David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Review of Symbolic Logic 2 (4):769-785 (2009)
This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a Fregean account of the objectivity and our knowledge of abstract objects. It is then argued that the resulting view faces no insurmountable metaphysical or epistemic obstacles
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References found in this work BETA
Michael A. E. Dummett (1991). Frege: Philosophy of Mathematics. Harvard University Press.
Hartry Field (1989). Realism, Mathematics & Modality. Basil Blackwell.
Gottlob Frege (1980). The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number. Northwestern University Press.
P. M. S. Hacker (2006). Passing by the Naturalistic Turn: On Quine's Cul-de-Sac. Philosophy 81 (2):231-253.
Citations of this work BETA
Gregory Lavers (2012). On the Quinean-Analyticity of Mathematical Propositions. Philosophical Studies 159 (2):299-319.
Gregory Lavers (2013). Frege, Carnap, and Explication: ‘Our Concern Here Is to Arrive at a Concept of Number Usable for the Purpose of Science’. History and Philosophy of Logic 34 (3):225-41.
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