Obligatory Irrelevance and the Computation of Ignorance Inferences

The standard grammatical theory of scalar implicature, as envisioned by Chierchia (2004), Fox (2007), and Chierchia, Fox, and Spector (2012), posits that scalar implicatures are derived in grammar, as a matter semantics, rather than pragmatically, as an implicature rooted in Grice’s maxim of quantity. Ignorance inferences, by contrast, e.g. those associated with plain disjunctive sentences, are derived pragmatically, as quantity implicatures. More generally, the standard theory predicts that for any utterance S and any relevant proposition φ which isn’t entailed, and whose negation isn’t entailed, by S, S gives rise to an inference of speaker ignorance about φ. We argue that this prediction is wrong: it fails to explain the contrast in ignorance inferences associated with at least (which obligatorily implies ignorance) vs. more than (which doesn’t) (Geurts and Nouwen 2007; Nouwen 2010, 2015). The problem is that, without stipulating restrictions on which propositions are relevant, the theory overgenerates ignorance inferences across the board. We argue that the solution is to close relevance under belief (if φ is relevant, then it’s also relevant whether the speaker believes φ). This move has the effect that ignorance inferences, like scalar implicatures, can only be derived in grammar, via a covert belief operator of the sort proposed by Meyer (2013) and discussed further by Fox (2016). The maxim of quantity, we show, then 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 argue that obligatory irrelevance provides the key to understanding the contrast in ignorance inferences exhibited by at least vs. more than. We also argue that translating our proposal into neo-Gricean terms, if at all possible, would yield a conceptually less appealing and empirically less adequate theory.