title: 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. We show that although these sentences are known to have a diagrammatic expression (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 sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people's assessment 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.
authors.affiliation: Centre National de la Recherche Scientifique, Institut Jean-Nicod, Paris, FranceCentre National de la Recherche Scientifique, Institut des Sciences Cognitives, Lyon, FranceUniversité Lyon II, France.
authors.forename: Guy
authors.initials: G
authors.lastname: Politzer
authors.forename: Jean-Baptiste
authors.initials: JB
authors.lastname: Henst
authors.forename: Claire
authors.initials: C
authors.lastname: Delle Luche
authors.forename: Ira A
authors.initials: IA
authors.lastname: Noveck