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On Mathematical Elucidation

On Mathematical Elucidation

José Seoane, “On Mathematical Elucidation,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1405–22, DOI 10.17990/RPF/2017_73_3_1405.

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On Mathematical Elucidation

Type Journal Article
Author José Seoane
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1405-1422
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1405
Language English
Abstract From the traditional point of view, mathematical elucidation is usually characterized fundamentally in terms of what it is not. What does elucidating mean in mathematics? It is not the appropriate tool for demonstrating theorems. Elucidatory processes do not end in theorems and their justification strategies are not proofs. The conclusions of such processes are called “theses” (in opposition to “theorems”), and relatively scarce philosophical attention has been given to the justification of such theses. The purpose of this paper is to outline a positive conception of mathematical elucidation, in an attempt to capture its specific features and, in particular, to explore the structure of the justifications of the theses. The main conclusion of this paper points to underlining the contribution of elucidatory processes to the dynamic rationality of mathematical practice.
Date Added 17/01/2018, 17:51:11
Modified 18/01/2018, 10:37:07

Tags:

  • Hilbert’s thesis,
  • mathematical elucidation,
  • mathematical rationality,
  • proof,
  • thesis

Notes:

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    Seoane, José. “Elucidando el concepto de demostración. Observaciones sobre Chateaubriand,” in Carnielli, Walter A. and da Silva, Jairo J. (eds.), “Logic, Language and Knowledge. Essays on Chateaubriand’s Logical Forms,” Manuscrito – Rev. Int. Fil. 31, no. 1, Campinas (2008).
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