How obligatory irrelevance, symmetric alternatives, and dense scales conspire: The case of modified numerals and ignorance

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.