## 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.

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 language | English |
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Pages (from-to) | 14-26 |

Number of pages | 13 |

Journal | CEUR workshop proceedings |

Volume | 883 |

Publication status | Published - 2012 |

Event | Logic & Cognition Workshop, ESSLLI 2012 - Opole, Poland Duration: 13 Aug 2012 → 17 Aug 2012 |

## Keywords

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