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Philosophia Mathematica Advance Access published online on July 1, 2006
Philosophia Mathematica, doi:10.1093/philmat/nkl015
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© The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Article

Carnap, Formalism, and Informal Rigour{dagger}

Gregory Lavers 1 *

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

* To whom correspondence should be addressed.
Gregory Lavers, E-mail: glavers{at}alcor.concordia.ca


  Abstract

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.

{dagger} Thanks to Richard Creath, Robert DiSalle, Diana Palmieri, and Christopher Pincock for reading this paper and suggesting improvements. Special thanks to William Demopoulos for many useful discussions and suggestions regarding this paper.
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