Partition by exhaustification: comments on Dayal 1996

Abstract

In this paper I argue for a new constraint on questions, namely that a question
denotation (a set of propositions) must map to a partition of a Stalnakerian Context-Set by
point-wise exhaustification (point-wise application of the function Exh). The presupposition
that Dayal attributes to an Answer operator follows from this constraint, if we assume a fairly
standard definition of Exh (Krifka, 1995). But the constraint is more restrictive thereby
deriving the sensitivity of higher order quantification to negative islands (Spector, 2008).
Moreover, when combined with recent proposals about the nature of Exh – designed
primarily to account for the conjunctive interpretation of disjunction (e.g. Bar-Lev and Fox,
2017) – Dayal’s presupposition follows only in certain environments. This observation
allows for an account of the “mention-some” interpretation of questions that makes specific
distributional predictions.
Keywords: exhaustivity, Free Choice, maximality, higher-order quantification, mentionsome,
negative-islands, partition, scalar implicatures, uniqueness.