Descartes intuitionniste ?
The aim of this article is to study Euclid’s plane geometry, relatively to Book I of the Elements, from a formal point of view. Instead of making appeal to some already existent logical framework, we introduce a new formal language, as well as a new system of rules, specifically tailored to give a f...
Wedi'i Gadw mewn:
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| Fformat: | Article ou chapitre numérique |
| Iaith: | Français |
| Cyhoeddwyd: |
2025
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| Mynediad Ar-lein: | Accès Université d'Orléans et IFPM |
| Crynodeb: | The aim of this article is to study Euclid’s plane geometry, relatively to Book I of the Elements, from a formal point of view. Instead of making appeal to some already existent logical framework, we introduce a new formal language, as well as a new system of rules, specifically tailored to give a faithful reconstruction of Euclid’s proof practice. Such a reconstruction shows that Euclid’s work can be understood as resting on a very peculiar inferential setting, involving much more mathematics than logic (understood as a general framework of reasoning): inference rules essentially deal with geometric objects and their relations, while no propositional connectives nor quantifiers are present. |
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