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On Euclidean diagrams and geometrical knowledge

Dal Magro, Tamires and García-Pérez, Manuel J. (2019) On Euclidean diagrams and geometrical knowledge. THEORIA. An International Journal for Theory, History and Foundations of Science, 34 (2). pp. 255-276. ISSN 2171-679X

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Abstract

We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Dal Magro, Tamirestamiresdma@gmail.com
García-Pérez, Manuel J.mjgarpe92@gmail.com
Additional Information: ISSN: 0495-4548 (print)
Keywords: mathematical practice; Euclidean geometry; diagrammatic reasoning; cognitive abilities
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Cognitive Science > Concepts and Representations
Depositing User: Unnamed user with email theoria@ehu.es
Date Deposited: 03 Oct 2019 23:51
Last Modified: 03 Oct 2019 23:51
Item ID: 16487
Journal or Publication Title: THEORIA. An International Journal for Theory, History and Foundations of Science
Publisher: Euskal Herriko Unibertsitatea / Universidad del País Vasco
Official URL: https://www.ehu.eus/ojs/index.php/THEORIA/article/...
DOI or Unique Handle: 10.1387/theoria.20026
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Cognitive Science > Concepts and Representations
Date: May 2019
Page Range: pp. 255-276
Volume: 34
Number: 2
ISSN: 2171-679X
URI: http://philsci-archive.pitt.edu/id/eprint/16487

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