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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.

The early David Lewis was a staunch critic of the Truthmaker Principle. To endorse the principle, he argued, is to accept that states of affairs are truthmakers for contingent predications. But states of affairs violate Hume's prohibition of necessary connections between distinct existences. So Lewis offered to replace the Truthmaker Principle with the weaker principle that ‘truth supervenes upon being’. This chapter argues that even this principle violates Hume's prohibition. Later Lewis came to ‘withdraw’ his doubts about the Truthmaker Principle, invoking counterpart theory to show how it is possible to respect the principle whilst admitting only things that do not violate Hume's prohibition. What this really reveals is that the Truthmaker Principle is no explanatory advance on the supervenience principle. Extending Lewis's use of counterpart theory also allows us to explain away the necessary connections that threatened to undermine his earlier statements of supervenience.

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 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.

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’.

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.

In the first part of this chapter, I sketch out three grades of modal realism. After developing modal realism, I examine David Lewis's modal theory. I argue that Lewis's theory satisfies none of the grades of modal realism, and that it is really a case of modal reductionism. In particular, I demonstrate that Counterpart Theory is a rejection of the view that objects have properties accidentally or essentially. Moreover, I claim that Lewis merely models things such as propositions, possible worlds or state of affairs, and that he, in fact, is an antirealist with regard to such entities.

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.

After a primer on logical, causal, and theological determinisms, as well as an introduction to naïve, Frankfurt, conditional-analysis, soft-fact, altered-law, and altered-past compatibilisms, a new puzzle emerges for consideration in this chapter: the puzzle of mirror determinism and mirror incompatibilism. This chapter takes a critical look at this new kind of determinism; contrasts it with another lesser-known kind, many-brothers determinism; and canvasses the options for a compatibilistic resolution to its associated threats to freedom and moral responsibility. In addition to discussing the metaphysics of images and surfaces, the chapter also contains a discussion of the unexpected uses of counterpart theory.