Universal but Unrelational

Paul Pietroski, Rutgers

Abstract

Given the resources of modern logic, theorists can describe universal quantification in terms of a relation exhibited by certain sets. Correlatively, one might say that 'Every circle is blue' is true (in a context C) if and only if (in C) the blue things include the circles, and that 'Each circle is blue' has this same truth condition—along with 'Each/Every one of the circles is blue' and 'All of the circles are blue'. But it has long been suspected that 'each' is somehow more distributive than 'every' and 'all'. In the talk, I'll begin by discussing some experiments that confirm this suspicion and a much stronger hypothesis: the meanings of 'each' and 'every' call for different concepts of universal quantification; 'each' connects its pronunciation with "Object File" representations, while 'every' connects its pronunciation with "Ensemble" representations. I'll then turn to a series of experiments that confirm another old suspicion: phrases like 'every circle' are understood as restricted quantifiers, as opposed to phrases in which the determiner expresses a genuine relation. Given the sentence 'Every circle is blue', 'circle' is understood as specifying the circles, but 'is blue' is not understood as specifying the blue things. And while one might say that 'Every circle is blue' is true if and only if the things that are both blue and circles are identical to (or improperly include) the circles, the sentence is not understood in this (degenerately relational) way. Rather, 'Every circle is blue' seems to be understood as follows: the circles are such that every one of them is blue. (Aristotle's gloss—[the property of being] blue belongs to every circle—was better than Generalized Quantifier Theory.) Along the way, I’ll argue that taken together, the experiments support the idea that theories of linguistic meaning should be viewed as theories of understanding, and not as mere specifications of (alleged) extensions of expressions.