A Priori Concepts in Euclidean Proof

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



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Peter Epstein
Brandeis University

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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.
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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.

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