Foundations of Science

, Volume 17, Issue 1, pp 51–89

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

Authors

  • Karin Usadi Katz
    • Department of MathematicsBar Ilan University
    • Department of MathematicsBar Ilan University
Article

DOI: 10.1007/s10699-011-9223-1

Cite this article as:
Katz, K.U. & Katz, M.G. Found Sci (2012) 17: 51. doi:10.1007/s10699-011-9223-1

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 RobinsonAdequalityArchimedean continuumBernoullian continuumBurgessCantorCauchyCompletenessConstructivismContinuityDedekindDu Bois-ReymondEpsilonticsErrett BishopFelix KleinFermat-Robinson standard partInfinitesimalLaw of excluded middleLeibniz-Łoś transfer principleNominalistic reconstructionNominalismNon-ArchimedeanRigorSimon StevinWeierstrass

Copyright information

© Springer Science+Business Media B.V. 2011