Any vs. Or and Indefinites vs. Modals

A sentence like Bill can order salad or soup intuitively implies the content of its disjunct alternatives, i.e. (in this case) the proposition that Bill can order salad and that Bill can order soup. This “free choice” (FC) inference does not follow from the traditional semantics of can (as an existential quantifier over worlds), or from the basic boolean semantics of or. The same FC inference is available in sentences like Bill can order any side dish. Here, FC conjoins the contents of what are known as the sentence’s “subdomain” alternatives (that Bill can order dish1, can order dish2, etc.). An influential view of FC derives the inference from (recursive) exhaustification (e.g. Fox 2007). The view also plays a crucial role in some accounts of the distribution of any; Crnic 2019, for example, proposes that any is acceptable whenever its host phrase entails its subdomain alternatives. The puzzle we identify here, and propose a solution to, is the following: exhaustification makes identical predictions when or/any are embedded under existential quantifiers, and while in these configurations there does seem to be an FC-like inference of disjunction—e.g. some students enrolled in German or French suggests that some enrolled in German and some enrolled in French—any is not acceptable in the same position. We propose, building on Geurts 2009 and Sudo 2016, 2023, that indefinites, but not modals, bind into their alternatives. This anaphoricity (of the former but not the latter) delivers the relevant difference: in the case of indefinites/quantifiers there is no entailment to the subdomain alternatives, whereas in the case of modals there is. It follows that, despite exhaustification, any is not licensed under quantifiers, but licensed under modals.