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The Interpretation of Classically Quantified Sentences: A Set‐Theoretic Approach
Author(s) -
Politzer Guy,
Henst JeanBaptiste,
Delle Luche Claire,
Noveck Ira A.
Publication year - 2006
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1207/s15516709cog0000_75
Subject(s) - representation (politics) , interpretation (philosophy) , negation , set (abstract data type) , diagrammatic reasoning , expression (computer science) , natural language processing , computer science , mental representation , meaning (existential) , mathematics , artificial intelligence , cognition , psychology , neuroscience , politics , political science , law , psychotherapist , programming language
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.