At least not false, at most possible

between truth and assertibility of superlative quantifiers

Maria Spychalska

pp. 571-602

in: Justine Jacot, Philip Pärnamets (eds), Games, interactive rationality, and learning, Synthese 195 (2), 2018.

Abstract

Generalized Quantifier Theory defines superlative quantifiers at most n and at least n as truth-conditionally equivalent to comparative quantifiers fewer than n+1 and more than n (-)1. It has been demonstrated, however, that this standard theory cannot account for various linguistic differences between these two types of quantifiers. In this paper I discuss how the distinction between assertibility and truth-conditions can be applied to explain this phenomenon. I draw a parallel between the assertibility of disjunctions and superlative quantifiers, and argue that those assertibility conditions are essentially modal. I use epistemic logic to formalize the assertibility conditions and revisit some of the linguistic puzzles related to superlative quantification.