David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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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.
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References found in this work BETA
Stewart Shapiro (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.
Gottlob Frege (1991). Posthumous Writings. Wiley-Blackwell.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Philip Kitcher & Wesley Salmon (eds.) (1989). Scientific Explanation. Univ of Minnesota Pr.
Citations of this work BETA
Richard Heck & Robert May (2011). The Composition of Thoughts. Noûs 45 (1):126-166.
Justin Clarke-Doane (2014). Moral Epistemology: The Mathematics Analogy. Noûs 48 (2):238-255.
Michael R. Koss (2015). Some Obstacles Facing a Semantic Foundation for Constructive Mathematics. Erkenntnis 80 (5):1055-1068.
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