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The Ancient versus the Modern Continuum

The Ancient versus the Modern Continuum

Eduardo Noble and Max Fernández de Castro, “The Ancient versus the Modern Continuum,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1343–80, DOI 10.17990/RPF/2017_73_3_1343.

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The Ancient versus the Modern Continuum

Type Journal Article
Author Eduardo Noble
Author Max Fernández de Castro
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1343-1380
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1343
Language English
Abstract We discuss the differences between the ancient and the modern notion of mathematical continuity. We focus on three ancient approaches to the continuum, namely the monist, the atomist and the Aristotelian approach. Afterwards, we analyze the construction of real numbers by Dedekind, Weierstrass and Cantor. The modern continuum is characterized by these constructions, but is a more general notion. We compare the ancient conception of continuity and the modern approach in order to show that the modern concept of mathematical continuity cannot be interpreted as part of the ancient theoretical framework, or as some kind of extension of this framework.
Date Added 17/01/2018, 17:51:08
Modified 18/01/2018, 10:32:44

Tags:

  • Aristotle,
  • Cantor,
  • continuum,
  • Dedekind,
  • foundations of mathematics,
  • mathematical continuity,
  • mathematical practice,
  • philosophy of mathematics

Notes:

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