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Philosophia Mathematica Advance Access published online on January 16, 2008
Philosophia Mathematica, doi:10.1093/philmat/nkm047
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© The Author [2007]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Intuitionism and Logical Syntax{dagger}

Charles McCarty*

* Departments of Philosophy and Computer Science, Indiana University, Bloomington, Indiana 47405-7000, U.S.A. dmccarty{at}indiana.edu

In Logical Syntax of Language, Rudolf Carnap became a chief proponent of the doctrine that the statements of intuitionism carry nonstandard intuitionistic meanings. This doctrine is linked to Carnap's ‘Principle of Tolerance’ and claims he made on behalf of his notion of pure syntax. From premises independent of intuitionism, we argue that the doctrine, the Principle, and the attendant claims are mistaken, especially Carnap's repeated insistence that, in defining languages, logicians are free of commitment to mathematical statements intuitionists would reject.

{dagger} I am grateful to Nathan Carter, Gary Ebbs, Janet Folina, Luise Prior McCarty, Stewart Shapiro, Neil Tennant, Christopher Tillman, Beth Tropman, Wen-fang Wang, and two anonymous referees for their comments and suggestions.


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