Foundations of Science

, Volume 18, Issue 1, pp 43–74

Ten Misconceptions from the History of Analysis and Their Debunking

Authors

  • Piotr Błaszczyk
    • Institute of MathematicsPedagogical University of Cracow
    • Department of MathematicsBar Ilan University
  • David Sherry
    • Department of PhilosophyNorthern Arizona University
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 RobinsonAdequalityArchimedean continuumBernoullian continuumCantorCauchyCognitive biasCompletenessConstructivismContinuityContinuumdu Bois-ReymondEpsilonticsFelix KleinFermat-Robinson standard partInfinitesimalLeibniz–Łoś transfer principleLimitMathematical rigorNominalismNon-ArchimedeanSimon StevinStolzSum theoremWeierstrass

Copyright information

© Springer Science+Business Media B.V. 2012