Euclid's diagrammatic logic and cognitive science

Yacin Hamami, John Mumma

Research output: Contribution to journalConference paper

1 Citation (Scopus)

Abstract

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
and van Lambalgen [1] is a good candidate for this purpose.
Original languageEnglish
Pages (from-to)14-26
Number of pages13
JournalCEUR workshop proceedings
Volume883
Publication statusPublished - 2012
EventLogic & Cognition Workshop, ESSLLI 2012 - Opole, Poland
Duration: 13 Aug 201217 Aug 2012

Keywords

  • Euclidean diagrammatic reasoning
  • Euclidean geometry
  • geometrical cognition
  • psychology of reasoning

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