I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces (to 'gunky' spaces): a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.

Decompositional analysis is the process of constructing explanations of the characteristics of whole systems in terms of characteristics of parts of those whole systems. Cognitive psychology is an endeavour that develops explanations of the capacities of the human organism in terms of descriptions of the brain's functionally defined information-processing components. This paper details the nature of this explanatory strategy, known as functional analysis. Functional analysis is contrasted with two other varieties of decompositional analysis, namely, structural analysis and capacity analysis. After (...) an examination of these three varieties of analysis, there follows a consideration of a mistake to avoid when conducting decompositional analyses in psychology, and a possible limitation on their explanatory scope. (shrink)

In this paper I respond to Trenton Merricks's (2005) paper ‘Composition and Vagueness’. I argue that Merricks's paper faces the following difficulty: he claims to provide independent motivation for denying one of the premisses of the Lewis-Sider vagueness argument for unrestricted composition, but the alleged motivation he provides begs the question.

I argue that, unlike your brain, you are not composed of other things: you are simple. My argument centers on what I take to be an uncontroversial datum: for any pair of conscious beings, it is impossible for the pair itself to be conscious. Consider, for instance, the pair comprising you and me. You might pinch your arm and feel a pain. I might simultaneously pinch my arm and feel a qualitatively identical pain. But the pair we form would not (...) feel a thing.1 Pairs of people themselves are incapable of experience. Call this The Datum. What explains The Datum? I think the following exhaust the reasonable options. (1) Pairs of people lack a sufficient number of immediate parts. (2) Pairs of people lack immediate parts capable of standing in the right sorts of relations to each other and their environment. (3) Pairs of people lack immediate parts of the right nature. (4) Pairs of people are not structures (they are unstructured collections of their two immediate parts). (5) Some combination of (1) – (4). Finally, (6) pairs of people are not simple. (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive (...) to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

In R. Holte and A. Howe (eds.), Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07).

I first explore the notion of the world's being such that everything in it is a proper part. I then explore the notion of the world's being such that everything in it both is and has a proper part. Given two well recognized assumptions, I argue that both notions represent genuine metaphysical possibilities. Finally I consider, but dismiss, some possible objections.

There are various theses that go by the name ‘mereological essentialism’, but common to all is the thought that things have their parts essentially. The most obvious way of stating this is: for all objects x, for all parts y of x, x has y as a part in every world in which x exists. But there are various ways to read this claim.

This paper is an investigation of metaphysical nihilism: the view that there could have been no contingent or concrete objects. I begin by showing the connections of the nihilistic theses to other philosophical doctrines. I then go on to look at the arguments for and against metaphysical nihilism in the literature and find both to be flawed. In doing so I will look at the nature of abstract objects, the nature of spacetime and mereological simples, the existence of the empty (...) set, the dependence of universals on particulars, and other general questions of ontology. (shrink)

In “Tropes and Ordinary Physical Objects”, Kris McDaniel argues that ordinary physical objects are fusions of monadic and polyadic tropes. McDaniel calls his view “TOPO”—for “Theory of Ordinary Physical Objects”. He argues that we should accept TOPO because of the philosophical work that it allows us to do. Among other things, TOPO is supposed to allow endurantists to reply to Mark Heller’s argument for perdurantism. But, we argue in this paper, TOPO does not help endurantists do that; indeed, we argue (...) that anyone who accepts TOPO should reject endurantism. (shrink)

David Lewis (1986) criticizes moderate views of composition on the grounds that a restriction on composition must be vague, and vague composition leads, via a precisificational theory of vagueness, to an absurd vagueness of existence. I show how to resist this argument. Unlike the usual resistance, however, I do not jettison precisificational views of vagueness. Instead, I blur the connection between composition and existence that Lewis assumes. On the resulting view, in troublesome cases of vague composition, there is an object, (...) which definitely exists, about which it is vague whether the relevant borderline parts compose it. (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)

I compare a Lewisian defence of monism with Kit Fine's defence of pluralism. I argue that the Lewisian defence is, at present, the clearer in its explanatory intent and ontological commitments. I challenge Fine to explain more fully the nature of the entities that he postulates and the relationship between continuous material objects and the parts of those rigid embodiments in terms of which he proposes to explain crucial, modal and sortal, features of those objects.

We introduce several theories of composition, including Nihilism, according to which there are no composite objects; Universalism, according to which any objects whatsoever compose something; and an intermediate position we attribute to common sense. We argue that neither common sense nor science can give us an adequate reason to rule out any of these theories. We suggest that as long as one cannot rule out the hypothesis that composite objects are much rarer than common sense takes them to be, one (...) should adopt a policy of regulating one's talk and verbalised thought in accordance with the fiction that common sense is right about composition. (shrink)

This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states of affairs. The (...) theory is accompanied with a formal model. I prove that the theory is sound and complete with respect to this model. (shrink)

I defend coincidentalism (the view that some pluralities have more than one mereological fusion) and restricted composition (the view that some pluralities lack mereological fusions) against recent arguments due to Theodore Sider.

Though capturing powerful analytical principles, this excellent article misses ways in which psychology and neuroscience bear on reciprocity and decision-making. I suggest more explicit consideration of scale. We may go further beyond gene-culture dualism by articulating how varieties of living systems, while ultimately drawing from both genetic and cultural streams, evolve sufficiently as unitary targets of selection to mediate higher-level complex systems. (Published Online April 27 2007).

What is the relation between a whole and its parts? The metaphysics of structure and composition is much discussed in modern philosophy; now Verity Harte provides the first sustained examination of Plato's rich but neglected discussion of the topic, and shows how it can illuminate current debates. This book is an invaluable resource both for scholars of Plato and for modern metaphysicians.

