Formal Alternatives as a Solution to the Proviso Problem

Abstract

This paper investigates a particular problem concerning presupposition accommo-dation. Let ψ and X be sentences, and suppose ψ presupposes X. We represent this as ψ{X}.1 Suppose the speaker and hearer of a conversation are in context c. Suppose further that the speaker wishes to update the context c with the information in ψ, an operation we represent as c[ψ{X}]. ψ{X} imposes a requirement on c that has to be met for the update to take place: c already has to entail X. In terms of update operations, this means that if we try updating c with X, we just get back c: c[X] = c. When this condition is met, we say that c satisfies X, or that c is a fixed point for [X]. But what if c is not a fixed point for [X]? What happens when the condition is not met? There are at least two possible outcomes: (i) either communication breaks down, or (ii) we make some repair [Y] to c so that update will be defined after all, i.e. we update c with Y, c[Y], so that c[Y] ends up satisfying X. Call this repair process accommodation Lewis (1979). We then update the new context resulting from accommodation of Y with ψ,c[Y][ψ]. The question I explore in these pages

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