Authors
Benjamin Wilck
Humboldt-University, Berlin
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.
Keywords Euclid’s Elements   mathematical objects   definitions   Platonic method of division   Aristotle   substance   genus   differentia   linguistic markers
Categories (categorize this paper)
DOI 10.30965/26664275-02302005
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,056
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.

Analytics

Added to PP index
2020-12-25

Total views
103 ( #99,525 of 2,427,676 )

Recent downloads (6 months)
103 ( #6,300 of 2,427,676 )

How can I increase my downloads?

Downloads

My notes