Friends of states of affairs and structural universals appeal to a relation, structure-making, that is allegedly a kind of composition relation: structure-making ?builds? facts out of particulars and universals, and ?builds? structural universals out of unstructured universals. D. M. Armstrong, an eminent champion of structures, endorses two interesting theses concerning composition. First, that structure-making is a composition relation. Second, that it is not the only (fundamental) composition relation: Armstrong also believes in a mode of composition that he calls mereological, and (...) which he takes to be the only kind of composition recognized by his philosophical adversaries, such as David Lewis. Armstrong, accordingly, is a kind of pluralist about compositional relations: there is more than one way to make wholes from parts. In this paper, I critically evaluate Armstrong's compositional pluralism. (shrink)

Hud Hudson presents an innovative view of the metaphysics of human persons according to which human persons are material objects but not human organisms. In developing his account, he formulates and defends a unique collection of positions on parthood, persistence, vagueness, composition, identity, and various puzzles of material constitution. The author also applies his materialist metaphysics to issues in ethics and in the philosophy of religion. He examines the implications for ethics of his metaphysical views for standard arguments addressing the (...) moral permissibility of our treatment of human persons and their parts, fetuses and infants, the irreversibly comatose, and corpses. He argues that his metaphysics provides the best foundation in the philosophy of religion for the Christian doctrine of the resurrection of the body. Hudson addresses a broad range of metaphysical issues, but among his most strikingly original contributions are his defense of the "Partist" view and his argument for the compatibility of Christianity with a materialistic theory of human persons. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying (...) each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

Let us say that an extended object is “composed wholly of simples” just in case it is an aggregate of absolutely unextended parts spread throughout an extended region—that is, just in case there is a set S such that: every member is a point-sized part of the object, and for every x, x is part of the object if and only if it has a part in common with some member of S. Could a truly extended substance be composed entirely (...) of unextended parts? Reflection upon the fact that it must be at least possible for extended objects to touch one another suggests that the answer to this question is: No. (shrink)

I argue that Universalism (the thesis that mereological composition is unrestricted) entails Extensionalism (the thesis that sameness of composition is sufficient for identity) as long as the parthood relation is transitive and satisfies the Weak Supplementation principle (to the effect that whenever a thing has a proper part, it has another part disjoint from the first).

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are either self-defeating (...) or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

The topic of this book is material objects. Like most interesting concepts, the concept of a material object is one without precise boundaries.

According to the Weak Supplementation Principle (WSP)—a widely received principle of mereology—an object with a proper part, p , has another distinct proper part that doesn't overlap p . In a recent article in this journal, Nikk Effingham and Jon Robson employ WSP in an objection to endurantism. I defend endurantism in a way that bears on mereology in general. First, I argue that denying WSP can be motivated apart from the truth of endurantism. I then go on to offer (...) an explanation of WSP's initial appeal, argue that denying WSP fails to have untoward consequences for the rest of mereology, and show that the falsity of WSP is consistent with a primary guiding thought behind it. (shrink)

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

A tropel is a particular property: the redness of a rose, the roundness of the moon. It is generally supposed that tropes are individuated by primitive quantity: this redness, that roundness. I argme that the trope theorist is far better served by individuating tropes by spatiotemporal relation: here redness, there roundness. In short, tropes are not this-suches but here-suches.

What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to it.

This paper is an articulation and defense of a trope-bundle theory of material objects. After some background remarks about objects and tropes, I start the main defense in Section III by answering a charge frequently made against the bundle theory, namely that it commits a conceptual error by saying that properties are parts of objects. I argue that there’s a general and intuitive sense of “part” in which properties are in fact parts of objects. This leads to the question of (...) qualitative unity: in virtue of what are certain properties unified as parts of an object? In Section IV I defend an account of unity for complex material objects. It turns on the thesis that the properties of such objects are structural properties. After addressing some objections, I turn in Section V to the question of unity for simple material objects. Here a different and more radical account is needed, for simples, since they do not have structural properties, are not subsumed by the account of Section IV. I defend the view that a simple object just is a simple property, so that identity delivers the desired unity. (shrink)

In Parts of Classes and "Mathematics is Megethology" David Lewis shows how the ideology of set membership can be dispensed with in favor of parthood and plural quantification. Lewis's theory has it that singletons are mereologically simple and leaves the relationship between a thing and its singleton unexplained. We show how, by exploiting Kit Fine's mereology, we can resolve Lewis's mysteries about the singleton relation and vindicate the claim that a thing is a part of its singleton.

