The Mental Representation of Universal Quantifiers
Tyler Knowlton, Paul Pietroski, Justin Halberda, Jeffrey Lidz
October 2019

A sentence like "every circle is blue" might be understood in terms of individuals and their properties (e.g., for each thing that’s a circle, it’s blue) or in terms of a relation between groups (e.g., the blue things include the circles). Formally, theorists can use the tools of first-order logic and/or the more powerful tools of second-order logic to specify the contents of universally quantified statements. We offer new evidence that this formal distinction is psychologically realized and has behavioral repercussions. Participants were shown displays of dots and asked to evaluate statements 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 every- or all-statements compared to each-statements. This suggests that every- and all-statements are mentally represented in second-order terms that highlight comparison of groups whereas each-statements are represented in first-order terms that focus on individuals. Since the statements that participants evaluate are truth-conditionally equivalent, our results also bear on questions concerning how meanings are related to truth-conditions.
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Reference: lingbuzz/004486
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keywords: natural language quantifiers, meaning, logic, experimental semantics, semantics
previous versions: v1 [February 2019]
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