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Philosophia Mathematica 2005 13(2):135-159; doi:10.1093/philmat/nki009
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Philosophia Mathematica (III), Vol. 13 No. 2 © Oxford University Press, 2005, all rights reserved

How to Nominalize Formalism{dagger}

Jody Azzouni*

*Department of Philosophy, Tufts University Medford, Mass. 02115-7068, U. S. A. jodyazzouni{at}mindspring.com

Formalism shares with nominalism a distaste for abstracta. But an honest exposition of the former position risks introducing abstracta as the stuff of syntax. This article describes the dangers, and offers a new escape route from platonism for the formalist. It is explained how the needed role of derivations in mathematical practice can be explained, not by a commitment to the derivations themselves, but by the commitment of the mathematician to a practice which is in accord with a theory of derivations.


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