A Priori Concepts in Euclidean Proof

Proceedings of the Aristotelian Society 118 (3):407-417 (2018)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,354

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Kant's Views on Non-Euclidean Geometry.Michael Cuffaro - 2012 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 25:42-54.
Kant's Philosophy of Geometry.William Mark Goodwin - 2003 - Dissertation, University of California, Berkeley
Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
Kant and the Impossibility of Non‐Euclidean Space.Tufan Kıymaz - 2019 - Philosophical Forum 50 (4):485-491.
Kant and non-euclidean geometry.Amit Hagar - 2008 - Kant Studien 99 (1):80-98.

Analytics

Added to PP
2018-11-06

Downloads
125 (#145,339)

6 months
18 (#192,006)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Peter Epstein
Brandeis University

Citations of this work

Add more citations

References found in this work

Kant and the exact sciences.Michael Friedman - 1992 - Cambridge: Harvard University Press.
The bounds of sense: an essay on Kant's Critique of pure reason.P. F. Strawson - 1966 - [New York]: Harper & Row, Barnes & Noble Import Division. Edited by Lucy Allais.
Meditations on first philosophy: with selections from the Objections and Replies.René Descartes - 1960 - New York: Cambridge University Press. Edited by John Cottingham & Bernard Williams.
The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 80--133.
Meditations on First Philosophy: With Selections From the Objections and Replies.René Descartes - 1960 - Cambridge, England: Oxford University Press UK. Edited by John Cottingham & Bernard Williams.

View all 13 references / Add more references