Counterpart theories for everyone
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Counterpart theories for everyone Achille C. Varzi1 Received: 5 May 2018 / Accepted: 25 May 2020 © The Author(s) 2020
Abstract David Lewis’s counterpart theory (CT) is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic (ML), suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions (all worlds are equally real, individuals are world-bound) that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted. Keywords David Lewis · Counterpart theory · Modal realism · Kripke models
1 Introduction David Lewis’s Counterpart Theory (CT) is naturally seen as a bold alternative to the standard analysis of our modal discourse—a “rival way”, in Lewis’s own words (1968, p. 114).1 According to CT, when we engage in de re modal discourse about a 1 I shall use ‘CT’ for the basic theory presented in Lewis (1968), disregarding later revisions [(obtained e.g. by providing for a multiplicity of counterpart relations, as in Lewis (1971)) or extensions (e.g. to the analysis of counterfactuals, as in Lewis (1973)). The phrase ‘counterpart theory’ (lowercase) and cognates will refer more generally to any view in keeping with the spirit of CT, though not necessarily with the details.
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Achille C. Varzi [email protected] Department of Philosophy, Columbia University, New York, NY 10027, USA
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particular individual, say Hubert Humphrey, we do not speculate about how Humphrey himself is at other possible worlds. Rather, we speculate about Humphrey’s otherwordly counterparts. A statement such as ‘Humphrey might have won the presidential election’ would be true, not because there is a possible world at which Humphrey wins the election, but because there is a counterpart of Humphrey’s, in some possible world, who wins. There are indeed two respects in which this account departs crucially from the standard one. The first is that the counterpart relation falls short of identity. Someone other than Humphrey enters into the story of how it is that Humphrey might have won the el
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