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 Sherry

doi:10.1007/s10699-017-9534-y

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 Sherry

Research output: Contribution to journal › Article › peer-review

8 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 language	English
Pages (from-to)	267-296
Number of pages	30
Journal	Foundations of Science
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s10699-017-9534-y
State	Published - 1 Jun 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media B.V.

Funding

V. Kanovei was supported in part by the RFBR Grant Number 17-01-00705. M. Katz was partially funded by the Israel Science Foundation Grant Number 1517/12. We are grateful to Dave L. Renfro for helpful suggestions.

Funders	Funder number
Russian Foundation for Basic Research	17-01-00705
Israel Science Foundation	1517/12

Keywords

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

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10.1007/s10699-017-9534-y

Cite this

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

Abstract

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Keywords

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