Tyler in Linguistics and Philosophy

On the psychological representations that give the meanings of "every" and "each".

Fresh in Linguistics and Philosophy, "The mental representation of universal quantifiers" from recent alum Tyler Knowlton with advisors Jeffrey Lidz, Paul Pietroski and Justin Halberda. Drawn from Tyler's dissertation work, the paper gives experimental data to support the claim that "every and all are understood in second-order terms that encourage group representation, while each is understood in first-order terms that encourage individual representation."

Abstract

A sentence like every circle is blue might be understood in terms of individuals and their properties (e.g., for each thing that is a circle, it is blue) or in terms of a relation between groups (e.g., the blue things include the circles). Relatedly, theorists can specify the contents of universally quantified sentences in first-order or second-order terms. We offer new evidence that this logical first-order vs. second-order distinction corresponds to a psychologically robust individual vs. group distinction that has behavioral repercussions. Participants were shown displays of dots and asked to evaluate sentences with each, every, or all combined with a predicate (e.g., big dot). We find that participants are better at estimating how many things the predicate applied to after evaluating sentences in which universal quantification is indicated with every or all, as opposed to each. We argue that every and all are understood in second-order terms that encourage group representation, while each is understood in first-order terms that encourage individual representation. Since the sentences that participants evaluate are truth-conditionally equivalent, our results also bear on questions concerning how meanings are related to truth-conditions.