In a recent article in this journal, Achille Varzi (2009) argues that mereological universalism (U) entails mereological extensionalism (E). The thesis that U entails E (call it ‘T’) has important implications. For example, as is well known, T plays a crucial role in Peter van Inwagen’s argument against universalism (1990: 74–79). In what follows, I show that Varzi’s arguments for T rely on a tendentious assumption about parthood.

A bronze statue is a lump of bronze – or so it might appear. But appearances are not always to be trusted, and this one is notoriously problematic. To see why, imagine a bronze statue (perhaps a statue of David) and ask yourself: Which lump of bronze is the statue? Presumably, it is the lump that makes up the statue (or, as we say, the lump that constitutes the statue). After all, why should the statue be any other lump of (...) bronze? But if that is right, if the statue is the lump of bronze that constitutes it, then why can the lump of bronze survive being melted down whereas the statue it constitutes cannot? It seems that in fact the bronze statue is not the lump of bronze that constitutes it, since the statue and the lump of bronze have different persistence conditions. But then is it some other lump of bronze? Is it a lump of bronze at all? These questions are troubling; they appear to have no easy answers. (shrink)

Part One of this paper is a case against classical mereology and for Heyting mereology. This case proceeds by first undermining the appeal of classical mereology and then showing how it fails to cohere with our intuitions about a measure of quantity. Part Two shows how Heyting mereology provides an account of sets and classes without resort to any nonmereological primitive.

I discuss puzzles involving coinciding material objects (such as statues and their constitutive lumps of clay) and propose solutions.

I argue that a solution to puzzles concerning the relationship ofobjects and their properties – a version of the `bundle' theory ofparticulars according to which ordinary objects are mereologicalfusions of monadic and relational tropes – is also a solution topuzzles of material constitution involving the allegedco-location of material objects. Additionally, two argumentsthat have played a prominent role in shaping the current debate,Mark Heller's argument for Four Dimensionalism and Peter vanInwagen's argument against Mereological Universalism, are shownto be unsound given this version (...) of the bundle theory. (shrink)

Possibilism—the view that there are non-actual, merely possible entities—is a surprisingly resilient doctrine.1 One particularly hardy strand of possibilism—the modal realism championed by David Lewis—continues to attract both foes who seek to demonstrate its falsity (or at least stare its advocates into apostasy) and friends who hope to defend modal realism (or, when necessary, modify modal realism so as to avoid problematic objections).2 Although I am neither a foe nor friend of modal realism (but some of my best friends are!), (...) like many I continue to be fascinated by the doctrine. (shrink)

In this paper I argue that the hoary theological doctrine of divine concurrence poses no deep threat to Leibniz’s views on theodicy and creaturely activity even as those views have been traditionally understood. The first three sections examine respectively Leibniz’s views on creation, conservation and concurrence, with an eye towards showing their sys­tematic compatibility with Leibniz’s theodicy and metaphysics. The fourth section takes up remaining worries arising from the bridging principle that conservation is a continued or continuous creation, and argues (...) that they can be allayed once two readings of the prin­ciple are distinguished. What emerges from the discussion as a whole is, I hope, a clearer picture of Leibniz’s views on the nature of monadic causation, his understanding of the relationship between divine and creaturely activity, and his position with respect to later medieval and early modern debates over secondary causation. (shrink)

