Euclidean diagrams and mathematical justification

  • Tamires Dal Magro Universidade Federal de Santa Catarina (UFSC), Brasil
Keywords: Philosophy of mathematical practice, Proof, Euclid, Diagrammatical Reasoning

Abstract

This work presents a historical overview of the problems dealt with by three major conceptions in the philosophy of mathematics: traditional, maverick and conciliatory. In the second and third sections, I focus on showcasing (1) how the use of diagrams in mathematics, and more specifically in Euclidean geometry, was strongly criticized by authors aligned with the first conception and (2) the impact of those criticisms in the re-evaluation and revindication of the legitimacy of the use of diagrams in Euclid by authors aligned with the last two conceptions.

Author Biography

Tamires Dal Magro, Universidade Federal de Santa Catarina (UFSC), Brasil

Tamires Dal Magro is a postdoctoral researcher (PNPD / CAPES) in the area of Epistemology and Logic at the Federal University of Santa Catarina (UFSC), Brazil. PhD in Philosophy from the State University of Campinas (UNICAMP, Brazil). Her current research is specially focused on problems related to mathematical practice, symbolic knowledge, Euclidean geometry, cognitive foundations of mathematics, proofs by reductio ad absurdum, heterogeneous proofs, theories of representation and diagrammatic reasoning. She has published her work on Synthese, Theoria and Crítica

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Published
2020-09-30
How to Cite
[1]
Dal Magro, T. 2020. Euclidean diagrams and mathematical justification. Disputatio. 9, 14 (Sep. 2020), 73-102. DOI:https://doi.org/10.5281/zenodo.4603480.
Section
Articles and Essays