A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

Details A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

2011-04-03

arxiv.org/abs/1104.0375v3

Foundations of Science 2011 (online first) http://dx.doi.org/10.1007/s10699-011-9223-1

Mathematics

History and Overview

56 pages; 3 figures. Corrected misprints

Scientific paper

10.1007/s10699-011-9223-1

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.

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