Zeroing in on Exclusively Exclusive Content

Christopher Kennedy

Bylilina and Nouwen (2018) use the NPI-licensing properties of zero to argue that plural count nouns must be analyzed as having domains with the structure of a complete lattice, containing minimal objects whose count is zero. In this paper, I consider a wider array of data which indicates that the traditional analysis of plural count noun domains as join semi-lattices, lacking minimal objects, is correct. It follows from this view that sentences in which zero combines with a plural count noun are contradictions, but they come to have contingent truth conditions, I claim, because exhaustification can sometimes return exclusively exclusive content. Building on recent proposals by Bassi, del Pinal and Sauerland (2021). I argue that the content of exhaustification just is exclusion of alternatives, and whether the prejacent is entailed depends on whether the exclusive proposition is not-at-issue vs. at-issue.