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This chapter considers the proposal that counterpart theory should be adopted as a solution to the problems about identity across possible worlds discussed in the previous chapters: a solution that requires neither bare identities, extrinsically determined identities, nor non-trivial individual essences. It concludes that unless one is already committed to counterpart theory on other grounds (such as the adoption of David Lewis’s version of realism about possible worlds), one has insufficient reason to prefer a counterpart-theoretic solution to a ‘bare identities’ solution to the problems.

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.

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 paper explores a different version of the counterpart theory - that the actualist can coherently combine a belief in primitive thisness and genuine identity across possible worlds with a version of counterpart theory that permits one to make sense of contingent identity and distinctness, i.e., if the claims that one thing might have been two, and that distinct things might have been identical. The theses called haecceitism is analysed, and it is argued that this doctrine can be reconciled with a version of counterpart theory, and with the coherence of contingent identity. The impact of this account of counterparts and identity on the abstract semantics of quatified modal logic is considered.

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 is (fairly) uncontroversial: a is possibly-Φ when a counterpart of a is Φ in some world. It becomes (more) controversial only once the italicized relations are constrained in some way. For Saul Kripke, the counterpart relation was identity while objects could exist in more than one world. For David Lewis, the counterpart relation was a similarity relation while objects could not exist in more than one world. Further controversy: identity is an equivalence relation but similarity is not. Different constraints are developed here. The counterpart relation is sortal-relative sameness. Individuals may exist in more than one world but can be sortal-relatively the same as something other than themselves in some different possible world. Sortal-relative sameness is a weak equivalence relation. This intermediate version of counterpart theory is put to use in solving a puzzle of material constitution.

This chapter draws out some parallels between Chisholm's Paradox and puzzles about identity through time. It focuses on the example of Old Number One, the Bentley racing car in which Wolf ‘Babe’ Barnato won the Le Mans 24 hour race in 1929 and (debatably) 1930. Attempts in 1990 to sell a certain car, also referred to as Old Number One, were resisted by some on the grounds that too many upgrades, modifications, and repairs had taken place for the 1929 car to be considered the same car as the 1990 car. The chapter argues for the coherence of a ‘no fact of the matter’ verdict about such puzzles, and develops apparatus that involves a novel conception of degrees of truth in terms of higher-order levels of vagueness, thereby avoiding the need for talk of ‘degrees of identity’.

The Theory of Worldbound Individuals (T.W.I.) is the view that each object exists in just one possible world. In this chapter, I argue that (a) there is no good reason to accept T.W.I. and (b) T.W.I. has implausible consequences. I begin by demonstrating that traditional arguments for T.W.I., including the Problem of Transworld Identification, are based on confusion and do not pose problems for the thesis that objects exist in more than one possible world. In the final section of the chapter, I argue that T.W.I. entails that every object has all of its properties essentially. Moreover, T.W.I. entails this even if it is fortified with David Lewis's Counterpart Theory.

The simplest (and, arguably, correct at the level of descriptive adequacy) semantics for quantified modal logic uses objects that exist in multiple worlds. David Lewis's counterpart theoretic semantics was an attempt to replace this with something more metaphysically palatable, but fails at the descriptive level, not validating the intuitively correct logic. It turns out to be surprisingly difficult to define a semantics that combines the virtues of these extremes. This chapter notes a new difficulty, argues that various obvious solutions for it won’t do, and tentatively suggests one that uses more sophisticated logical machinery than is usual in discussions of modal semantics.

If four‐dimensionalism is an ontological, rather than conceptual or ordinary‐language, thesis, some traditional objections are misguided. It then does not require any particular semantics for tensed claims, does not imply any conceptual or epistemic priority of stage‐talk, and does not preclude a distinction in ordinary thought between processes and things. A more metaphysical traditional objection is that four‐dimensionalism precludes genuine change, but there is no good reason to regard the four‐dimensionalist's conception of change as non‐genuine. A better objection: four‐dimensionalism assigns the wrong modal properties to continuants. Reply: everyone, not just a four‐dimensionalist, should accept a ‘flexible’ account of de re modal predication. Counterpart theory is one such account, but not the only one. Best objection: four‐dimensionalism precludes motion in homogeneous substances. Reply: it is only four‐dimensionalism plus Humean supervenience that has the consequence, and even then, motion in homogenous substances may be allowed in many cases, assuming a holistic account of genidentity.