Evidence for projection of cleft exhaustivity

Abstract

This paper argues that negated clefts, as well as other types of embedded clefts, trigger a previously undescribed inference, which I term potential exhaustivity. Although negated clefts do not trigger an actual exhaustivity inference, they imply that the rejected alternative was under consideration as a potential exhaustive answer to the question under discussion addressed by the cleft. Therefore, negated clefts are infelicitous when the common ground already entails that the rejected alternative cannot serve as an exhaustive answer. This finding challenges the prevailing assumption that cleft exhaustivity does not project, thereby providing compelling evidence that exhaustivity is a presupposition. Furthermore, it is proposed that the potential exhaustivity inference should not be seen as a component of the exhaustivity presupposition itself; instead, it emerges due to an independently-motivated constraint on presupposition accommodation.