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Publication details

Document type
Journal articles

Document subtype
Full paper

Title
Categoricity and Mathematical Knowledge

Participants in the publication
Fernando Ferreira (Author)
Dep. Matemática
CMAFcIO - Centro de Matemática, Aplicações Fundamentais e Investigação Operacional

Summary
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 of Publication
2017-12-30

Institution
UNIVERSIDADE DE LISBOA

Where published
Revista Portuguesa de Filosofia

Publication Identifiers
ISSN - 0870-5283

Publisher
Aletheia - Associacao Cientifica e Cultural

Volume
73
Number
3-4

Number of pages
13
Starting page
1423
Last page
1436

Document Identifiers
DOI - https://doi.org/10.17990/rpf/2017_73_3_1423
URL - http://dx.doi.org/10.17990/rpf/2017_73_3_1423

Keywords
epistemology of mathemtics categoricity theorems formal and informal reasoning infallibility platonism


Export

APA
Fernando Ferreira, (2017). Categoricity and Mathematical Knowledge. Revista Portuguesa de Filosofia, 73, 1423-1436. ISSN 0870-5283. eISSN . http://dx.doi.org/10.17990/rpf/2017_73_3_1423

IEEE
Fernando Ferreira, "Categoricity and Mathematical Knowledge" in Revista Portuguesa de Filosofia, vol. 73, pp. 1423-1436, 2017. 10.17990/rpf/2017_73_3_1423

BIBTEX
@article{40327, author = {Fernando Ferreira}, title = {Categoricity and Mathematical Knowledge}, journal = {Revista Portuguesa de Filosofia}, year = 2017, pages = {1423-1436}, volume = 73 }