The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, or of atomless gunk. The difficulty for these (...) views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world. (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).

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 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.

Following Wiggins’ seminal article, On Being in the Same Place at the Same Time, this article presents the first comprehensive account of the relation of material constitution, an asymmetrical, transitive relation which totally orders distinct ‘entities’ (individuals, pluralities or masses of stuff) which ‘spatially coincide.’ Their coincidence in space is explained by a recursive definition of ‘complete-composition’, weaker than strict mereological indiscernibility, which also explains the variety of logically independent similarities in such cases. This account is ‘analytical’, dealing with ‘putative’ (...) cases in general. The main strategy is to rationally reconstruct Aristotle’s notion of material cause. It is developed more fully with a theory of how to justify admitting generable and perishable things into the natural world, in The Kinds of Things: A Theory of Personal Identity Based on Transcendental Argument (Open Court, 1996). (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, ...

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)

This anthology introduces advanced undergraduates and beginning graduate students to today's debates in metaphysics. The book consists of essays by contemporary metaphysicians, and all but one appear here for the first time. For each of nine topics, there are two essays, one "pro-" and one "con-".

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..

I argue for a property mereology and for mereological bundle theory. I then apply this theory to the one over many problem (universals) and puzzles concerning persistence and material constitution.

In his excellent book, Four-Dimensionalism: An Ontology of Persistence and Time (Sider, 2001), Theodore Sider defends a version of four-dimensionalism which he calls the ‘stage-theory’. This paper focuses on Sider's argument from vagueness and argues that, due to the problematic nature of the argument from vagueness, Sider’s case in favor of four-dimensionalism is in the end not successful.

I argue that extended simples are possible. The argument given here parallels an argument given elsewhere for the claim that the shape properties of material objects are extrinsic, not intrinsic as is commonly supposed. In the final section of the paper, I show that if the shape properties of material objects are extrinsic, the most popular argument against extended simples fails.

Since the publication of Peter van Inwagen's book, Material Beings,1 there has been a growing body of philosophical literature on the topic of composition. The main question addressed in both van Inwagen's book and subsequent discussions of the topic is a question that van Inwagen calls "the Special Composition Question." The Special Composition Question is, roughly, the question Under what circumstances do several things compose, or add up to, or form, a single object? For the purposes of formulating a more (...) precise version of the Special Composition Question, we can adopt the following technical terms. (shrink)

The terms `endurance' and `perdurance' are commonly thought to denote distinct ways for an object to persist, but it is surprisingly hard to say what these are. The common approach, defining them in terms of temporal parts, is mistaken, because it does not lead to two coherent philosophical alternatives: endurance so understood becomes conceptually incoherent, while perdurance becomes not just true but a conceptual truth. Instead, we propose a different way to articulate the distinction, in terms of identity rather than (...) temporal parts: an object endures if its identity is determined at every moment at which it exists. We make precise what it means for the identity of an object to be determined at a moment. We also discuss what role the endurance / perdurance distinction, so understood, should play in the debates about time, material objects and personal identity. (shrink)

I formulate a theory of persistence in the endurantist family and pose a problem for the conjunction of this theory with orthodox versions of special or general relativity. The problem centers around the question: Where are things?

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)

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)

Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic (...) spacetime ; Length contraction and time dilation ; Invariant properties of special relativistic spacetime -- Persisting objects in classical spacetime. Enduring, perduring, and exduring objects in Galilean spacetime ; The argument from vagueness ; From minimal D-fusions to temporal parts ; Motivating a sharp cutoff ; Some objections and replies ; Implications -- Persisting objects in Minkowski spacetime. Enduring, perduring, and exduring objects in Minkowski spacetime ; Flat and curved achronal regions in Minkowski spacetime ; Early reflections on persisting objects in Minkowski spacetime : Quine and Smart ; "Profligate ontology"? ; Is achronal universalism tenable in Minkowski spacetime? ; "Crisscrossing" and immanent causation -- Coexistence in spacetime. The notion of coexistence ; Desiderata ; Coexistence in Galilean spacetime ; Coexistence in Minkowski spacetime : CASH ; Alexandrov-Stein present and Alexandrov-Stein coexistence ; AS-Coexistence v. CASH : symmetry, multigrade, and objectivity ; As-coexistence v. CASH : relevance ; The mixed past of coexistence ; No need in the extended now -- Strange coexistence? Coexistence and existence@ ; The asymmetry thesis ; The absurdity thesis ; Collective CASH value of coexistence ; Collective existence@ and coexistence in classical spacetime ; Collective existence@ and coexistence in Minkowski spacetime ; Contextuality ; Chronological incoherence ; Some objections -- Shapes and other arrangements in Minkowski spacetime. How rigid is a granite block? ; Perspectives in space ; Perspectives in spacetime ; Are shapes intrinsic to objects? ; The causal objection ; The micro-reductive objection ; Pegs, boards, and shapes ; Perduring objects exist. (shrink)

This chapter 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.

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.

Thomas Sattig develops a comprehensive framework for doing philosophy of time, and offers an original three-dimensionalist picture of the material world. He brings together a variety of different perspectives, linking our ordinary conception of time with the physicist's conception, and linking metaphysical questions about time with questions in the philosophy of language.

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.

Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in this paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism [three-dimensionalism] and perdurantism [four-dimensionalism, the doctrine of temporal parts]) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on the (...) fact that four-dimensional entities extended in space as well as time are relativistically invariant in a way three-dimensional entities are not. (shrink)

I give reasons to suggest that the various ‘homogeneous substance’ objections to perdurance theory should not be regarded as raising serious difficulties. The main strategy is to show that there are equally exotic possibilities involving extended mereological simples that may turn the tables on the endurance theorist, insofar as she will have difficulties with these cases analogous to those she raises for the perdurantist. I conclude that such exotic cases are less useful that we might suppose in adjudicating between these (...) competing doctrines of persistence. (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)

Existing puzzles about coinciding objects can be divided into two types, corresponding to the manner in which they bear upon the endurantism v. perdurantism debate. Puzzles of the first type, which involve temporary spatial co-location, can be solved simply by abandoning endurantism in favor of perdurantism, whereas those of the second type, which involve career-long spatial co-location, remain equally puzzling on both views. I show that the possibility of backward time travel would give rise to a new type of puzzle. (...) The new puzzles confront perdurantists and can be solved just by shifting to endurantism. (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)

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)

This paper looks at the question of what regions of space are possibly exactly occupied by a material object.

This is a defense of endurantism against an alleged paradox.

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

This chapter develops a three-dimensionalist account of temporal supervenience — the temporal-regions account — and argues that the latter shares the main virtues and avoids the main drawbacks of its four-dimensionalist rival. The three-dimensionalist account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of objects, and that the facts of temporal instantiation logically supervene on the atemporal instantiation of properties by temporally unextended spacetime regions occupied by objects. Structural similarities of (...) the temporal-regions account and the temporal-parts account are pointed out, and the temporal-regions account is shown to avoid the problems that threaten the temporal-parts account. The remainder of the chapter deals with various consequences and apparent difficulties of three-dimensionalist supervenience. (shrink)

The paper presents a thorough exploration of the problem of persistence in a relativistic context. Using formal methods such as mereology, formal theories of location and the so called intrinsic formulation of special relativity we provide a new, more rigorous and more comprehensive taxonomy of persisting entities. This new taxonomy differs significantly from the ones that are present in the recent literature.

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)