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Medientyp:
E-Artikel
Titel:
WE HOLD THESE TRUTHS TO BE SELF-EVIDENT: BUT WHAT DO WE MEAN BY THAT?
Beteiligte:
SHAPIRO, STEWART
Erschienen:
Cambridge University Press (CUP), 2009
Erschienen in:
The Review of Symbolic Logic, 2 (2009) 1, Seite 175-207
Sprache:
Englisch
DOI:
10.1017/s175502030909011x
ISSN:
1755-0203;
1755-0211
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>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.</jats:p>