Modelling implicatures from modified numerals

Abstract

It has been argued that comparative and superlative quantifiers (such as “more than” and “at least”) fail to yield scalar implicatures in unembedded declarative contexts (Krifka, 1999; Fox and Hackl, 2006). However, recent experimental work has shown that such implicatures are available, and that these are constrained by considerations of granularity or numeral salience (Cummins et al., 2012). That is, “more than n” triggers a pragmatic upper-bound, the value of which depends on the numeral n. However, Cummins et al. further show that this effect is weakened by prior mention of the numeral n, a finding that they interpret in terms of priming effects. In this paper I discuss a recent theoretical proposal that accommodates these findings by arguing for a model of numerical quantifier usage based on multiple constraint satisfaction. This approach provides a means of accounting for the influence of contextual factors on the speaker's choice of utterance. It also makes predictions as to how a rational hearer should use context in their interpretation of utterances. Here I explore how this can yield the diversity of interpretations exhibited by participants in Cummins et al. (2012). More generally I consider how such an account predicts that a hearer will infer context on the basis of an utterance, and examine how this offers a potential explanation for the previously observed failure of implicature in the domain of modified numerals. I discuss the implications of this for experimental semantic and pragmatic methodologies, with particular reference to the numeral domain.