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How Are Alternatives Computed?

It is widely assumed that focusing a phrase indicates that alternatives to the phrase are considered. The question is, how are alternatives to a given phrase determined? There are a number of proposed answers to this question (Rooth 1985, 1992; von Stechow 1989; Jacobs 1983, among others). These accounts, however, typically deal only with logically simple phrases; when more complex phrases are considered, they turn out to be inadequate. Current theories fail to provide a principled relation between the alternatives induced by a complex phrase and those induced by its component parts; moreover, they predict incorrect truth conditions in some cases. The heart of the problem with these accounts lies in the assumption that the same combinatory rules used in determining the meanings of expressions also apply in determining the alternatives induced by them. Instead, I argue that alternatives are induced by presupposition, and that focus induces alternatives only to the extent that it gives rise to presuppositions. The problem of determining the alternatives is thereby reduced to the problem of determining presupposition in context: the rules for computing alternatives are the same rules that govern the derivation of presupposition. These rules are different from the combinatory rules used to compute the ordinary meaning, and thus avoid the problems which plague previous approaches