History of Philosophy & Logical Analysis 23 (2):362-397 (2020)
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Abstract |
Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at all. Instead, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object.
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Keywords | Euclid’s Elements mathematical objects definitions Platonic method of division Aristotle substance genus differentia linguistic markers |
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DOI | 10.30965/26664275-02302005 |
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References found in this work BETA
Grundlagen der Arithmetik: Studienausgabe MIT Dem Text der Centenarausgabe.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
Die Grundlagen der Arithmetik: Eine Logische Mathematische Untersuchung Über den Begriff der Zahl.Gottlob Frege - 1988 - Felix Meiner Verlag.
Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1981 - Dover Publications.
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