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WE HOLD THESE TRUTHS TO BE SELF-EVIDENT: BUT WHAT DO WE MEAN BY THAT?

Published online by Cambridge University Press:  01 March 2009

STEWART SHAPIRO
STEWART SHAPIRO*
Affiliation:
Department of Philosophy, The Ohio State University and Arché Research Centre, University of St. Andrews
*
*THE OHIO STATE UNIVERSITY COLUMBUS, OH 43210 AND ARCHÉ RESEARCH CENTRE UNIVERSITY OF ST. ANDREWS ST. ANDREWS, FIFE, SCOTLAND, KY16 9AL E-mail:[email protected]
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Abstract

At the beginning of Die Grundlagen der Arithmetik (§2) [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 1 , March 2009 , pp. 175 - 207
Copyright
Copyright © Association for Symbolic Logic 2009

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