The controversy between Frege and Hilbert
In this paper, I shall focus my attention on two subjects of the debate between Frege and Hilbert held around 1900 concerning the foundations of geometry: a) the difference between axioms and definitions, b) the proofs of independence of axioms. Concerning the first point, I will hold that Hilbert a...
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Universidad de Costa Rica
2018
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| Acceso en línea: | https://revistas.ucr.ac.cr/index.php/filosofia/article/view/35084 |
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FILOSOFIA350842019-01-24T00:27:29Z The controversy between Frege and Hilbert Fernández de Castro, Max Definitions Proof of independence and consistency Concepts Logical consequence In this paper, I shall focus my attention on two subjects of the debate between Frege and Hilbert held around 1900 concerning the foundations of geometry: a) the difference between axioms and definitions, b) the proofs of independence of axioms. Concerning the first point, I will hold that Hilbert and Frege had different conceptions of ‘concept’ and that Hilbert’s position is problematic. Later, I shall explore Patricia Blanchette’s interpretation that Frege’s objections to Hilbert’s proofs of consistency and independence arise from his different notions of logical consequence. I will suggest that this interpretation is not correct, even if it fits well with most of the textual evidence, because it gives rise to certain puzzling consequences. Universidad de Costa Rica 2018-10-31 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Contribution application/pdf https://revistas.ucr.ac.cr/index.php/filosofia/article/view/35084 Revista de Filosofía de la Universidad de Costa Rica; Vol. 57 No. 147 (2018): Revista de Filosofía; 113-128 Revista de Filosofía de la Universidad de Costa Rica; Vol. 57 Núm. 147 (2018): Revista de Filosofía; 113-128 2215-5589 0034-8252 spa https://revistas.ucr.ac.cr/index.php/filosofia/article/view/35084/34630 Derechos de autor 2018 Revista de Filosofía de la Universidad de Costa Rica |
| institution |
Universidad de Costa Rica |
| collection |
Revista de Filosofía de la Universidad de Costa Rica |
| language |
spa |
| format |
Online |
| author |
Fernández de Castro, Max |
| spellingShingle |
Fernández de Castro, Max The controversy between Frege and Hilbert |
| author_facet |
Fernández de Castro, Max |
| author_sort |
Fernández de Castro, Max |
| description |
In this paper, I shall focus my attention on two subjects of the debate between Frege and Hilbert held around 1900 concerning the foundations of geometry: a) the difference between axioms and definitions, b) the proofs of independence of axioms. Concerning the first point, I will hold that Hilbert and Frege had different conceptions of ‘concept’ and that Hilbert’s position is problematic. Later, I shall explore Patricia Blanchette’s interpretation that Frege’s objections to Hilbert’s proofs of consistency and independence arise from his different notions of logical consequence. I will suggest that this interpretation is not correct, even if it fits well with most of the textual evidence, because it gives rise to certain puzzling consequences. |
| title |
The controversy between Frege and Hilbert |
| title_short |
The controversy between Frege and Hilbert |
| title_full |
The controversy between Frege and Hilbert |
| title_fullStr |
The controversy between Frege and Hilbert |
| title_full_unstemmed |
The controversy between Frege and Hilbert |
| title_sort |
controversy between frege and hilbert |
| publisher |
Universidad de Costa Rica |
| publishDate |
2018 |
| url |
https://revistas.ucr.ac.cr/index.php/filosofia/article/view/35084 |
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AT fernandezdecastromax thecontroversybetweenfregeandhilbert AT fernandezdecastromax controversybetweenfregeandhilbert |
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