The Interpretation of Classically Quantified Sentences: A set-theoretic approach

Abstract : 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. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions.
Liste complète des métadonnées

Littérature citée [54 références]  Voir  Masquer  Télécharger
Contributeur : Guy Politzer <>
Soumis le : mardi 13 février 2007 - 02:03:24
Dernière modification le : jeudi 11 janvier 2018 - 06:19:08
Document(s) archivé(s) le : mardi 6 avril 2010 - 22:25:05


  • HAL Id : ijn_00130614, version 1



Guy Politzer, Jean-Baptiste Van Der Henst, Claire Delle Luche, Ira Noveck. The Interpretation of Classically Quantified Sentences: A set-theoretic approach. Cognitive Science, Wiley, 2006, 30 (4), pp.691-723. 〈ijn_00130614〉



Consultations de la notice


Téléchargements de fichiers