A priori concepts in euclidean proof
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Epstein, PF
Abstract
With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our grasp of the content of geometrical concepts plays a central role; moreover, our grasp of this content is a priori.
Description
Keywords
5003 Philosophy, 50 Philosophy and Religious Studies, 5002 History and Philosophy Of Specific Fields
Journal Title
Proceedings of the Aristotelian Society, Supplementary Volume
Conference Name
2017 Joint Session
Journal ISSN
0309-7013
1467-9264
1467-9264
Volume Title
118
Publisher
Oxford University Press (OUP)
Publisher DOI
Rights
All rights reserved