reality which could not be ascribed to images that depict fictional events. That reality would have no other source than the reality of the events being depicted, and thus the reality of the images could be said to be derived from that of the events. Yet the images would be something more than the events. Some commentators, perceiving an inconsistency in the idea that an aggregate could have its being in the mind but a reality that it derives from its substantial constituents, have sought to avoid this result by weakening Leibniz's thesis of the convertibility of being and unity (see §2 and n. 18 above). According to Hoffman, Leibniz considers being and unity only extensionally equivalent: "Something has being if and only if it has unity, but what its being consists in might be different from what its unity consists in" (Hoffman, "Being," 118). This allows him to grant that Leibnizian aggregates can have their unity only in the mind without having to admit that they have their being only in the mind. Hartz sees the convertibility LEIBNIZIAN BODIES 24 To this a second point may be added. In the first edition of the Critique of Pure Reason, Kant astutely observes that talk of things being in us or outside of us is subject to an unavoidable ambiguity.42 On the one hand, this talk may be understood physically or spatially (in his terminology: empirically). In this sense, to be outside of us is to be located some distance away from us, whereas to be in us is to be located in a region of space that is a (proper) part of the space we occupy. On the other hand, talk of internal or external objects may be understood metaphysically (in Kant's terminology: transcendentally). To say that a thing is internal to us in this sense is just to say, not that it is spatially located within us, but rather that it has its being in us and through us. Such a thing is internal in the sense in which, for example, a modification is internal to the substance it modifies. To say that a thing is external to us in this sense is just to say that it does not have its being in or through us, that is, that it has its being in itself (e.g., another substance), or in some third thing that has its being in itself, as with the modification of another substance. Now, up to this point, when I have spoken of phenomena as internal to the mind or soul, or of other substances as external to the same, I have had the metaphysical sense in mind: the point was not that phenomena are spatially contained within the mind, or that other substances are located outside the mind in a spatial sense, but that phenomena have their being in and through the mind, whereas other substances do not. So the puzzle was not how something located in one place could be an aggregate of things located elsewhere; rather, the puzzle was how something having its being (metaphysically) in one substance could be an aggregate of substances that are (metaphysically) external to that substance. But now suppose that we shift from this metaphysical level of description to the physical (or spatial) level. Physically speaking, a phenomenon is (at least typically) located outside of me. For instance, the table is external in the sense that I represent it as being ten feet in front of me. On Leibniz's view, however, the foundational of being and unity as restricted to substances, and thus as not applying to aggregates (Hartz, Final System, 217n1). However, both of these views conflict with the passage from NE 146 quoted above (§2), in which Leibniz argues that because aggregates have a mental unity, they must also have a kind of mental being (i.e., that of a mental content or object of perception). On the view I am proposing, there is no inconsistency in saying that aggregates have their unity and being in the mind, but a reality that they derive from their substantial constituents; there is thus no need for such maneuvers. 42. See Immanuel Kant, Critique of Pure Reason, A372-73. LEIBNIZIAN BODIES 25 substances of this phenomenon are, in at least a loose or virtual sense, located in the same place, insofar as they each represent the world from their own (spatial) point of view, and thus each represent themselves as occupying a certain position in space.43 (In representing an object as ten feet in front of me, I represent myself as ten feet from that object, etc.) Hence, even though in the metaphysical sense a phenomenon is internal to the substance, whereas its foundational substances are external to that substance, in the physical sense those foundational substances are located within the phenomenon; for each of them has a location which is a proper part of the spatial region occupied by the phenomenon. Thus, Leibniz's talk of monads as constituents of, and as internal to, a phenomenon having its being in another monad, is justified not only by the fact that the phenomenon's reality is constituted by the reality of those monads, but also by the fact that, at least in a loose or virtual sense, those monads are spatially located within it. Returning now to the advantages of my view, another is that it affords a plausible explanation of Leibniz's idea that phenomena result from their foundational monads. As we saw in the previous section, one thing can be said to result from others, in his terminology, just in case, having posited the latter things, we must immediately be understood to have posited the former thing as well (A VI, 4, 310). So to say that a phenomenon results from monads is just to say that if we posit the monads, we must thereby be understood to have posited the phenonenon. But how could this be? Rutherford suggests that if we assume the pre-established harmony, then 43. On the idea that monads have a kind of situation in space, see GP II, 253/DeV 267-69; cf. GP II, 339/DesB 99; GP II, 450-51/DesB 255. In the first of these texts, Leibniz remarks that "even if monads are not extended, they nonetheless have a certain kind of situation [situs] in extension, that is, they have a certain ordered relation of coexistence to other things, namely, through the machine in which they preside." He adds: "And I think that no finite substances exist separated from every body, thus neither do they lack situation or order with respect to other coexisting things in the universe." These remarks suggest the view that a monad has situation in space in virtue of having a body. In contrast, the view I am ascribing to him is that a monad has situation in virtue of representing the universe from a certain point of view, or in other words, in virtue of representing itself as (or as part of) a certain body. On this view, both the monad's having a body and its situation in space follow from its representational point of view. For helpful discussions of this issue, see Adams, Leibniz, 249-55; J. A. Cover and Glenn A. Hartz, "Are Leibnizian Monads Spatial?" History of Philosophy Quarterly 11:3 (1994) 295-316. LEIBNIZIAN BODIES 26 the existence of a phenomenon would be entailed by the existence of its foundational monads. 