Cognitive Science 30 (4):691-723 (2006)
AbstractWe 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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Citations of this work
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References found in this work
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.
When Children Are More Logical Than Adults: Experimental Investigations of Scalar Implicature.Ira A. Noveck - 2001 - Cognition 78 (2):165-188.