How to Nominalize Formalism &dagger

Philosophia Mathematica 13 (2):135-159 (2005)
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Abstract

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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10.1093/philmat/nki009

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Jody Azzouni
Tufts University

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
The derivation-indicator view of mathematical practice.Jody Azzouni - 2004 - Philosophia Mathematica 12 (2):81-106.
Thick Epistemic Access.Jody Azzouni - 1997 - Journal of Philosophy 94 (9):472-484.
Theory, observation and scientific realism.Jody Azzouni - 2004 - British Journal for the Philosophy of Science 55 (3):371-392.
Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciences.[author unknown] - 1996 - British Journal for the Philosophy of Science 47 (4):621-626.

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