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.

Highlights

  • 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 counterpart theory (CT), when we engage in de re modal discourse about aB Achille C

  • Synthese (2020) 197:4691–4715 particular individual, say Hubert Humphrey, we do not speculate about how Humphrey himself is at other possible worlds

  • Someone other than Humphrey enters into the story of how it is that Humphrey might have won the election

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Summary

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). According to CT, when we engage in de re modal discourse about a. CT is formulated instead in the extensional language of classical elementary logic and, includes explicit commitment to modal realism: “The domain of quantification is to contain every possible world and everything in every world” (1968, p.114).. One can subscribe to the reality of time and still be free to choose between a counterpart-based account of persistence—the so-called stage view—or an identity-based account—endurantism.5) But, more importantly, there is a sense in which explicit world quantification is not necessary to the counterpart approach, either It isn’t necessary insofar as the main idea of CT can be recovered and formulated in pure semantic terms, consigning all world quantification to the metalanguage exactly as in the standard account. For the rest of us, it may serve as a further illustration, if such were needed, of the huge potential of Lewis’s legacy, regardless of how one feels about the full metaphysical package with which it was delivered

Modal realism with identity
Counterpart semantics
Neutral embeddings
Neutral semantics
Model theory
Modal principles
Modal logic for everyone
Full Text
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