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Part of the problem of temporal supervenience is the problem of spatiotemporal location: how are objects located in spacetime? This chapter provides a detailed statement of various answers to this problem. The main answers are three-dimensionalism and four-dimensionalism. The three-dimensionalist holds that an object occupies many temporally unextended regions of spacetime, whereas the four-dimensionalist holds that an object occupies only a single temporally extended region of spacetime. Subsequently to stating these accounts of spatiotemporal location, the chapter discusses the relationship of three-dimensionalism and four-dimensionalism to other theses and theories, including the theory of temporal parts, endurantism, perdurantism, eternalism, and presentism.

This chapter presents a new account of temporal predication — the representational account — combined with four-dimensionalism to yield the temporal-parts account of temporal supervenience. This elegant account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of temporal parts of objects, and that the facts of temporal instantiation logically supervene on facts about the atemporal instantiation of properties by temporal parts of objects. It is further shown that the questions of temporal supervenience as well as the four-dimensionalist answers to these questions have interesting spatial and modal analogues. Despite its success in explaining the supervenience of facts of persistence and change, the temporal-parts account has objectionable consequences. Three problems are raised, the most serious of which is the problem of predicational overkill. Each of these problems concerns the account’s failure to capture certain ordinary temporal facts.

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.

This chapter examines David Lewis's view that we are temporal parts of animals. It examines three arguments for the view that persisting things have temporal parts–four‐dimensionalism. One is that it solves the problem of temporary intrinsics. The second is that it solves metaphysical problems about the persistence of material objects without the mystery of constitutionalism–though these solutions require a counterpart‐theoretic account of modality. The third is that it solves problems of personal identity–involving fission, for instance–in an attractive way. It is then argued that according to four‐dimensionalism, the bearers of such properties as thinking and acting are momentary stages, forcing us to choose between saying that we don't strictly think and saying that we don't persist.

This chapter argues that there can be coincident entities, numerically different things, having different persistence conditions, that are composed of exactly the same micro-entities. This means that the higher-order properties of such entities do not supervene on, and are not realized by, the ‘thin’ physical properties that are shared by the coincident entities. They are realized by ‘thick’ physical properties, ones individuated by the persistence conditions of the things that have them. The nature of the causal profiles of properties is argued to be incompatible with the four-dimensionalist, perdurance account of the nature of persisting entities. It is argued that these causal profiles provide a basis for saying what it is for a set of microentities to make up a single object.

The thesis that ordinary material objects are mereological sums in the standard sense has been remarkably popular among three-dimensionalists and four-dimensionalists alike. This chapter considers two prominent representatives: Judith Jarvis Thomson, for the three-dimensionalist camp; and David Lewis, for the four-dimensionalist camp. The question of why Thomson's temporalized and modalized version of standard mereology still does not adequately capture the characteristics of ordinary material objects is postponed until Chapter 4. The remainder of the chapter considers Lewis' argument in favor of Unrestricted Composition, in particular in the recently expanded version offered in Theodore Sider's, Four-Dimensionalism: An Ontology of Persistence and Time; as well as Lewis' defence of the Composition-as-Identity Thesis in his Parts of Classes. It is argued that the three-dimensionalist need not be swayed by either component of Lewis' view, since they are ultimately founded on question-begging reasoning.

The generic framework of Chapter 2 is used to formulate the rival views of persistence in classical (Galilean) spacetime, followed by a brief analysis of available regional modification schemes and a statement of achronal universalism. The remainder of the chapter is focused on the argument from vagueness to four‐dimensionalism, due to Lewis and Sider. The chapter develops a new objection to this argument, based on drawing a motivated distinction between synchronic and diachronic composition. Diachronic composition can be said to be causally grounded in a way synchronic composition is not. This allows one to construct a counterexample that blocks a crucial step in the argument from vagueness. While the three‐dimensionalist may welcome this objection as undermining the general case for four‐dimensionalism, I am inclined to consider it as encouraging important domestic restructuring in the four‐dimensionalist camp. In particular, the burdensome marriage between four‐dimensionalism and mereological universalism can be dissolved.

According to the doctrine of four-dimensionalism, our world and everything in it consists of stages or temporal parts; moreover, where an object exists at various times, it does so, according to the four-dimensionalist, in virtue of having distinct temporal parts at those times. While four-dimensionalism is often motivated by its purported solutions to puzzles about material objects and their persistence through time, it has also been defended by more direct arguments. Three such arguments stand out: (1) the argument from temporary intrinsic; (2) the argument from vagueness; and (3) the argument from recombination, Humean supervenience, and causal constraints. Each of these arguments originates in the work of four-dimensionalism's most prominent modern defender, David Lewis. The third of these arguments has received, by far, the least attention, critical or otherwise. This chapter addresses this imbalance.

