Four types of quantifiers at the interface between syntax and logic

Abstract

Abstract Without quantifiers and quantification the capacity to draw inferences is extremely impoverished. The typology of quantifiers across the languages of the world bears a clear resemblance relation to generalized quantifiers in logic, but it is significantly richer and more varied. In this paper I show how the main quantificational devices that Universal Grammar affords us fall into four natural classes: (i) Determiner quantifiers (e.g., every, many, some,…) (ii) Adverbial quantifiers (e.g., always, usually, frequently, …) (iii) Alternative-oriented quantifiers (e.g., only, even, also,…) and (iv) Polarity-sensitive quantifiers (e.g., any). Of these four classes, Determiner quantifiers are the ones that one finds in standard logical theories; they are, however, NOT universally attested across languages, while the other three classes seem to be. This articulated typology raises a number of key questions pertaining to the relation between language and cognition: How do these types of quantifiers come about? What is special about them? Why do languages insist in resorting to these quantifier types so pervasively?