Presuppositions and Local Contexts

In the last thirty years, the problem of presupposition projection has been taken to provide a decisive argument for a dynamic approach to meaning, one in which expressions are not evaluated with respect to the 'global' context of utterance, but rather with respect to a 'local context' obtained by updating the global one with expressions that occur earlier in the sentence. The computation of local contexts is taken by dynamic analyses to follow from a generalization of the notion of belief update. I argue that the dynamic approach is faced with a dilemma: in its pragmatic incarnation (Stalnaker), it is explanatory but not general; in its semantic incarnation (Karttunen and Heim), it is general but not explanatory. I suggest that the dilemma stems for a faulty understanding of 'local contexts', and I offer a new reconstruction of this notion which eschews belief update but offers a general and fully precise solution to the projection problem.