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Ten Misconceptions from the History of Analysis and Their Debunking

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Pedagogical University of Cracow, Kraków, Poland

    Piotr Błaszczyk

  2. Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel

    Mikhail G. Katz

  3. Department of Philosophy, Northern Arizona University, Flagstaff, AZ, 86011, USA

    David Sherry

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  1. Piotr Błaszczyk
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  2. Mikhail G. Katz
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  3. David Sherry
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Correspondence to Mikhail G. Katz.

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Piotr Błaszczyk supported by Polish Ministry of Science and Higher Education grant N N101 287639.

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Błaszczyk, P., Katz, M.G. & Sherry, D. Ten Misconceptions from the History of Analysis and Their Debunking. Found Sci 18, 43–74 (2013). https://doi.org/10.1007/s10699-012-9285-8

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  • DOI: https://doi.org/10.1007/s10699-012-9285-8

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