Too Many Alternatives: density, symmetry and other predicaments

Abstract

In a recent paper, Martin Hackl and I identified a variety of circumstances where scalar implicatures, questions, definite descriptions, and sentences with the focus particle only are absent or unacceptable (Fox and Hackl 2006, henceforth F&H). We argued that the relevant effect is one of maximization failure (MF): an application of a maximization operator to a set that cannot have the required maximal member. We derived MF from our hypothesis that the set of degrees relevant for the semantics of degree constructions is always dense (the Universal Density of Measurement, UDM). The goal of this paper is to present an apparent shortcoming of F&H and to argue that it is overcome once certain consequences of the proposal are shown to follow from more general properties of MF. Specifically, the apparent problem comes from evidence that the core generalizations argued for in F&H extend to areas for which an account in terms of density is unavailable. Nevertheless, I will argue that the account could still be right. Certain dense sets contain "too many alternatives" for there to be a maximal member, thus leading to MF. But, there are other sets that lead to the same predicament. My goal will be to characterize a general signature of MF in the hope that it could be used to determine the identity of alternatives in areas where their identity is not clear on independent grounds.

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Citations of this work

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