In this paper I argue that the hoary theological doctrine of divine concurrence poses no deep threat to Leibniz’s views on theodicy and creaturely activity even as those views have been traditionally understood. The first three sections examine respectively Leibniz’s views on creation, conservation and concurrence, with an eye towards showing their sys­tematic compatibility with Leibniz’s theodicy and metaphysics. The fourth section takes up remaining worries arising from the bridging principle that conservation is a continued or continuous creation, and argues (...) that they can be allayed once two readings of the prin­ciple are distinguished. What emerges from the discussion as a whole is, I hope, a clearer picture of Leibniz’s views on the nature of monadic causation, his understanding of the relationship between divine and creaturely activity, and his position with respect to later medieval and early modern debates over secondary causation. (shrink)

Substantial change occurs when a persisting object of some kind either begins or ceases to exist. Typically, this happens when one or more persisting objects of another kind or kinds are subjected to appropriate varieties of qualitative or relational change, as when the particles composing a lump of bronze are rearranged so as to create a statue. However, such transformations also seem to result, very often, in cases of spatiotemporal coincidence, in which two numerically distinct objects of different kinds exist (...) in exactly the same place at the same time, such as a statue and a lump of bronze. Various attempts to resist this way of describing the results of such transformations are examined and found wanting and objections to the possibility of cases of spatiotemporal coincidence are rebutted. (shrink)

Substantial change occurs when a persisting object of some kind either begins or ceases to exist. Typically, this happens when one or more persisting objects of another kind or kinds are subjected to appropriate varieties of qualitative or relational change, as when the particles composing a lump of bronze are rearranged so as to create a statue. However, such transformations also seem to result, very often, in cases of spatiotemporal coincidence, in which two numerically distinct objects of different kinds exist (...) in exactly the same place at the same time, such as a statue and a lump of bronze. Various attempts to resist this way of describing the results of such transformations are examined and found wanting and objections to the possibility of cases of spatiotemporal coincidence are rebutted. (shrink)

Many philosophers maintain that artworks, such as statues, are constituted by other material objects, such as lumps of marble. I give an argument against this view, an argument which appeals to mereological simples.

Introduction In the first four chapters of this book, I develop and defend a monistic account of human persons according to which human persons are highly ...

Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some technical errors in prominent (...) discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. (shrink)

The best reason to believe in temporal parts is to avoid commitment to coincidence—roughly, two objects occupying exactly the same space at exactly the same time. Most anti-coincidence arguments for temporal parts are fission arguments. Gaining some notice, however, are vagueness arguments. One goal of this paper is to clarify the way a temporal-parts ontology avoids coincidence, and another is to clarify the vagueness argument, highlighting the fact that it too is an anti-coincidence argument. The temporal-parts alternative to coincidence has (...) been challenged on the grounds that it leads to a kind of coincidence of its own. When something that is a temporal part of more than one person thinks about its future self, it must be thinking about a multitude of people. Thus, there must be many people thinking many thoughts in that region occupied by the thinking part. The third goal of this paper is debunking this attack on temporal parts. (shrink)

In this paper, I formulate, elucidate, and defend a version of modal realism with overlap, the view that objects are literally present at more than one possible world. The version that I defend has several interesting features: (i) it is committed to an ontological distinction between regions of spacetime and material objects; (ii) it is committed to compositional pluralism, which is the doctrine that there is more than one fundamental part-whole relation; and (iii) it is the modal analogue of endurantism, (...) which is the doctrine that objects persist through time by being wholly present at each moment they are located. (shrink)

In this paper, we argue that time travel is problematic for the endurantist. For it appears to be possible, given time travel, to construct a wall out of a single time travelling brick. This commits the endurantist to one of the following: (a) the wall is composed of the time travelling brick many times over; (b) the wall does not in fact exist at all; (c) the wall is identical to the brick. We argue that each of these options is (...) unsatisfactory. (shrink)

