Canonical Counterpart Theory

I n 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 L m be first-order modal language and L c be the language of counterpart theory. Sentences of L c are intended to interpret or elucidate the meanings of L m -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 L m , written in L c 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 L m into L c , 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 L m . And in fact, Hunter and Seager find certain L m -sentences multiply ambiguous with respect to L c ; but if a counterpart-theoretic model theory is possible, to say