Scope, monotonicity and maximal informativity cannot be underestimated! A compositional analysis of an apparent linguistic illusion

Abstract

We propose a compositional analysis of an apparent linguistic illusion that productively arises with sentences like The importance of this position cannot be underestimated, featuring the prefix under- and a negated possibility modal. On what we term the ‘intended’ interpretation, the sentence means that the position’s importance is very high, while on what we call the ‘pedantic’ interpretation, the sentence means that the position’s importance is very low. Although the intended reading has been claimed to be illusory, we demonstrate that it arises from an inter- action between the scope of the negated modal, the monotonicity of the underlying degree set, and maximal informativity (Beck 2013; Hohaus & Bade 2022).

Keywords: linguistic illusions, degree semantics, monotonicity, maximal informativity