Abstract

_Wh_-questions with the modal verb _can_ admit both mention-some (MS) and mention-all (MA) answers. This paper argues that we should treat MS as a grammatical phenomenon, primarily determined by the grammar of the _wh_-interrogative. I assume that MS and MA answers can be modeled using the same definition of answerhood (Fox in Mention-some interpretations, MIT seminar, 2013 ) and attribute the MS/MA ambiguity to structural variations within the question nucleus. The variations are: (i) the scope ambiguity of the higher-order _wh_-trace and (ii) the absence/presence of an anti-exhaustification operator. However, treating MS answers as complete answers in this way contradicts the widely adopted analysis of uniqueness effects in questions of Dayal (Locality in _wh_ quantification: Questions and relative clauses in Hindi, 1996 ), according to which the uniqueness effects of singular _which_-phrases arise from an exhaustivity presupposition, namely that a question must have a unique exhaustive true answer. To solve this dilemma, I propose that question interpretations presuppose Relativized Exhaustivity: roughly, the exhaustivity in questions is evaluated relative to the accessible worlds as opposed to the anchor/utterance world. Relativized Exhaustivity preserves the merits of Dayal’s exhaustivity presupposition while permitting MS; moreover, it explains the local-uniqueness effects in modalized singular _wh_-questions.