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Philosophia Mathematica Advance Access originally published online on July 1, 2006
Philosophia Mathematica 2008 16(1):4-24; doi:10.1093/philmat/nkl015
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Copyright © The Author 2006. Published by Oxford University Press.

Carnap, Formalism, and Informal Rigour{dagger}

Lavers Gregory*

*Department of Philosophy, Concordia University, 7141 de Maisonneuve Blvd W., Montréal (Québec) H3G 1M8 Canada.

Correspondence: glavers{at}alcor.concordia.ca

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic.


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