Foundations of Science

, Volume 18, Issue 1, pp 43–74

Ten Misconceptions from the History of Analysis and Their Debunking

Article

DOI: 10.1007/s10699-012-9285-8

Cite this article as:
Błaszczyk, P., Katz, M.G. & Sherry, D. Found Sci (2013) 18: 43. doi:10.1007/s10699-012-9285-8

Abstract

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others.

Keywords

Abraham Robinson Adequality Archimedean continuum Bernoullian continuum Cantor Cauchy Cognitive bias Completeness Constructivism Continuity Continuum du Bois-Reymond Epsilontics Felix Klein Fermat-Robinson standard part Infinitesimal Leibniz–Łoś transfer principle Limit Mathematical rigor Nominalism Non-Archimedean Simon Stevin Stolz Sum theorem Weierstrass 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Piotr Błaszczyk
    • 1
  • Mikhail G. Katz
    • 2
  • David Sherry
    • 3
  1. 1.Institute of MathematicsPedagogical University of CracowKrakówPoland
  2. 2.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  3. 3.Department of PhilosophyNorthern Arizona UniversityFlagstaffUSA

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