The Review of Symbolic Logic

Research Article

BENACERRAF’S DILEMMA AND INFORMAL MATHEMATICS

GREGORY LAVERSa1 c1

a1 Department of Philosophy, Concordia University

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.

(Received June 18 2009)

Correspondence:

c1 DEPARTMENT OF PHILOSOPHY, CONCORDIA UNIVERSITY, 1455 DEMAISONNEUVE BOULEVARD, MONTREAL, QUEBEC, CANADA H3G 1M8 E-mail: glavers@alcor.concordia.ca