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Philosophia Mathematica 2005 13(2):160-173; doi:10.1093/philmat/nki018
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Philosophia Mathematica (III), Vol. 13 No. 2 © Oxford University Press, 2005, all rights reserved

On Frege's Alleged Indispensability Argument{dagger}

Pieranna Garavaso*

*Division of the Humanities, University of Minnesota Morris Campus, Morris, Minnesota 56267-2132, U.S.A. garavapf{at}mrs.umn.edu

The expression ‘indispensability argument’ denotes a family of arguments for mathematical realism supported among others by Quine and Putnam. More and more often, Gottlob Frege is credited with being the first to state this argument in section 91 of the Grundgesetze der Arithmetik. Frege's alleged indispensability argument is the subject of this essay. On the basis of three significant differences between Mark Colyvan's indispensability arguments and Frege's applicability argument, I deny that Frege presents an indispensability argument in that very often quoted section of the Grundegesetze.


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