The Psycho-logic of Universal Quantifiers

Abstract

A universally quantified sentence like every frog is green is standardly thought to express a two-place second-order relation (e.g., the set of frogs is a subset of the set of green things). This dissertation argues that as a psychological hypothesis about how speakers mentally represent universal quantifiers, this view is wrong in two respects. First, each, every, and all are not represented as two-place relations, but as one-place descriptions of how a predicate applies to a restricted domain (e.g., relative to the frogs, everything is green). Second, while every and all are represented in a second-order way that implicates a group, each is represented in a completely first-order way that does not involve grouping the satisfiers of a predicate together (e.g., relative to individual frogs, each one is green).These “psycho-logical” distinctions have consequences for how participants evaluate sentences like every circle is green in controlled settings. In particular, participants represent the extension of the determiner’s internal argument (the cir- cles), but not the extension of its external argument (the green things). Moreover, the cognitive system they use to represent the internal argument differs depend- ing on the determiner: Given every or all, participants show signatures of forming ensemble representations, but given each, they represent individual object-files. In addition to psychosemantic evidence, the proposed representations provide explanations for at least two semantic phenomena. The first is the “conservativity” universal: All determiners allow for duplicating their first argument in their second argument without a change in informational significance (e.g., every fish swims has the same truth-conditions as every fish is a fish that swims). This is a puzzling gen- eralization if determiners express two-place relations, but it is a logical consequence if they are devices for forming one-place restricted quantifiers. The second is that every, but not each, naturally invites certain kinds of generic interpretations (e.g., gravity acts on every/#each object). This asymmetry can po- tentially be explained by details of the interfacing cognitive systems (ensemble and object-file representations). And given that the difference leads to lower-level con- comitants in child-ambient speech (as revealed by a corpus investigation), children may be able to leverage it to acquire every’s second-order meaning. This case study on the universal quantifiers suggests that knowing the meaning of a word like every consists not just in understanding the informational contribu- tion that it makes, but in representing that contribution in a particular format. And much like phonological representations provide instructions to the motor plan- ning system, it supports the idea that meaning representations provide (sometimes surprisingly precise) instructions to conceptual systems.