This chapter discusses the four dimensionalism view of identity. This view proposes that persisting objects are extended in time in a way that is similar to the way they are extended in space. It has been advocated as an appealing solution to some of the identity puzzles previously described because of the assumption that objects have temporal as well as spatial parts. This chapter characterizes the temporal and spatial parts of an object, and validates the applicability of four dimensionalism as a solution to the identity puzzles.

Discusses three claims that have been assumed in previous chapters: that we exist; that there is such a thing as absolute numerical identity; and that we are not composed of temporal parts. One could avoid many of the book's arguments by denying any one of these claims.

Four‐dimensionalism may be made vivid by pictures: an object with temporal parts persisting through time is like a road with spatial parts extending across space. The attraction of this picture emerges informally from consideration of change, statues, and lumps of clay, and the Ship of Theseus.

Four‐dimensionalism may be given a rigorous and canonical formulation acceptable to both its supporters and opponents; meaningful debate as to the truth of this thesis may then proceed. This is more difficult for three‐dimensionalism, since its defining slogan ‘objects are wholly present’ seems either trivial (‘at any time at which an object exists, anything that is then part of it exists’) or too strong (‘at any time at which an object exists, anything that is ever part of it exists’). Nevertheless, several theses in the neighbourhood of three‐dimensionalism may be stated, even if none is a canonical formulation. Finally, the three‐dimensionalism/four‐dimensionalism debate is orthogonal to the debate over presentism: both presentists and non‐presentists can articulate versions of three‐ and four‐dimensionalism whose truth may then be debated.

Some traditional arguments for four‐dimensionalism are weak: denying four‐dimensionalism does not prohibit the application of modern logic to natural language, does not imply the A‐theory of time and is consistent with special relativity. Others have some force but are inconclusive: the argument from analogies between time and space and Lewis's argument from temporary intrinsics. Some new arguments fare better. (1) Only four‐dimensionalists can admit certain (admittedly exotic) possibilities involving timeless objects and time travel into one's own past. (2) Either substantivalism or relationalism about space‐time is true. Given substantivalism (and a sensible, flexible theory of de re modal predication), one might as well identify continuants with regions of space‐time, which have temporal parts. Alternatively, one could identify continuants with instantaneous slices of space‐time and employ temporal counterpart theory; either way, we have a four‐dimensionalist metaphysics of continuants. On the other hand, relationalism about space‐time cannot be made to work without temporal parts. So either way, we have an argument for four‐dimensionalism. (3) It can never be vague how many objects exist; if temporal parts do not exist then a restrictive account of which filled regions of space‐time contain objects must be given; but no such account can be given that is plausible and non‐vague.

We need a general solution to a cluster of related paradoxes in which numerically distinct material objects appear to share exactly the same parts. Those paradoxes include the statue and the lump of clay, undetached parts, fission, fusion and longevity, vague identity, and conventional identity. A good solution is given by the ‘worm theory’, according to which continuants are aggregates of temporal parts; a better solution is given by the ‘stage theory’, according to which continuants are instantaneous temporal parts, whose temporal properties are understood via temporal counterpart theory. There are other solutions that do not appeal to temporal parts: Wiggins's constitution theory, Burke's dominance view, Gallois's temporary identity theory, eliminativism, and mereological essentialism. But these are arguably inferior: some are insufficiently general, others are subject to powerful criticisms.

This chapter analyzes the scholastic distinction between permanent and successive entities. Permanent entities in some sense exist all at once, whenever they exist, whereas successive entities exist only over time, not all at once.

This chapter refutes Theodore Sider's arguments on anti-commonsensical ontology in his book, Four Dimensionalism. Sider's defense consists of temporal parts and unrestricted mereological composition—that is, his definition of an object's “unity” is the sum of parts existing throughout time. Four-dimensionalism proposes a distinction between the objects observed by non-philosophers and the additional objects viewed by four-dimensionalists (we will call them “Siderian objects”)—the mereological construction of temporal parts. This constitutes the four-dimensionalist premise on the question of “what exists.” However, a reduction ad absurdum argument explores the ontology and linguistic implications of four-dimensionalism, in turn demonstrating that an acceptance of the existence of Siderian objects is not applicable to plain language. Ergo, Siderian objects do not exist. And if Siderian objects do not exist, then four-dimensionalism is false.