Review of Symbolic Logic 2 (1):175-207 (2009)
At the beginning of Die Grundlagen der Arithmetik (§2) , 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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References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
Citations of this work BETA
Some Obstacles Facing a Semantic Foundation for Constructive Mathematics.Michael R. Koss - 2015 - Erkenntnis 80 (5):1055-1068.
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