Why counterpart theory and four-dimensionalism are incompatible

Abstract

This is a version of an example from Alan Gibbard (1975): we make a statue by joining two pieces of clay; then we smash the piece, destroying the statue too. 1 Why Counterpart Theory and Four-Dimensionalism are Incompatible Suppose that God creates ex nihilo a bronze statue of a unicorn; later he annihilates it (call this 'scenario I'). 1 The statue and the piece of bronze occupy the same space for their entire career. If God had recast the bronze as a mermaid, the piece of bronze, not the statue, would have survived. As nothing can have and lack the capacity to survive the same change, they are distinct. Yet many philosophers find it incredible that two material things coincide ever, not to mention for their entire career.Four-dimensionalists hold that ordinary objects persist by having temporal parts at different times. This helps fourdimensionalists handle a number of cases of apparent coincidence.If God recasts the statue instead of annihilating it, for instance, the four-dimensionalist maintains that the space-time worm which is the unicorn statue is a proper part of a more temporally extended worm: the piece of bronze. As the bronze and the statue merely share a common part, coincidence is avoided.The same strategy avoids coincidence in cases where the bronze precedes the statue, which first exists when the piece of bronze 2 Four dimensionalism also avoids distinct-coincidents in cases where a whole animal is reduced to a proper part of itself, as in the case of the unfortunate cat, Tibbles, and his amputated tail (Geach, 1980); non-coincident space-time worms, a fat one and a thin one, end in a common proper-part.2 is cast into a shape. 2 However four-dimensionalism cannot by itself provide a general solution to coincidence puzzles. In scenario I, the statue and the bronze share all their temporal and spatial parts; hence two whole temporally-extended material things still coincide.Counterpart Theory (CT) offers a solution(Lewis 1986, sect. 4.5; Sider 2001: 113), one that four-dimensionalists tend to embrace. Suppose that in I the statue and the piece of bronze are the same four-dimensional object. The statue cannot survive being recast as a mermaid, the bronze can. According to CT, the first claim is true because no statue-counterpart of the statue is mermaid shaped, and the second is true because the bronze has a mermaid-shaped bronze counterpart. Counterpart relations are similarity relations. As one thing can have resemblance relations to different sets of things, depending on which of its features we emphasize, the fact that the bronze can, but the statue cannot, survive the same change does not entail that they are distinct. There is just one space-time worm, A, lasting from t1 to t10 (the moment of annihilation); the statue and the bronze are identical to A, which has different counterpart relations depending upon which of its features we emphasize. Four-Lewis, David (1986), On the Plurality of Worlds, Basil Blackwell. Sider, T. 2001. Four Dimensionalism: An Ontology of Persistence and Time. Oxford...

Moderate Monism, Sortal Concepts, and Relative Identity

“…I turn now to the arguments against moderate monism and begin with Jim Stone's (2005aStone's ( , 2005c (4) The statue does not survive radical reshaping.…”

Coincidence and modal predicates

“…Jim Stone (2005aStone ( , 2005c argues that the attempt to defend this combination of views by an appeal to counterpart theory fails, partly on the grounds that the version of counterpart theory that is required for the defence of the identity judgement in the 'permanent coincidence' case cannot provide a satisfactory account of the modal difference between the entities in the 'temporary coincidence' case. Jim Stone (2005aStone ( , 2005c argues that the attempt to defend this combination of views by an appeal to counterpart theory fails, partly on the grounds that the version of counterpart theory that is required for the defence of the identity judgement in the 'permanent coincidence' case cannot provide a satisfactory account of the modal difference between the entities in the 'temporary coincidence' case.…”

“…By contrast,Stone (2005c) reserves 'coincidence' (as opposed to 'overlap') for a relation according to which things share all their parts, including all their temporal parts, if there are such things as temporal parts. By contrast,Stone (2005c) reserves 'coincidence' (as opposed to 'overlap') for a relation according to which things share all their parts, including all their temporal parts, if there are such things as temporal parts.…”

“…13 Stone (2005c) presents further objections, in addition to the modal dilemma, to the combination of an Abelardian version of counterpart theory and a fourdimensionalist account of persistence. These include the objections mentioned in note 13 below, and those inFine 2003.…”

Moderate monism and modality

“…Jim Stone (2005, 2005a) argues against the coherence of moderate monism 2 Penelope Mackie (20071991, 1993) and a (modified) Lewisean counterpart‐theoretic account of de re modal predication.…”