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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Bibliographic Details
Main Authors: José Gil-Férez, M. Andrew Moshier, Alberto Naibo, Marco Panza, Jean-Michel Salanskis
Format: Article
Language:deu
Published: Éditions Kimé 2025-06-01
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.
ISSN:1281-2463
1775-4283