Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms

Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, David M. Schaps, David M Sherry

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms.Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

Original languageEnglish (US)
Pages (from-to)1-30
Number of pages30
JournalFoundations of Science
DOIs
StateAccepted/In press - Jun 24 2017

Keywords

  • Cauchy’s infinitesimal
  • Foundational paradigms
  • Quantifier alternation
  • Sum theorem
  • Uniform convergence

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

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    Bascelli, T., Błaszczyk, P., Borovik, A., Kanovei, V., Katz, K. U., Katz, M. G., Kutateladze, S. S., McGaffey, T., Schaps, D. M., & Sherry, D. M. (Accepted/In press). Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. Foundations of Science, 1-30. https://doi.org/10.1007/s10699-017-9534-y