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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 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 proposes that animalism, the temporal‐parts view, and nihilism are the best accounts of what we are. It then takes up metaphysical objections to animalism hinted at earlier. It is proposed that animalists answer them by endorsing a sparse ontology of material objects. It is then argued that we can work out what we are by discovering when composition occurs: if composition is universal, we are temporal parts of animals; if there is no composition, we do not exist; and intermediate theories of composition lead almost inevitably to animalism. Finally, the view that there is no theory of composition‐‐that composition is brute‐‐is claimed to rule out any good account of what we are.

This chapter focuses on the view that works of music are not types, but continuants or (as they are sometimes called) historical individuals. Two versions of the continuant view are discussed: musical perdurantism (which has been defended by Ben Caplan and Carl Matheson), and which takes a work of music to have its performances, playings, and other ‘embodiments’ as temporal parts; and the kind of view defended by Rohrbaugh, which takes a musical work to be a higher-level object, ontologically dependent upon, but not constituted by, its embodiments. The chapter outlines compelling objections to both versions of the continuant view, and argues that neither version can adequately explain what the repeatability of a work of music consists in.

Chapter 2 includes an argument aimed at showing that substances as I think property bearers must be simple. This chapter offers a second consideration favoring the simplicity of substances based on a traditional characterization of substances as non-dependent entities. An entity made up of substances depends on the substances that make it up, so would not, on such a view, count as a substance. Substantial parts of objects are distinguished from properties, on the one hand, and, on the other hand, from spatial and temporal parts. The chapter includes a discussion of the possibility of substantial complexity ‘all the way down’, and the question whether the universe could contain an infinite number of substances — an infinite number of electrons, for instance. The implications of particle entanglement in quantum physics are discussed in light of the possibility that entanglement yields new simple emergent substances in which constituent particles ‘lose their identity’ as substances.

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.

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.

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.

Argues that the very existence of time—and, more particularly, the temporal unity of the world as one world in time—is dependent upon the existence of concrete individual substances persisting through time, with the consequence that persisting substances cannot coherently be conceived to be mere sequences or aggregates of successively existing entities, their supposed ‘temporal parts’. An argument due to David Lewis being in favour of the latter view, appealing to the so‐called problem of intrinsic change, is criticized for failing to recognize a solution to this problem, which distinguishes between temporal and atemporal modes of property exemplification.

This chapter makes a case for the application of equality to temporal parts of lives, and tries to answer the objections to it. It contends that the simultaneous segments view is the only persuasive way of applying equality to temporal parts of lives and then suggests that, in the end, we should have serious reservations about this view. The argument does not refute the simultaneous segments view, but it might motivate us to look for an account of justice between age groups with fewer problems.

Discusses some deep‐rooted differences between philosophers over the place of tense in an account of the nature of time, and defends the position that only a tensed view of time can ultimately explain satisfactorily what it is for things to exist in time and persist through change. The notion that persisting things have ‘temporal parts’ is critically examined and it is argued that a tensed view of time should reject the idea that time is a dimension in which reality is extended, in any way akin to the dimensions of space.

This chapter explains egalitarian priority and how it can be applied to temporal parts of lives. It argues that a view based on priority escapes the objections against applying equality to temporal parts of lives. The priority view was developed by Temkin and Parfit. Unlike equality, egalitarian priority is not a relative or comparative value. It is concerned with improving lives of low quality, not with changing the relationship between these lives and other lives. Its basic claim is that the value of a benefit depends, in part, on the quality of the life of the person who receives it.

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.

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.

This chapter considers some further questions about the views defended in Chapters 4 and 5, arguing that applying principles of justice to temporal parts of lives does not depend on any particular theory of the nature of personal identity. For example, applying such principles does not depend on awarding a special ontological status to temporal parts of lives, or thinking that a person consists of a series of related selves. The chapter also argues that the application does not depend on there being a significant amount of psychological change over the lifetime of the person. It discusses the relationship between egalitarian priority and prudence, and it defends an implication of the positive view that we make priority judgments both inside lives and across different lives with the same degree of strength.

This chapter deals with the view that identifies fairness among temporal parts of different lives with the distribution that would be chosen by prudence over the different temporal parts of one life. This idea is at the heart of Daniels's theory of justice between age groups, the prudential lifespan account. If, however, we decide to apply egalitarian principles to temporal parts of lives, it should not take this form. The chapter's criticisms of the prudential lifespan account include both intuitive judgments about the consequences that it is stated the theory would lead to, and more theoretical objections that question the basic ideas in the theory.