We hold these truths to be self-evident: But what do we mean by that?

Review of Symbolic Logic 2 (1):175-207 (2009)
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.
Keywords self-evidence   mathematics   proofs   toread
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DOI 10.1017/S175502030909011X
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References found in this work BETA
Posthumous Writings.Gottlob Frege - 1991 - Wiley-Blackwell.
Logic, Logic, and Logic.George Boolos - 1998 - Harvard University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
Scientific Explanation.Philip Kitcher & Wesley Salmon (eds.) - 1989 - Univ of Minnesota Pr.

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Citations of this work BETA
The Composition of Thoughts.Richard Heck & Robert May - 2011 - Noûs 45 (1):126-166.
Axioms in Mathematical Practice.D. Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.

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