A Priori Concepts in Euclidean Proof

Peter Epstein
Cambridge University
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.
Keywords diagrammatic reasoning  a priori reasoning  Euclidean geometry
Categories (categorize this paper)
DOI 10.1093/arisoc/aoy011
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 37,100
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

The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
Kant and the Exact Sciences.William Harper & Michael Friedman - 1995 - Philosophical Review 104 (4):587.
Crossing Curves: A Limit to the Use of Diagrams in Proofs.M. Giaquinto - 2011 - Philosophia Mathematica 19 (3):281-307.
Realism, Meaning and Truth.Crispin Wright - 1987 - Mind 96 (383):415-418.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Euclidean Functions of Computable Euclidean Domains.Rodney G. Downey & Asher M. Kach - 2011 - Notre Dame Journal of Formal Logic 52 (2):163-172.
The Theory-Ladenness of Observations, the Role of Scientific Instruments, and the Kantian a Priori.Ragnar Fjelland - 1991 - International Studies in the Philosophy of Science 5 (3):269 – 280.
Kant's Philosophy of Geometry.William Mark Goodwin - 2003 - Dissertation, University of California, Berkeley
Kant's Views on Non-Euclidean Geometry.Michael E. Cuffaro - 2012 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 25:42-54.
Non-Euclidean Geometry: Still Some Problems for Kant.Nicholas Griffin - 1991 - Studies in History and Philosophy of Science Part A 22 (4):661-663.
Another Constructive Axiomatization of Euclidean Planes.Victor Pambuccian - 2000 - Mathematical Logic Quarterly 46 (1):45-48.


Added to PP index

Total downloads
27 ( #244,068 of 2,308,282 )

Recent downloads (6 months)
27 ( #17,055 of 2,308,282 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature