This chapter argues that from a particularly weak recombination principle and plausible assumptions about the nature of parthood and location, it follows that it is possible that the mereological structure of the material world and that of space-time fail to correspond to one another in very radical ways. The chapter suggests, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of no less unappealing alternatives. It also discusses a few ways in which their possibility (...) is relevant to various important debates in metaphysics. (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.

are synthetic a priori judgements possible?" In both cases, i~thas usually been t'aken for granted in fife one case by Kant that synthetic a priori judgements were possible, and in the other case in contemporary,'d-". philosophical literature that contingent statements of identity are ppss. ible. I do not intend to deal with the Kantian question except to mention:ssj~".

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

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)

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

I argue that the conjunction of perdurantism (the view that objects are temporally extended) and universalism (the thesis that any old class of things has a mereological fusion) gives rise to undesired complications when combined with certain plausible assumptions concerning the semantics of tensed statements.

The idea that two objects can coincide—by sharing all their proper parts, or matter—yet be non-identical, results in the “Problem of Coincident Objects”: in what relation do objects stand if they are not identical but share all their proper parts? One solution is to introduce material constitution. In this paper, I argue that this is ad hoc since, first, this solution cannot be generalized to solve similar problems, and, second, there are pseudo cases of coincidence that should not trigger the (...) introduction of material constitution and these cannot be distinguished in any principled way from the allegedly real cases of coincidence. (shrink)

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

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)

This study in fundamental ontology calls for rethinking some pedestrian assumptions about what there is and provides the motivation for a new theory of reference. It contains clear, crisp discussions of mereology, identity, reference, and necessity and should be valuable to metaphysicians and philosophers of language.

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Say that mereological harmony is the view that there is at least some mirroring between the mereological structure of material objects and the mereological structure of their locations: each, in some way, mirrors the other. As it turns out, there is a confusing array of systems of harmony available to the substantivalist. In this paper, I attempt to bring some order to these systems. I explore some systems found in the literature, as well as some natural systems which haven’t been (...) discussed. Along the way, I explore a number of metaphysical consequences of the different systems of harmony. The paper ends with a roadmap of possible views for the substantivalist. (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)

How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question lies at the heart of any metaphysical exploration of the material world, and it plays a crucial part in debates about personal identity and survival. This book explores and compares three theories of persistence — endurance, perdurance, and stage theories — investigating the ways in which they attempt to account (...) for the world around us. Having provided valuable clarification of its two main rivals, the book concludes by advocating stage theory. Such a basic issue about the nature of the physical world naturally has close ties with other central philosophical problems. This book includes discussions of change and parthood, of how we refer to material objects at different times, of the doctrine of Humean supervenience, and of the modal features of material things. In particular, it contains new accounts of the nature of worldly vagueness, and of what binds material things together over time, distinguishing the career of a natural object from an arbitrary sequence of events. Each chapter concludes with a reflection about the impact of these metaphysical debates upon questions about our personal identity and survival. (shrink)

Katherine Hawley explores and compares three theories of persistence -- endurance, perdurance, and stage theories - investigating the ways in which they attempt to account for the world around us. Having provided valuable clarification of its two main rivals, she concludes by advocating stage theory.

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)

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.

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)

This is a book about the concept of a physical thing and about how the names of things relate to the things they name. It questions the prevalent view that names 'refer to' or 'denote' the things they name. Instead it presents a new theory of proper names, according to which names express certain special properties that the things they name exhibit. This theory leads to some important conclusions about whether things have any of their properties as a matter of (...) necessity. This will be an important book for philosophers in metaphysics and the philosophy of language, though it will also interest linguists concerned with the semantics of natural language. (shrink)

I argue that from a very weak recombination principle and plausible assumptions about the nature of parthood and location it follows that it's possible that the mereological structure of the material world and that of spacetime fail to correspond to one another in very radical ways. I defend, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of equally radical alternatives. I also discuss a few ways in which their possibility is relevant to various (...) debates in metaphysics. (shrink)

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)

This is a book about the concept of a physical thing and about how the names of things relate to the things they name. It questions the prevalent view that names 'refer to' or 'denote' the things they name. Instead it presents a new theory of proper names, according to which names express certain special properties that the things they name exhibit. This theory leads to some important conclusions about whether things have any of their properties as a matter of (...) necessity. This will be an important book for philosophers in metaphysics and the philosophy of language, though it will also interest linguists concerned with the semantics of natural language. (shrink)

This provocative book attempts to resolve traditional problems of identity over time. It seeks to answer such questions as 'How is it that an object can survive change?' and 'How much change can an object undergo without being destroyed'? To answer these questions Professor Heller presents a theory about the nature of physical objects and about the relationship between our language and the physical world. According to his theory, the only actually existing physical entities are what the author calls 'hunks', (...) four-dimensional objects extending across time and space. This is a major contribution to ontological debate and will be essential reading for all philosophers concerned with metaphysics. (shrink)

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.

ONE KIND OF PHILOSOPHICAL PUZZLEMENT arises when we have an apparent conflict of intuitions. If we are philosophers, we then try to show that the apparent conflict of intuitions is only an apparent conflict and not a real one. If we fail, we may have to say that what we took to be an apparent conflict of intuitions was in fact a conflict of apparent intuitions, and then we must decide which of the conflicting apparent intuitions is only an apparent (...) intuition. But if we succeed, then both of the intuitions will be preserved. Since there was an apparent conflict, we will have to conclude that the formulation of at least one of the intuitions was defective. And though the formulation may be imbedded in our ordinary language, we will have to say that, strictly and philosophically, a different formulation is to be preferred. But to make it clear that we are not rejecting the intuition we are reformulating, we must show systematically how to interpret the ordinary formulation into the philosophical one. The extent to which we can show this will be one mark of our success in dealing with the philosophical puzzle. Another will be the extent to which our proposed solution contributes to the solution of still other philosophical puzzles. (shrink)

Material objects extend through space by having different spatial parts in different places. But how do they persist through time? According to some philosophers, things have temporal parts as well as spatial parts: accepting this is supposed to help us solve a whole bunch of metaphysical problems, and keep our philosophy in line with modern physics. Other philosophers disagree, arguing that neither metaphysics nor physics give us good reason to believe in temporal parts.

Why might someone consider the answer to the titular question to be trivial? Perhaps because she has read some mereology and understands that mereologists distinguish between parthood on the one hand and proper parthood on the other. She understands that, at least when talking in the language of mereology, a thing is necessarily not a proper part of itself, but is necessarily a part of itself. Whether the English word “part” expresses parthood or proper parthood does not seem too important, (...) seeing as either can be taken as primitive and one defined in terms of the other. Thus, whether something is part of itself or not is indeed a trivial matter of definition. If by “part” one means parthood, everything is part of itself. If by “part” one means proper parthood, nothing is part of itself. (shrink)