A uniqueness puzzle: How many-questions and non-distributive predication

Abstract

We discuss a novel observation about the meaning of how many-questions, viz. a uniqueness implication that arises in cases that feature non distributive predicates, such as How many students solved this problem together?. We attempt an analysis of this effect in terms of Dayal’s (1996) Maximal Informativity Presupposition for questions. We observe that such an analysis must be reconciled with the unexpected absence of uniqueness implications in cases where the non-distributive predicate appears under a possibility modal. We explore two possible solutions: (i) the postulation of a scopally mobile maximality operator in degree questions of the sort proposed in Abrus´an and Spector (2011); (ii) the proposal that the informativity to be maximized is based on pragmatic, contextual, entailment rather than semantic entailment. We explain why neither solution is satisfactory. We also observe that a Maximal Informativity Presupposition fails to capture uniqueness implications in how many-questions with predicates that are weakly distributive in the sense of Buccola and Spector (2016), such as How many students in the seminar have the same first name?. We conclude that uniqueness implications in how many-questions must have a source that is independent of Dayal’s (1996) Maximal Informativity Presupposition.