Reconciling Inquisitive Semantics and Generalized Quantifier Theory

Abstract

This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive Semantics (IS). After discussing the difficulty in treating quantifiers under the existing IS framework, I propose a new treatment of quantifiers that combines features of IS and the Generalized Quantifier Theory (GQT). My proposal comprises two main points: (i) assuming that the outputs of all quantifiers given non-inquisitive inputs are non-inquisitive; and (ii) deriving a predicate \(X^*\) of type \(s\!\!\rightarrow \!\!(e^n\!\!\rightarrow \!\! t)\) corresponding to each predicate X of type \(e^n\!\!\rightarrow \!\! T\). By using \(X^*\), we can then restore the traditional treatment of GQT under the IS framework. I next point out that to properly handle the pair list reading of some questions with “every”, we have to revert to the old treatment of every. I also introduce (and prove) a theorem that shows that the new treatment of every is just a special case of the old treatment, and conclude that the new treatment of all quantifiers other than every plus the old treatment of every is sufficient for the general purpose of treating quantified statements and questions.