I have previously argued in a paper with Robson that a particular time travel scenario favours perdurantism over endurantism on the grounds that endurantists must give up on the Weak Supplementation Principle. Smith has responded, arguing that the reasons we provided are insufficient to warrant this conclusion. This paper agrees with that conclusion (for slightly different reasons: that even the perdurantist has to give up on the Weak Supplementation Principle) but argues that the old argument can be supplanted with a (...) new one. (shrink)

Mereological principles are sometimes used to support general claims about the structure and arrangement of objects in the world. I focus initially on one such mereological principle, the weak supplementation principle (WSP). It is not obvious that (WSP) is prescribed by ordinary thinking about parthood. Further, (WSP) is not needed for a fairly strong formal characterization of the part–whole relation. For these reasons, some arguments relying on (WSP) might be countered by simply denying (WSP). I argue more generally that there (...) is no reason to assume that one core mereology functions as a common basis for all plausible metaphysical theories. (shrink)

I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures all of the structure (...) of classical mereology. (shrink)

It is commonly assumed that facts would be complex entities made out of particulars and universals. This thesis, which I call Compositionalism, holds that parthood may be construed broadly enough so that the relation that holds between a fact and the entities it ‘ties’ together counts as a kind of parthood. I argue firstly that Compositionalism is incompatible with the possibility of certain kinds of fact and universal, and, secondly, that such facts and universals are possible. I conclude that Compositionalism (...) is false. What all these kinds of fact and universal have in common is a violation of supplementation principles governing any relation that may be intelligibly regarded as a kind of parthood. Although my arguments apply to Compositionalism generally, I focus on recent work by David Armstrong, who is a prominent and explicit Compositionalist. (shrink)

A lot of people believe that distinct objects can occupy precisely the same place for the entire time during which they exist. Such people have to provide an answer to the 'grounding problem' – they have to explain how such things, alike in so many ways, nonetheless manage to fall under different sortals, or have different modal properties. I argue in detail that they cannot say that there is anything in virtue of which spatio-temporally coincident things have those properties. However, (...) I also argue that this may not be as bad as it looks, and that there is a way to make sense of the claim that such properties are primitive. (shrink)

Do Russellian propositions have their constituents as parts? One reason for thinking not is that if they did, they would generate apparent counterexamples to plausible mereological principles. As Frege noted, they would be in tension with the transitivity of parthood. A certain small rock is a part of Etna but not of the proposition that Etna is higher than Vesuvius. So, if Etna were a part of the given proposition, parthood would fail to be transitive. As William Bynoe has noted (...) (speaking of facts rather than propositions), they would seem to violate certain supplementation principles. Consider the singular proposition, concerning identity, that it is identical with itself. Given the relevant form of Russellianism, this proposition would have identity as a proper part, but it would not have any parts disjoint from identity, and indeed it would not have even a single pair of disjoint parts, in violation of various supplementation principles. This chapter offers a unified solution to the problems about transitivity and supplementation. One key ingredient in the solution is the view that parthood is a four-place relation expressed by ‘x at y is a part of z at w’. Another key ingredient is the view that the semantic contents of predicates and sentential connectives have ‘slots’ or ‘argument positions’ in them. (Both ingredients are independently motivated elsewhere.) Four-place analogues of the transitivity and supplementation principles are set out, and it is argued that these are not threatened by the examples from Frege and Bynoe. (shrink)

John Hawthorne is widely regarded as one of the finest philosophers working today. He is perhaps best known for his contributions to metaphysics, and this volume collects his most notable papers in this field. Hawthorne offers original treatments of fundamental topics in philosophy, including identity, ontology, vagueness, and causation. Six of the essays appear here for the first time, and there is a valuable introduction to guide the reader through the selection.

I argue that there are is no informative statement of necessary and sufficient conditions for being a mereological simple.

A team of leading philosophers presents original work on theories of parthood and location. Topics covered include how we ought to axiomatise our mereology; whether we can reduce mereological relations to identity or to locative relations; whether Mereological Essentialism is true; and what mereology and propositions can tell us about one another.