No abstract.

Inferences that result from exhaustification of a sentence S depend on the set of alternatives to S. In this paper, we present some inference patterns that are problematic for previous theories of alternatives and propose some structural constraints on the derivation of formal alternatives which derive the observations.

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 $\phi $. 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.

Buccola & Haida (2019) explore the consequences of a semantic-pragmatic theory in which relevance is closed under speaker belief. A primary consequence of this closure condition, they show, is that the Maxim of Quantity commits speakers to expressing their epistemic state about every relevant proposition. We argue that this commitment, dubbed Strong Epistemic Transparency, explains the contrast in ignorance inferences exhibited by non-strict comparative expressions like at least vs. strict ones like more than (hence the class A/B distinction of Nouwen 2010). We also discuss how our analysis might be extended to account for the observations of Cummins, Sauerland & Solt (2012) and Enguehard (2018) that the modifier more than does not block scalar inferences of round numerals.