The Interpretation of Classically Quantified Sentences: A Set-Theoretic Approach

Cognitive Science 30 (4):691-723 (2006)
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We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions.



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Author Profiles

Ira Noveck
Centre National de la Recherche Scientifique
Guy Politzer
Institut Jean Nicod

Citations of this work

How Diagrams Can Support Syllogistic Reasoning: An Experimental Study.Yuri Sato & Koji Mineshima - 2015 - Journal of Logic, Language and Information 24 (4):409-455.

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Relevance.D. Sperber & Deirdre Wilson - 1986 - Communication and Cognition: An Interdisciplinary Quarterly Journal 2.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.
Psychology of Reasoning: Structure and Content.P. C. Wason & P. N. Johnson - 1974 - Philosophy and Rhetoric 7 (3):193-197.
A History of Formal Logic.I. M. Bocheński & Ivo Thomas - 1961 - Science and Society 27 (4):492-494.

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