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

Stewart Shapiro

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)175-207
Number of pages33
JournalThe Review of Symbolic Logic
Volume2
Issue number1
DOIs
Publication statusPublished - Mar 2009

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