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Categoricity and Mathematical Knowledge

Categoricity and Mathematical Knowledge

Fernando Ferreira, “Categoricity and Mathematical Knowledge,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1423–36, DOI 10.17990/RPF/2017_73_3_1423.

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Categoricity and Mathematical Knowledge

Type Journal Article
Author Fernando Ferreira
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1423-1436
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1423
Language English
Abstract We argue that the basic notions of mathematics (number, set, etcetera) can only be properly formulated in an informal way. Mathematical notions transcend formalizations and their study involves the consideration of other mathematical notions. We explain the fundamental role of categoricity theorems in making these studies possible. We arrive at the conclusion that the enterprise of mathematics is not infallible and that it ultimately relies on degrees of evidence.
Date Added 17/01/2018, 17:51:13
Modified 18/01/2018, 10:39:15


  • categoricity theorems,
  • epistemology of mathematics,
  • formal and informal reasoning,
  • infallibility,
  • Platonism


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