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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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2025-06-01
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| Series: | Philosophia Scientiæ |
| Online Access: | https://journals.openedition.org/philosophiascientiae/4742 |
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| author | José Gil-Férez M. Andrew Moshier Alberto Naibo Marco Panza Jean-Michel Salanskis |
| author_facet | José Gil-Férez M. Andrew Moshier Alberto Naibo Marco Panza Jean-Michel Salanskis |
| author_sort | José Gil-Férez |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-43055bbb4c084c8e94ce35d0302d3066 |
| institution | Kabale University |
| issn | 1281-2463 1775-4283 |
| language | deu |
| publishDate | 2025-06-01 |
| publisher | Éditions Kimé |
| record_format | Article |
| series | Philosophia Scientiæ |
| spelling | doaj-art-43055bbb4c084c8e94ce35d0302d30662025-08-20T03:48:06ZdeuÉditions KiméPhilosophia Scientiæ1281-24631775-42832025-06-012929312710.4000/13yi2Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some ExamplesJosé Gil-FérezM. Andrew MoshierAlberto NaiboMarco PanzaJean-Michel SalanskisThe 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.https://journals.openedition.org/philosophiascientiae/4742 |
| spellingShingle | José Gil-Férez M. Andrew Moshier Alberto Naibo Marco Panza Jean-Michel Salanskis Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples Philosophia Scientiæ |
| title | Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples |
| title_full | Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples |
| title_fullStr | Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples |
| title_full_unstemmed | Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples |
| title_short | Formalizing the Logic and Proofs of Book I of Euclid’s Elements: Some Examples |
| title_sort | formalizing the logic and proofs of book i of euclid s elements some examples |
| url | https://journals.openedition.org/philosophiascientiae/4742 |
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