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

Foundations of Science 17 (1):51-89 (2012)
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
Keywords Abraham Robinson  Adequality  Archimedean continuum  Bernoullian continuum  Burgess  Cantor  Cauchy  Completeness  Constructivism  Continuity  Dedekind  Du Bois-Reymond  Epsilontics  Errett Bishop  Felix Klein  Fermat-Robinson standard part  Infinitesimal  Law of excluded middle  Leibniz-Łoś transfer principle  Nominalistic reconstruction  Nominalism  Non-Archimedean  Rigor  Simon Stevin  Weierstrass
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Karin U. Katz & Mikhail G. Katz (2011). Cauchy's Continuum. Perspectives on Science 19 (4):426-452.

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