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.

Funding

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

FundersFunder number
Israel Science Foundation1294/06

    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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