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

Philosophy

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

6 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 (US)
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 - Jun 1 2018

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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10.1007/s10699-017-9534-y

Cite this

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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{\textquoteright}s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy{\textquoteright}s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy{\textquoteright}s proof closely and show that it finds closer proxies in a different modern framework.",

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AU - Bascelli, Tiziana

AU - Błaszczyk, Piotr

AU - Borovik, Alexandre

AU - Kanovei, Vladimir

AU - Katz, Karin U.

AU - Katz, Mikhail G.

AU - Kutateladze, Semen S.

AU - McGaffey, Thomas

AU - Schaps, David M.

AU - Sherry, David

PY - 2018/6/1

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AB - 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.

KW - Cauchy’s infinitesimal

KW - Foundational paradigms

KW - Quantifier alternation

KW - Sum theorem

KW - Uniform convergence

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

Abstract

Keywords

ASJC Scopus subject areas

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