On the source of distributive inferences

This paper reports on two experiments investigating the relationship between distributive and negated universal inferences arising from disjunction embedded under universal quantifiers. It has been claimed that distributive inferences can be derived independently from negated universal inferences with nominal, but not with modal quantifiers (Sayre-McCord 1986, Crnič, Chemla & Fox 2015, Fusco 2015, Booth 2022). Experiment 1 tested this claim by comparing cases involving the determiner every and cases involving the modal must, where must expressed epistemic necessity. Experiment 2 followed up by testing the same two quantifiers, but this time with must expressing deontic necessity. The results from both experiments support the view that distributive inferences can arise independently of negated universal inferences with both types of operator. While the findings for every essentially reproduce those of Crnič, Chemla & Fox (2015), the findings for must are new and go against the aforementioned claim. As such, we take these findings to pose a challenge for accounts of distributive inferences that cannot derive them independently of negated universal inferences across universal quantifiers. We outline two recent accounts of distributive inferences that can meet this challenge. EARLY ACCESS