Euclid's Diagrammatic Logic and Cognitive Science

Logic & Cognition Workshop at ESSLLI 2012

Yacin Hamami1 ; John Mumma2 ; 2 Max Planck Institute for the History of Science ; Berlin

Others  :  http://ceur-ws.org/Vol-883/paper2.pdf
PID  :  43433

来源: CEUR

【 摘 要 】

For more than two millennia, Euclid's Elements set the stan-dard for rigorous mathematical reasoning. The reasoning practice the text embodied is essentially diagrammatic, and this aspect of it has been captured formally in a logical system termed Eu [2, 3]. In this paper, we review empirical and theoretical works in mathematical cognition and the psychology of reasoning in the light of Eu. We argue that cognitive intuitions of Euclidean geometry might play a role in the interpretation of diagrams, and we show that neither the mental rules nor the mental models approaches to reasoning constitutes by itself a good candidate for investigating geometrical reasoning. We conclude that a cognitive framework for investigating geometrical reasoning empirically will have to account for both the interpretation of diagrams and the reasoning with diagrammatic information. The framework developed by Stenning