Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

Putative counterexamples to the Principle of Identity of Indiscernibles (PII) are notoriously inconclusive. I establish ground rules for debate in this area, offer a new response to such counterexamples for friends of the PII, but then argue that no response is entirely satisfactory. Finally, I undermine some positive arguments for PII.

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)

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)

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)

The Handbook of Metaphysics and Ontology reflects the conviction that the history of metaphysics and current work in metaphysics and ontology can each throw valuable light on the other. Thus it is designed to serve both äs a means of making more widely accessible the results of recent scholarship in the history of philosophy, and also äs a unique work of reference in reladon to the metaphysical themes at the centre of much current debate in analyüc philosophy. The work contains (...) more man 450 shorter articies on specific themes and methods in metaphysics and ontology, together with biographical essays summarizing the thinking of the most important philosophers within the traditions dealt with. In addition, it contains about 20 longer survey arücles mapping out both historically and systemadcally the main areas of metaphysics and ontology. AU contributions have been speciaüy commissioned for this project from leading authorities in their respective fields. A special feature of the work is the pardcular attention that is paid to topics and issues of relevance to contemporary philosophical debates. The work includes also a series of arücles on the logical and mathematical tools of metaphysics and on the applications of metaphysical ideas within linguisdcs, psychology, cognitive science, and mathemadcs. (shrink)

Many metaphysicians accept the view that, necessarily, any collection of things composes some further thing. Necessarily, my arms, legs, head, and torso compose my body; necessarily, my arms, my heart, and the table compose something y; necessarily, my heart and the sun compose something z; and so on. 1 Though there have been a few recent attempts to argue against the necessity of this principle of unrestricted composition the consensus is that if it is true, it is necessarily true. 2In (...) what follows I will join the few dissenters and argue that this principle of unrestricted composition is not necessarily true. If I am right, it follows that either some principle of restricted composition is necessarily true or the existence of composite objects is a contingent matter. I will end by indicating why the latter option seems the most plausible. 3I proceed by reductio. Assume the following: Unrestricted composition is necessarily true.That is, assume that necessarily, any collection of things composes something. Then, necessarily, the collection of everything composes something. That is, necessarily, there exists a universal object U having all things as parts, not itself being a proper part of anything. Hence, by our assumption, we get: There must be a universal object U.It is important to note that this is so whether the world is finite or infinite. Holding that in worlds of finite cardinality there is a universal object U while in worlds of infinite cardinality there is no universal object U amounts to accepting a restricted form of composition. 4Now consider the following scenario. Everything in this world is spatially extended and just one half of something else that is also spatially extended. That is, for any thing in this world, there is something else of which …. (shrink)

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of (...) a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology. (shrink)

This paper takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for unextended material atoms.

As is well known, Aristotelian natural philosophy, and many other systems of natural philosophy since, have relied heavily on teleology and teleological causation. Somehow, the purpose or end of an obj ect can be used to predict and explain what that object does: once you know that the end of an acorn is to become an oak, and a few things about what sorts of circumstances are conducive to the attainment of this end, you can predict a lot about the (...) sprouting of the acorn and the subsequent behaviour of the piece of vegetation that results. Once you know that a rock seeks to move towards the centre of the Earth, you gain some insight into why it falls when released, and why it deforms the carpet or foot that it lands on. Once you know that the rabbit seeks to preserve itself, you can predict it will run from the fox. And so on. There are at least three features of Aristotle’s teleology, and more generally of an Aristotelian frame of mind about teleology, that may induce suspicion. One is that an end can serve as a "cause": as well as the sort of causation we all recognize, efficient causation, there are other forms, one of which is teleological causation. However, this can look less odd if we think of causes as things that figure in "because" answers to "why" questions. Whether or not self-preservation, or the rabbit’s continued existence, or something similar, causes the rabbit to run, the reply "because it seeks to continue in existence" certainly makes sense as an answer, or part of an answer, to a question about why it ran from the fox. (At present we are only. (shrink)

