I argue that two competing accounts of persistence, three and four dimensionalism, are in fact metaphysically equivalent. I begin by clearly defining three and four dimensionalism, and then I show that the two theories are intertranslatable and equally simple. Through consideration of a number of different cases where intuitions about persistence are contradictory, I then go on to show that both theories describe these cases in the same manner. Further consideration of some empirical issues arising from the theory of special (...) relativity lead me to conclude that the two theories are equally explanatory, and thus finally that they are metaphysically equivalent. (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)

Closest-continuer or best-candidate accounts of persistence seem deeply unsatisfactory, but it’s hard to say why. The standard criticism is that such accounts violate the ‘only a and b’ rule, but this criticism merely highlights a feature of the accounts without explaining why the feature is unacceptable. Another concern is that such accounts violate some principle about the supervenience of persistence facts upon local or intrinsic facts. But, again, we do not seem to have an independent justification for this supervenience claim. (...) Instead, I argue that closest continuer accounts are committed to unexplained correlations between distinct existences, and that this is their fundamental flaw. We can have independent justification for rejecting such correlations, but what the justification is depends upon much broader issues in ontology. There is no one-size-fits all objection to closest-continuer accounts of persistence. (shrink)

Two versions of global supervenience have recently been distinguished from each other. I introduce a third version, which is more likely what people had in mind all along. However, I argue that one of the three versions is equivalent to strong supervenience in every sense that matters, and that neither of the other two versions counts as a genuine determination relation. I conclude that global supervenience has little metaphysically distinctive value.

This is a symposium on my book, Writing the Book of the World, containing a precis from me, criticisms from Dorr, Fine, and Hirsch, and replies by me.

The strongest version of the principle of the Identity of Indiscernibles states that of necessity, there are no distinct things with all their universals in common (where such putative haecceities as being Aristotle do not count as universals: I use 'universal' rather than 'property' here and in what follows for the simple reason that 'universal' is the term of art that most safely excludes haecceities from its instances). It is commonly supposed that Max Black's famous paper 'The identity of indiscernibles' (...) (2) refutes this thesis. (Armstong's [1], chapter 9 is representative here.) Black argues ([2], p. 156) that it is perfectly possible that there be a world consisting solely of two indiscernible spheres at some distance to each other and that this world constitutes a counterexample to the principle above. The strongest version of the bundle theory of substance claims that of necessity, the substances that make up the world are bundles of universals.1 It is commonly supposed that a consequence of Black's defeat of the principle of the Identity of Indiscernibles is that this bundle theory of substance is mistaken. (Again, Armstong's [1] is representative.) I shall argue that Black's thought experiment does not defeat the bundle theory and that, as a result, the bundle theory can be used to salvage the principle of the Identity of Indiscernibles. (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)

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)

Eric T. Olson has argued that those who hold that two material objects can exactly coincide at a moment of time, with one of these objects constituting the other, face an insuperable difficulty in accounting for the alleged differences between the objects, such as their being of different kinds and possessing different persistence-conditions. The differences, he suggests, are inexplicable, given that the objects in question are composed of the same particles related in precisely the same way. In response, I show (...) that the differences are not at all inexplicable once it is recognized that the conditions for a persisting object to be composed by certain particles at a moment of time must involve facts concerning other moments of time, and that the relevant facts are different for persisting objects of different kinds. Philosophers who neglect this sort of constraint on composition principles may be said to be victims of the 'cinematographic fallacy'. (shrink)

The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

Statues and lumps of clay are said by some to coincide - to be numerically distinct despite being made up of the same parts. They are said to be numerically distinct because they differ modally. Coincident objects would be non-modally indiscernible, and thus appear to violate the supervenience of modal properties on nonmodal properties. But coincidence and supervenience are in fact consistent if the most fundamental modal features are not properties, but are rather relations that are symmetric as between coincident (...) entities, relations such as "opposite-possibly surviving being squashed". (shrink)

Theodore Sider distinguishes two notions of global supervenience: strong global supervenience and weak global supervenience. He then discusses some applications to general metaphysical questions. Most interestingly, Sider employs the weak notion in order to undermine a familiar argument against coincident distinct entities. In what follows, I reexamine the two notions and distinguish them from a third, intermediate, notion (intermediate global supervenience). I argue that (a) weak global supervenience is not an adequate notion of dependence; (b) weak global supervenience does not (...) capture certain assumptions about coincidence relations; (c) these assumptions are better accommodated by the stronger notion of intermediate global supervenience; (d) intermediate global supervenience, however, is also not an adequate notion of dependence; and (e) strong global supervenience is an adequate notion of dependence. It also fits in with anti-individualism about the mental. It does not, however, serve to rebut arguments against coincident entities. (shrink)

I offer an argument in defense of four-dimensionalism, the view that objects are temporally, as well as spatially extended. The argument is of the inference-to-the-best-explanation variety and is based on relativistic considerations. It deals with the situation in which one and the same object has different three-dimensional shapes at the same time and proceeds by asking what sort of thing it must be in order to present itself in such different ways in various "perspectives" (associated with moving reference frames) without (...) being different from itself. I argue that the best answer is that the object must be four-dimensional. It will then have differing 3D shapes in different perspectives because such shapes are intrinsic properties of its 3D parts. (shrink)

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)

What is the relation between a clay statue andthe lump of clay from which it is made? According to the defender of the standardaccount, the statue and the lump are distinct,enduring objects that share the same spatiallocation whenever they both exist. Suchobjects also seem to share the samemicrophysical structure whenever they bothexist. This leads to the standard objection tothe standard account: if the statue and thelump of clay have the same microphysicalstructure whenever they both exist, how canthey differ in their (...) de re temporalproperties, de re modal properties and soon? In this paper I develop amereological answer to this question – thestatue and the lump differ with respect totheir parts and this explains theirdifference with respect to de re temporalproperties, de re modal properties andthe like. (shrink)

We have two aims in this paper. The first is to provide the reader with a critical guide to recent work on relativity and persistence by Balashov, Gilmore and others. Much of this work investigates whether endurantism can be sustained in the context of relativity. Several arguments have been advanced that aim to show that it cannot. We find these unpersuasive, and will add our own criticisms to those we review. Our second aim, which complements the first, is to demarcate (...) the most defensible form of relativistic endurantism. A recurring theme of this paper is that even those philosophers who do worry about relativity have not taken it seriously enough. (shrink)

David Lewis's cohabitation theory suffered damaging criticism from Derek Parfit. Though many have defended versions of Lewis's theory Parfit's criticism has not been answered. This paper shows how to defend the cohabitation theory against Parfit's criticism.