High and low uniqueness in singular wh-interrogatives

While simple singular wh-interrogatives carry a uniqueness presupposition, this is not so when they contain possibility modals. Hirsch & Schwarz (2019) account for this contrast by assuming (i) that questions can have multiple maximally informative true answers and (ii) that uniqueness is triggered lexically inside the scope of interrogative. We show that their proposal overgenerates on two accounts. Firstly, it predicts too weak a presupposition for modalized interrogatives. Secondly, it predicts unattested interpretations for interrogatives containing negation. We show that both issues can be solved using exhaustification operators. On the one hand, we obtain the desired presupposition for modalized interrogatives by assuming the lexical trigger for uniqueness to be a presuppositional variant of an exhaustification operator (Bassi, Del Pinal & Sauerland 2019). On the other, we show that unattested readings of negation can be blocked by assuming that questions presuppose that the pointwise exhaustification of their answers partitions the context of evaluation (Fox 2019). We argue that proper empirical coverage for singular wh-interrogatives requires the interaction of both exhaustification operations.