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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lavers, Gregory 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, Vol. 34, Issue. 3, p. 225.


    Lavers, Gregory 2012. On the Quinean-analyticity of mathematical propositions. Philosophical Studies, Vol. 159, Issue. 2, p. 299.


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BENACERRAF’S DILEMMA AND INFORMAL MATHEMATICS

  • GREGORY LAVERS (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020309990153
  • Published online: 01 December 2009
Abstract

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 Benacerraf’s dilemma. The account builds upon Georg Kreisel’s 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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*DEPARTMENT OF PHILOSOPHY, CONCORDIA UNIVERSITY, 1455 DEMAISONNEUVE BOULEVARD, MONTREAL, QUEBEC, CANADA H3G 1M8 E-mail:glavers@alcor.concordia.ca
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P Benacerraf . (1973). Mathematical truth. Journal of Philosophy, 70(19), 661679.

B. Hale , & C Wright . (2002). Benacerraf’s dilemma revisited. European Journal of Philosophy, 10(1), 101129.

G Kreisel . (1967). Informal rigour and completeness proofs. In I. Lakatos , editor. Problems in the Philosophy of Mathematics. New York, NY: Humanities Press, pp. 138186.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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