Benjamin Wilck
Humboldt-University, Berlin
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.
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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Philosophy of Mathematics.Øystein Linnebo - 2017 - Princeton, NJ: Princeton University Press.

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