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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | deu |
| Published: |
Éditions Kimé
2025-06-01
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| Series: | Philosophia Scientiæ |
| Online Access: | https://journals.openedition.org/philosophiascientiae/4742 |
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| Summary: | 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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| ISSN: | 1281-2463 1775-4283 |