44 However, this entailment lacks the sort of immediacy Leibniz requires for resulting, since the phenomenon would result from the monads not by metaphysical or conceptual necessity but only by exigency (cf. GP II, 435/DesB 227). Another thought which might occur to us is that if we posit the monads which ground a certain phenomenon, we must thereby be understood to posit that phenomenon, because it belongs to the nature of those monads to perceive the entire universe and thus to contain that phenomenon within them. But the problem with this is that we must also posit in this way all the other phenomena those monads contain, most of which they in no way ground. What we need is a sense in which, having posited those monads which ground a certain phenomenon, we must thereby be understood to have posited that phenomenon (and its constituent phenomena), but no others. A better solution to the difficulty can be found by appealing once again to the distinction between being and existence. It is true that in positing the existence of those monads which ground a certain phenomenon, we must thereby be understood to have posited the being of all the phenomena within them. But importantly, we need not be understood to have posited the reality or existence of those phenomena. Indeed some of their phenomena will be imaginary. As for the phenomenon they ground, however, the situation is different. In positing the existence of these monads, we must posit not only that this phenomenon has its being within them, but also that it is real and that it exists. For we are positing not only the phenomenon but its foundation. We can therefore say that a phenomenon results from its foundational monads in the sense that, having posited the existence of those monads, we must immediately be understood to have posited the reality and existence of that phenomenon as well. This reading also affords a plausible gloss on Leibniz's suggestion that bodies are not simply mental but "semi-mental" (GP II, 304, 306/DesB 31, 35; cf. GP II, 504, 506/DesB 351, 356). In his recent paper on Leibniz's idealism, Rutherford claims that "If an aggregate were merely a thought or perceived thing, then it would be wholly mental, not semi-mental."45 From the perspective of my reading, however, this is not the case. As I have said, a phenomenon can be understood to derive its reality from its foundational monads. In the same way, it can be understood to derive its existence from 44. Rutherford, "Idealist," 181-83. 45. Rutherford, "Idealist," 176. LEIBNIZIAN BODIES 27 those monads: if the monads ceased to exist, so would the phenomenon. Hence, even though, as a phenomenon, a body's being and unity would reside only in the perceiver, thus rendering the body in itself mental, it would have an existence and reality that are more than merely mental in virtue of being grounded in and derived from an external foundation. This may well be the sense in which Leibniz considers bodies to be semi-mental. Finally, I can now clarify how this proposal differs from the views of others who have stressed the importance of Leibniz's technical definitions. Of particular significance are the views of Rutherford and Arthur. A central point on which the three of us agree is that when Leibniz affirms Aggregation and Inclusion, his point is simply that a body has monads as its immediate requisites. However, neither Rutherford nor Arthur see how something having its being only in the mind could have monads as its immediate requisites. From Rutherford's perspective, if an aggregate were a phenomenon in the sense of an appearance or mental content, then it would be "a mere idea or image" and as such would lack the sort of reality bodies are supposed to possess.46 Similarly, Arthur rejects the conception of bodies as "phenomena in the sense of mental phenomena of perceivers" on the ground that, so conceived, bodies could not be understood to presuppose monads in the way a thing presupposes its immediate requisites. 47 For both Rutherford and Arthur, then, an aggregate of monads must be something other than a phenomenon in the mind, and thus must be a phenomenon, if at all, in some attenuated sense. In contrast, my view purports to explain how even a phenomenon in what Rutherford calls the "narrower and more usual" sense can be understood as an aggregate of monads. 5. Conclusion I have argued that in his discussions of the relationship between the bodies of everyday experience and the fundamental constituents of the created world, Leibniz uses terms such as 'ingredient', 'constituent', and 'aggregate' in technical senses which allow for the surprising result that something having its being only in the mind can be an aggregate of things outside the mind, and the equally surprising result that the latter things can be considered constituents of the former. If this is correct, then the result is a remarkable one. In one fell swoop it renders perfectly intelligible a large number of passages that commentators have traditionally found 46. Rutherford, "Idealist," 177. 47. Arthur, "Presupposition," 103. LEIBNIZIAN BODIES 28 rather puzzling and that have led some to posit ambiguities and others to attempt explanations of why Leibniz would repeatedly and sometimes simultaneously advance conflicting theories of the nature of body. From the point of view I have been defending here, most if not all of these passages make perfect sense. When, for instance, Leibniz says in a single paragraph that bodies are assemblages of monads, but also that they are only well-founded phenomena that are "different in different observers" and "like exact and enduring dreams", and that material things are "nothing outside perceptions" (GP III, 622-23), he detects no tension because on his understanding of what it means to be an assemblage, that is, an aggregate, something having its being in one monad can be an assemblage of other monads. In his idiolect, an aggregate is simply a thing that depends immediately on multiple other things, its immediate requisites, for its being, existence, or reality. As a being of perception or of the imagination, a phenomenon in one monad admittedly does not depend on other monads in this way for its being. However, it can be supposed to depend on other monads in this way for its reality and existence, since without a foundation in some external reality, a phenomenon cannot be considered real, and thus cannot be said to exist. In positing the reality and existence of a phenomenon, we must by that very fact be understood to have posited the reality and existence of its foundation. Hence, a phenomenon that is "nothing outside perceptions" can, in a sense, be an aggregate of monads having their being outside of perception. In short, Aggregation and Inclusion cohere perfectly with Phenomenalism, just as Leibniz seems to think.48 Stephen Puryear Department of Philosophy and Religious Studies North Carolina State University Raleigh, NC 27695-8103 USA smpuryear@ncsu.edu 48. Ancestors of this paper were read to audiences at Oxford University, North Carolina State University, Loyola University Chicago, and Indiana University-Purdue University Indianapolis. I would like to thank them, and especially the anonymous referees who provided comments on earlier drafts, for their helpful feedback. Special thanks also to Shane Duarte, who challenged and sharpened my thinking on this topic through several lengthy discussions.