Obligatory Irrelevance and the Computation of Ignorance Inferences

In recent work, Fox (2016) has argued, on the basis of both empirical and conceptual considerations, that relevance (the set of propositions relevant in an utterance context) is closed under speaker belief: if phi is relevant, then it's also relevant whether the speaker believes f. We provide a formally explicit implementation of this idea and explore its theoretical consequences and empirical predictions. As Fox (2016) already observes, one consequence is that ignorance inferences (and scalar implicatures) can only be derived in grammar, via a covert belief operator of the sort proposed by Meyer (2013). We show, further, that the maxim of quantity no longer enriches the meaning of an utterance, per se, but rather acts as a filter on what can be relevant in an utterance context. In particular, certain alternatives (of certain utterances) are shown to be incapable of being relevant in any context where the maxim of quantity is active - a property we dub obligatory irrelevance. We show that the resulting system predicts a quite restricted range of interpretations for sentences with the scalar item some, as compared to both neo-Gricean (Geurts, 2010; Horn, 1972; Sauerland, 2004) and grammatical (Chierchia et al., 2012; Fox, 2007; Meyer, 2013) theories of scalar implicature, and we argue that these predictions seem largely on the right track.