Journal Article

How to Nominalize Formalism†

Jody Azzouni

in Philosophia Mathematica

Volume 13, issue 2, pages 135-159
Published in print June 2005 | ISSN: 0031-8019
Published online June 2005 | e-ISSN: 1744-6406 | DOI: https://dx.doi.org/10.1093/philmat/nki009
How to Nominalize Formalism†

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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.

Journal Article.  11930 words. 

Subjects: Philosophy of Mathematics and Logic ; Mathematics

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