Spreading ignorance

This squib compares two notions of alternatives. On a familiar pragmatic view, alternatives are relevant propositions a speaker could have conveyed instead of, or in addition to, the asserted sentence. On the inquisitive-semantic view, alternatives are part of a sentence’s semantic value, typically tied to specific lexical operators, and correspond to maximal ways of supporting that sentence. We compare these notions by examining ignorance inferences (IIs) triggered by disjunctive sentences of varying complexity. We introduce a novel phenomenon, Ignorance Spreading, in which a conjunction embedded under disjunction yields IIs about the individual conjuncts. We argue that this phenomenon distinguishes the two notions: an implicature approach can derive the observed inferences if the relevant sub-alternatives are available for pragmatic reasoning, whereas an inquisitive account over maximal inquisitive alternatives undergenerates. We take this to show that an adequate theory of IIs must access structurally available sub-alternatives, not just maximal alternatives introduced by disjunction. We conclude by noting remaining challenges for current theories of IIs.