A Priori Concepts in Euclidean Proof

Authors
Peter Epstein
Cambridge University
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.
Keywords diagrammatic reasoning  a priori reasoning  Euclidean geometry
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DOI 10.1093/arisoc/aoy011
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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.

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