In his Material Beings, Peter van Inwagen distinguishes two questions about parthood. What are the conditions necessary and sufficient for some things jointly to compose a whole? What are the conditions necessary and sufficient for a thing to have proper parts? The first of these, the Special Composition Question (SCQ), has been widely discussed, and David Lewis has argued that an important constraint on any answer to the SCQ is that it should not permit borderline cases of composition. This is (...) a far-reaching claim, since many plausible-seeming accounts of composition do permit borderline cases. Ned Markosian has recently directed our attention to the second, the neglected Inverse Special Composition Question (ISCQ). I will argue that those who accept Lewis’s constraint on answers to the SCQ should accept an analogous constraint on answers to the ISCQ, and I will discuss the effects of such a constraint. (shrink)

‘Fusion’ is a philosophical term of art, with a variety of uses. First, it is often a synonym for ‘sum’. In this sense, a is a fusion of b, c and d iff b, c and d are parts of a, and every part of a shares a part with b, c or d. So a cat is a fusion of the cells which compose it, and the same cat is a fusion of the molecules which compose it. Relatedly, ‘fusion’ (...) can refer to the occurrence of such composition: philosophers disagree about whether fusion is widespread, about whether it can be a vague matter, and so on. (shrink)

Vague existence can seem like the worst kind of vagueness in the world, or seem to be an entirely unintelligible notion. This bad reputation is based upon the rumour that if there is vague existence then there are non-existent objects. But the rumour is false: the modest brand of vague existence entailed by certain metaphysical theories of composition does not deserve its bad reputation.

In other words, suppose we sought to describe the conditions under which composition takes place. This is Peter van Inwagen’s “special composition question” [van Inwagen 1990: 21-32]. The thesis of restricted composition rejects two extreme answers to this question: nihilism (according to which C is never satisfied) and universalism (according to which C is always satisfied). Defenders of restricted composition – who say both that composition sometimes takes places, but deny that it always takes places – are faced with the (...) charge that restricted composition entails the vagueness of composition, which is said to be impossible. Here I defend restricted composition against this objection, originally due to David Lewis [1986: 211-13] and elaborated by Ted Sider [2001: 121-32 and 2003]. (shrink)

E.J. Lowe is one of the few philosophers who defend both the existence of spatially coincident entities and the Principle of Weak Extensionality that no two objects which have proper parts have exactly the same proper parts at the same time. Lowe maintains that when spatially coincident things like the statue and the lump of bronze are in a constitution relation, the constituted entity (the statue) has parts that the constituting entity (the lump) doesn’t, hence the compatibility with Weak Extensionality. (...) My contention is that his argument for why the statue has parts the lump of bronze lacks can also be used to show that the lump of bronze has parts the statue doesn’t. This will mean that there is no basis for saying the statue and the lump are in a constitution relation. I argue for accepting a modified account of constitution and abandoning the Principle of Weak Extensionality. (shrink)

: Pierre Bayle is the most forthright and systematic early modern proponent of the actual parts doctrine, the period's counterpart to the 'doctrine of arbitrary undetached parts' familiar from current analytic mereology and metaphysics. In this paper I introduce both the actual parts account of the internal structure of matter and the rival system of potential parts. I then identify Bayle as the leading advocate of the actual parts doctrine and examine his arguments for this account.

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)

Our object is to study the interaction between mereology and David Lewis’ theory of subject-matters, elaborating his observation that not every subject matter is of the form: how things stand with such-and-such a part of the world. After an informal introduction to this point in Section 1, we turn to a formal treatment of the partial orderings arising in the two areas – the part-whole relation, on the one hand, and the relation of refinement amongst partitions of the set of (...) worlds, on the other. (We follow Lewis – approximately – in identifying subject-matters with such partitions.) We emphasize a certain duality, formulated in (2.6) and (2.7) in Section 2, between the corresponding lattice operations – mereological joins with partition-lattice meets, mereological meets with partition-lattice joins. Section 3 presents some issues that are raised by consideration of the informally familiar idea of logical subtraction. These include, in particular, a problem about the need for a notion of independence different from the usual logical notion(s) going by that name. The apparatus of Section 2 promises to throw some light on this problem, as we indicate in Section 4. Section 5 ties up some loose ends and suggests an area in which further work would be desirable. (shrink)

An axiomatic treatment of the relation part of is shown to lead naturally to an account of the ways in which parts of things are matched. The determination of matchings by the properties of parts and by the relations between parts is discussed and shown to be relevant to certain classificatory problems in science. The connexions between matchings and symmetries of parts are explored, and a general account is given of the ways in which ambiguities in the matching of parts (...) may be resolved. (shrink)

In his Treatise on the Golden Lion, Fazang says that wholes are in each of their parts and that each part of a whole is every other part of the whole. In this paper, I offer an interpretation of these remarks according to which they are not obviously false, and I use this interpretation in order to rigorously reconstruct Fazang's arguments for his claims. On the interpretation I favor, Fazang means that the presence of a whole's part suffices for the (...) presence of the whole and that the presence of any such part is both necessary and sufficient for the presence of any other part. I also argue that this interpretation is more plausible than its extant competitors. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition (PUC), which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential (...) to Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)

We consider the so-called problem of the many, formulated by Peter Unger. It arises because ordinary material things do not have precise boundaries: it is always possible to find borderline parts of which it is not true to say either that they are parts or that they are not. Unger’s conclusion is that there are no ordinary things at all. We describe the solutions of Peter van Inwagen and David Lewis, and make some critical comments upon them. After that we (...) present our own suggestion which is based on ideas developed by Leibniz in connection with problems of unity and plurality. We suggest that what the problem of the many teaches us is that in order to understand what ordinary things are, we have to take seriously the Leibnizian-Kantian distinction between phenomena and things-in-themselves. (shrink)