Canonical Counterpart Theory

Analysis 42 (1):33 - 37 (1982)

Abstract
In a recent article in Analysis, Graeme Hunter and William Seager (1981) attempt to rescue counterpart theory (CT) from some objections of Hazen 1979. They see these objections as arising from ‘uncritical use of the translation scheme originally proposed by Lewis’, and intend to meet them by refraining from use of that scheme. But they do not offer a new scheme; they say ‘…it is no more necessary to have one to capture the sense of modal idiom than it is to capture the sense of quantificational idiom…Appeal to truth value is the single most important criterion of correct translation’ (Hunter and Seager 1981:72). Thus, where the scheme of Lewis (1968) translates a truth by a falsehood or conversely, Hunter and Seager simply produce a sentence which they claim to be a better translation, without articulating any structural principles they employ to arrive at their candidate. A friend of CT should not be happy with this procedure. Let Lm be first-order modal language and Lc be the language of counterpart theory. Sentences of Lc are intended to interpret or elucidate the meanings of Lm-sentences in the strong sense that they should be the outputs of an adequate theory of meaning, which we can formulate as a model theory, for Lm, written in Lc plus set theory. The interest of CT resides in its potential to provide an alternative approach to the model theory of modal logic, and from the clauses of any such alternative model theory we should be able to read off a translation scheme for Lm into Lc, just as we can in the standard case. If CT’s motivation is sound, which Hunter and Seager do not dispute, yet there is no translation scheme and so no counterpart-theoretic model theory, one might suspect some defect in the original language Lm. And in fact, Hunter and Seager find certain Lm-sentences multiply ambiguous with respect to Lc; but if a counterpart-theoretic model theory is possible, to say..
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DOI 10.1093/analys/42.1.33
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References found in this work BETA

Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16 (1963):83-94.
Counterpart Theory and Quantified Modal Logic.David K. Lewis - 1968 - Journal of Philosophy 65 (5):113-126.
Counterpart-Theoretic Semantics for Modal Logic.Allen Hazen - 1979 - Journal of Philosophy 76 (6):319-338.
ModelTtheory for Modal Logic. Part I — The de Re/de Dicto Distinction.Kit Fine - 1978 - Journal of Philosophical Logic 7 (1):125 - 156.

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