The Effective as the Actual and as the Calculable in Jean Cavaillès
Jean Cavaillès’ definition of mathematics as effective thought or effective work is central to his analysis of the “objective becoming” of mathematics. This concept crosses two referents: the effective as the actual and the history of effective calculability. I examine Cavaillès’ treatment of two ph...
Wedi'i Gadw mewn:
| Cyhoeddwyd yn: | URI:https://journals.openedition.org/noesis, |
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| Prif Awdur: | |
| Fformat: | Article ou chapitre numérique |
| Iaith: | Anglais |
| Cyhoeddwyd: |
Noesis
2024
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| Pynciau: | |
| Mynediad Ar-lein: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Crynodeb: | Jean Cavaillès’ definition of mathematics as effective thought or effective work is central to his analysis of the “objective becoming” of mathematics. This concept crosses two referents: the effective as the actual and the history of effective calculability. I examine Cavaillès’ treatment of two phases of the mathematical history of the concept: first, debates between the French analysts around effective definability, and, second, Gödel, Church and Kleene’s work on effective computability. Cavaillès’ temporalisation of the concept of the effective is seen to inform his rejection of any a priori theory of science and correlative relativisation of the transcendental, and thus his theory of discontinuous logical time. |
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