According to Peter van Inwagen, visible inanimate objects do not, strictly speaking, exist. In defending this controversial thesis, he offers fresh insights on such topics as personal identity, commonsense belief, existence over time, the phenomenon of vagueness, and the relation between metaphysics and ordinary language.

Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...) mereology (the study of part/whole relations), topology (the study of spatial continuity and compactness), and the theory of spatial location proper. This leads to a unified framework for spatial representation understood quite broadly as a theory of the representation of spatial entities. The framework is then tested against some classical metaphysical questions such as: Are parts essential to their wholes? Is spatial colocation a sufficient criterion of identity? What (if anything) distinguishes material objects from events and other spatial entities? The concluding chapters deal with applications to topics as diverse as the logical analysis of movement and the semantics of maps. (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.

Some philosophers say that a whole is “nothing over and above” its parts. Most also take general extensilonal mereology to be treating wholes as “nothing over and above” their parts. It is not always clear, however, what exactly is meant by the phrase “nothing over and above.” Nor is it obvious why the phrase is associated with mereology, and what purpose it serves there. In the words of Peter Van Inwagen : “This slippery phrase has had a lot of employment (...) in philosophy, but what it means is never explained by its employers.” This paper sheds light on the various senses in which one might hold that a whole is “nothing over and above” its parts, and on how these senses are related both to each other and to mereology. (shrink)

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.

The paper deals with the notions of grounding and of existential dependence. It is shown that cases of existential dependence seem to be systematically correlated to cases of grounding and hence the question is raised what sort of tie might hold the two notions together so as to account for the observed correlation. The paper focusses on three possible ties between grounding and existential dependence: identity, definition, and grounding. A case for the definitional tie is made.

The main contribution of this paper is a novel account of ontological dependence. While dependence is often explained in terms of modality and existence, there are relations of dependence that slip through the mesh of such an account. Starting from an idea proposed by Jonathan Lowe, the article develops an account of ontological dependence based on a notion of explanation; on its basis, certain relations of dependence can be established that cannot be accounted by the modal-existential account. Dependence is only (...) one of two main topics of this paper, for it is approached via a discussion of the category of substance. On a traditional view, substances can be characterised as independent entities. Before the background of a modal-existential account of dependence, this idea appears problematic. The proposed notion of explanatory dependence is shown to vindicate the traditional approach to substance. (shrink)

In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We (...) formulate an axiomatization of mereological structures, different from Tarski’s axiomatization aspresented in [10] . We prove that these axiomatizations are equivalent . Of course, these axiomatizations are definitionally equivalent to thevery first axiomatization of mereology from [5], where the relation of being aproper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology”from [9] is essentially weaker than Leśniewski’s mereology. (shrink)

What is the relation between parts taken together and the whole that they compose? The recent literature appears to be dominated by two different answers to this question, which are normally thought of as being incompatible. According to the first, parts taken together are identical to the whole that they compose. According to the second, the whole is grounded in its parts. The aim of this paper is to make some theoretical room for the view according to which parts ground (...) the whole they compose while being, at the same time, identical to it. (shrink)

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)

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.

Perichoresis, or “mutual indwelling,” is a crucial concept in Trinitarian theology. But the philosophical underpinnings of the concept are puzzling. According to ordinary conceptions of “indwelling” or “being in,” it is incoherent to think that two entities could be in each other. In this paper, I propose a mereological way of understanding “being in,” by analogy with standard examples in contemporary metaphysics. I argue that this proposal does not conflict with the doctrine of divine simplicity, but instead affirms it. I (...) conclude by discussing how mutual indwelling relates to the concepts of unity and identity. (shrink)

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...) classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

In the last several years, paraconsistent mereology has begun to be developed and applied to a range of philosophical issues, from puzzles about boundaries, to the Meinongian ‘problem of nothingness’, to the metaphysics of unity. Because these formal systems are fresh out of the package, as it were, there will inevitably be some wrinkles that need ironing out. In this note, I’ll point out a problem with the system in Priest (2014a, 2014b), and suggest a natural fix.

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity (...) relative to sort fails, because whole and parts can be of the same sort. (shrink)

The purpose of the book is to clarify the notion of existential dependence and cognate notions, such as supervenience and the notion of an internal relation. I defend the view that such notions are best understood in terms of the concept of metaphysical grounding, i.e. the concept of one fact obtaining in virtue of other facts, where ‘in virtue of’ has a distinctively metaphysical meaning.

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)

A number of philosophers have recently become receptive to the idea that, in addition to scientific or causal explanation, there may be a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some constitutive form of determination. I myself have long been sympathetic to this idea of constitutive determination or ‘ontological ground’; and it is the aim of the present paper to help put the idea on a firmer (...) footing - to explain how it is to be understood, how it relates to other ideas, and how it might be of use in philosophy. (shrink)

The connection between whole and part is intimate: not only can we share the same space, but I’m incapable of leaving my parts behind; settle the nonmereological facts and you thereby settle what is a part of what; wholes don’t seem to be an additional ontological commitment over their parts. Composition as identity promises to explain this intimacy. But it threatens to make the connection too intimate, for surely the parts could have made a different whole and the whole have (...) had different parts. In this paper I attempt to offer an account of parthood that is intimate enough but not too intimate: the parts generate the whole, but they are not themselves the whole. (shrink)

I endorse Composition as Identity, broadly and loosely understood as the thesis that a composite whole is nothing over and above its parts, and the parts nothing over and above the whole. Thus, given an object, x, composed of n proper parts, y1, ..., yn, I feel the tension between my Quinean heart and its Lewisian counterpart. I feel the tension between my obligation to countenance n+1 things, x and the y’s, each of which is a distinct portion of reality, (...) and my inclination to count just 1 thing, x, or just n things, the y’s, the former encompassing the same amount of reality as the latter. This paper is an attempt to reconstruct this tension and to explain it away without forgoing the intimate link between counting and countenancing. (shrink)