Presupposition projection from quantificational sentences: trivalence, local accommodation, and presupposition strengthening

Abstract

The main goal of this paper is to make sense of conflicting data pertaining to the way quantifier phrases project the presuppositions of their arguments. More specifically, I will try to argue that the facts can be understood within trivalent approaches to presupposition projection, when coupled with two independently needed mechanisms (a) one which strengthens presuppositions (needed to deal with the so called “proviso problem”) and (b) another which incorporates presuppositions into truth conditions at various scope positions (“local accommodation”). A secondary goal is to provide some sketchy remarks on how the trivalent predictions could be derived in a classical bivalent system with the aid of a modified bridge principle – a modification of the principle suggested in Stalnaker (1974) to connect formal presuppositions to pragmatic conditions of language use.