Having an iota of talent: A gradable HPSG analysis of the syntactic distribution and semantics of the minimizer an iota

Abstract

The exhaustificational account predicts that the polarity distribution of minimizers is due to the effect that exhaustificational/focal operators have on their semantics: they cause minimizers and their alternatives to be organized in likelihood scales while requiring the former to be in the lowest position. This approach excludes positive sentences as licensing environments for minimizers, but a defining characteristic of partitive minimizers, such as an iota, is that they can occur in these kinds of sentences. The aim of this paper is to give a scalar account of the polarity distribution of the minimizer an iota that determines its polarity as being the product of satisfying an absolute minimum standard provided by a relevant gradable predicate: in positive contexts, the minimizer meets the standard, while it does not in negative contexts. The proposal is implemented for the phrase an iota of talent, utilizing the combinatoric tools of LRS and the feature geometry of HPSG. This treatment motivates a lexicalist alternative to proposals engaging with polarity phenomena based on exhausitifcational operators.