Conjunctive strengthening more broadly

Disjunctive sentences can in certain cases convey strengthened, conjunctive inferences, a phenomenon also observed with indefinites. This behavior has been captured on the grammatical theory of exhaustification and alternatives, on which strengthening is modulated by what alternatives are generated by grammar. We examine a series of predictions of the theory arising from a grammatical property shared by disjunction and indefinites: their ability to undergo scope shift in certain configurations in which their alternatives—conjunction and universal quantifiers—cannot. We show that in such configurations, the absence of corresponding conjunctive and universal alternatives may allow exhaustification to generate conjunctive inferences. We present evidence that this indeed occurs, building on and extending earlier observations of Santorio (2018, 2020) and Bar-Lev and Fox (2020).