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

Karin Usadi Katz, Mikhail G. Katz

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24 Scopus citations

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.

Original languageEnglish
Pages (from-to)51-89
Number of pages39
JournalFoundations of Science
Volume17
Issue number1
DOIs
StatePublished - Mar 2012

Bibliographical note

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

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
  • Nominalism
  • Nominalistic reconstruction
  • Non-Archimedean
  • Rigor
  • Simon Stevin
  • Weierstrass

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