The Psycho-logic of Universal Quantifiers
Tyler Knowlton
July 2021 

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 circles), but not the extension of its external argument (the green things). Moreover, the cognitive system they use to represent the internal argument differs depending 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 generalization 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 potentially be explained by details of the interfacing cognitive systems (ensemble and object-file representations). And given that the difference leads to lower-level concomitants 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 contribution that it makes, but in representing that contribution in a particular format. And much like phonological representations provide instructions to the motor planning system, it supports the idea that meaning representations provide (sometimes surprisingly precise) instructions to conceptual systems.

Format:	[ pdf ]
Reference:	lingbuzz/006114 (please use that when you cite this article)
Published in:	PhD Dissertation, University of Maryland
keywords:	quantification, psychosemantics, psycholinguistics, meaning, verification, semantics
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