Foundations of Science 18 (1):43-74 (2013)

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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
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DOI 10.1007/s10699-012-9285-8
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References found in this work BETA

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
What is Mathematical Truth?Hilary Putnam - 1975 - In Mathematics, Matter and Method. Cambridge University Press. pp. 60--78.

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Citations of this work BETA

Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.

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