Dogmas and the Changing Images of Foundations
I offer a critical review of several different conceptions of the activity of foundational research, from the time of Gaus s to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical exc...
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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2005-08-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/91 |
| _version_ | 1797402510392033280 |
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| author | José Ferreirós |
| author_facet | José Ferreirós |
| author_sort | José Ferreirós |
| collection | DOAJ |
| description | I offer a critical review of several different conceptions of the activity of foundational research, from the time of Gaus s to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of apriori structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist alternative, guiding Riemann, Poincaré, Weyl and others, that seeks to perfect available conceptual systems with the aim to avoid conceptual limitations and expand the range of theoretical options. I shall contend that, at times, assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images. To round the discussion, I mention some traits of an alternative program that investigates the epistemology of mathematical knowledge. |
| first_indexed | 2024-03-09T02:26:16Z |
| format | Article |
| id | doaj.art-fc99fc6ef4344404a8933d362b74e08d |
| institution | Directory Open Access Journal |
| issn | 1281-2463 1775-4283 |
| language | deu |
| last_indexed | 2024-03-09T02:26:16Z |
| publishDate | 2005-08-01 |
| publisher | Éditions Kimé |
| record_format | Article |
| series | Philosophia Scientiæ |
| spelling | doaj.art-fc99fc6ef4344404a8933d362b74e08d2023-12-06T15:54:43ZdeuÉditions KiméPhilosophia Scientiæ1281-24631775-42832005-08-015274210.4000/philosophiascientiae.91Dogmas and the Changing Images of FoundationsJosé FerreirósI offer a critical review of several different conceptions of the activity of foundational research, from the time of Gaus s to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of apriori structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist alternative, guiding Riemann, Poincaré, Weyl and others, that seeks to perfect available conceptual systems with the aim to avoid conceptual limitations and expand the range of theoretical options. I shall contend that, at times, assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images. To round the discussion, I mention some traits of an alternative program that investigates the epistemology of mathematical knowledge.http://journals.openedition.org/philosophiascientiae/91 |
| spellingShingle | José Ferreirós Dogmas and the Changing Images of Foundations Philosophia Scientiæ |
| title | Dogmas and the Changing Images of Foundations |
| title_full | Dogmas and the Changing Images of Foundations |
| title_fullStr | Dogmas and the Changing Images of Foundations |
| title_full_unstemmed | Dogmas and the Changing Images of Foundations |
| title_short | Dogmas and the Changing Images of Foundations |
| title_sort | dogmas and the changing images of foundations |
| url | http://journals.openedition.org/philosophiascientiae/91 |
| work_keys_str_mv | AT joseferreiros dogmasandthechangingimagesoffoundations |