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

^*Corresponding author for this work

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

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)	1-30
Number of pages	30
Journal	Foundations of Science
Early online date	24 Jun 2017
DOIs	https://doi.org/10.1007/s10699-017-9534-y
Publication status	Published - 2017

Keywords

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

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10.1007/s10699-017-9534-y

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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.",

keywords = "Cauchy{\textquoteright}s infinitesimal, Foundational paradigms, Quantifier alternation, Sum theorem, Uniform convergence",

author = "Tiziana Bascelli and Piotr B{\l}aszczyk and Alexandre Borovik and Vladimir Kanovei and Katz, {Karin U.} and Katz, {Mikhail G.} and Kutateladze, {Semen S.} and Thomas McGaffey and Schaps, {David M.} and David Sherry",

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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 - 2017

Y1 - 2017

N2 - 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.

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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SN - 1233-1821

SP - 1

EP - 30

JO - Foundations of Science

JF - Foundations of Science

ER -

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

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Keywords

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