Ten Misconceptions from the History of Analysis and Their Debunking

Piotr Błaszczyk, Mikhail G. Katz, David M Sherry

Research output: Contribution to journalArticle

22 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)43-74
Number of pages32
JournalFoundations of Science
Volume18
Issue number1
DOIs
StatePublished - 2013

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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

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

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