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also (...) suggests how The Structure of Appearance introduces issues which Goodman later continues in his essays and in the Languages of Art. There remains the task of understanding Good man's project as a whole; to see the deep continuities of his thought, as it ranges from logic to epistemology, to science and art; to see it therefore as a complex yet coherent theory of human cognition and practice. What we can only hope to suggest, in this note, is the b. road Significance of Goodman's apparently technical work for philosophers, scientists and humanists. One may say of Nelson Goodman that his bite is worse than his bark. Behind what appears as a cool and methodical analysis of the conditions of the construction of systems, there lurks a radical and disturbing thesis: that the world is, in itself, no more one way than another, nor are we. It depends on the ways in which we take it, and on what we do. (shrink)

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)

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To (...) follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory. (shrink)

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)

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)

Orthodoxy has it that mereological composition can never be a vague matter, for if it were, then existence would sometimes be a vague matter too, and that's impossible. I accept that vague composition implies vague existence, but deny that either is impossible. In this paper I develop degree-theoretic versions of quantified modal logic and of mereology, and combine them in a framework that allows us to make clear sense of vague composition and vague existence, and the relationships between them.

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

Precis of my book by this title, for a symposium.

Naive mereology studies ordinary, common-sense beliefs about part and whole. Some of the speculations in this article on naive mereology do not bear directly on Peter van Inwagen's "Material Beings". The other topics, (1) and (2), both do. (1) Here is an example of Peter Unger's "Problem of the Many". How can a table be a collection of atoms when many collections of atoms have equally strong claims to be that table? Van Inwagen invokes fuzzy sets to solve this problem. (...) I claim that an alternative treatment of vagueness, supervaluations over many-value valuations, provides a better solution. (2) The Special Composition Question asks how parts compose a whole. One who rejects van Inwagen's answer in terms of constituting a life need not provide some alternative answer. Even if all answers to the Special Question fail, there are a multitude of less general composition questions that are not so difficult. (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.

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.

Monists about material constitution typically argue that when Statue is materially constituted by Clay, Statue is just Clay. Pluralists about material constitution deny that constitution is identity: Statue is not just Clay. When Clay materially constitutes Statue, Clay is not identical to Statue. I discuss three familiar puzzles involving grounding, overdetermination and conceptual issues, and develop three new puzzles stemming from the connection between mereological composition and material constitution: a mereological puzzle, an asymmetry puzzle, and a structural puzzle.

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

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers (...) regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail. (shrink)

Philosophical questions concerning parts and wholes have received a tremendous amount of the attention of contemporary analytic metaphysicians. In what follows, I discuss some of the central questions. The questions to be discussed are: how general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood relation enjoyed by (...) material objects? (shrink)

Multilocation and Minimal Mereology do not mix well. It has been pointed out that Three-Dimensionalism, which can be construed as multilocation-friendly, runs into trouble with Weak Supplementation. But in fact, regardless of one’s theory of persistence, if someone posits the possibility of any one of several kinds of multilocation, he or she will not be able to maintain the necessity of any of the three axioms of Minimal Mereology: the Transitivity of Proper Parthood, the Asymmetry of Proper Parthood, and Weak (...) Supplementation. In fact, positing even the mere conceivability of cases involving multilocation will require the denial of the analyticity of Minimal Mereology. In response to this, some have claimed that we ought to relativise parthood, either to one region or to two. Unfortunately, if we replace the axioms of Minimal Mereology with region-relativised counterparts, we will not be able to capture the intuitions that supported the original axioms. The only adequate solution, I maintain, is to restrict multilocation to a domain outside the scope of the rules we intuitively take to govern the parthood relation. For those who take Minimal Mereology to be necessary and universal, that will mean relinquishing the possibility of multilocation. (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)

If the property _being a methane molecule_ is a universal, then it is a structural universal: objects instantiate _being a methane molecule_ just in case they have the right sorts of proper parts arranged in the right sort of way. Lewis argued that there can be no satisfactory account of structural universals; in this paper I provide a satisfactory account.