Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples
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...
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| Autori principali: | , , , , |
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| Natura: | Article ou chapitre numérique |
| Lingua: | Français |
| Pubblicazione: |
2025
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| Accesso online: | Accès Université d'Orléans et IFPM |
| Riassunto: | 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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