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

Wepresentaset-theoreticmodelofthementalrepresentationofclassicallyquantifiedsentences(AllP are Q, Some P are Q, Some P are not Q,and No P are Q). We take inclusion, exclusion, and their negations tobeprimitiveconcepts.Weshowthatalthoughthesesentencesareknowntohaveadiagrammaticexpression (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can alsobeexpressedsyntacticallyintheformofalgebraicformulas.Wehypothesizedthatthequantifiedsentenceshaveanabstractunderlyingrepresentationcommontotheformulasandtheirassociatedsetsofdiagrams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people's assessmentofhowwelleachofthe5diagramsexpressesthemeaningofeachofthequantifiedsentences.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.

• Type: Journal
• Year: 2006
• Where: COGSCI
• Authors: Guy Politzer, Jean-Baptiste Van der Henst, Claire Delle Luche, Ira A. Noveck
• Keywords: Circles, COGSCI 2006, Negations Tobeprimitiveconcepts.Weshowthatalthoughthesesentencesareknowntohaveadiagrammaticexpression, Semantic Representation