, Volume 17, Issue 1, pp 51-89
Date: 12 Mar 2011

A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography

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Abstract

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

Mikhail G. Katz: Supported by the Israel Science Foundation grant 1294/06.