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 Citations (Scopus)

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

Fingerprint

Paradigm
Epistemological
Prototype
Undergraduate

Keywords

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

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

Cite this

Bascelli, T., Błaszczyk, P., Borovik, A., Kanovei, V., Katz, K. U., Katz, M. G., ... 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

Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. / Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David M.

In: Foundations of Science, 24.06.2017, p. 1-30.

Research output: Contribution to journalArticle

Bascelli, T, Błaszczyk, P, Borovik, A, Kanovei, V, Katz, KU, Katz, MG, Kutateladze, SS, McGaffey, T, Schaps, DM & Sherry, DM 2017, 'Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms', Foundations of Science, pp. 1-30. https://doi.org/10.1007/s10699-017-9534-y
Bascelli T, Błaszczyk P, Borovik A, Kanovei V, Katz KU, Katz MG et al. Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. Foundations of Science. 2017 Jun 24;1-30. https://doi.org/10.1007/s10699-017-9534-y
Bascelli, Tiziana ; Błaszczyk, Piotr ; Borovik, Alexandre ; Kanovei, Vladimir ; Katz, Karin U. ; Katz, Mikhail G. ; Kutateladze, Semen S. ; McGaffey, Thomas ; Schaps, David M. ; Sherry, David M. / Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. In: Foundations of Science. 2017 ; pp. 1-30.
@article{6156fc3c98f6457795e0f0f8f6c67ade,
title = "Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms",
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.",
keywords = "Cauchy’s infinitesimal, Foundational paradigms, Quantifier alternation, Sum theorem, Uniform convergence",
author = "Tiziana Bascelli and Piotr Błaszczyk 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 Sherry, {David M}",
year = "2017",
month = "6",
day = "24",
doi = "10.1007/s10699-017-9534-y",
language = "English (US)",
pages = "1--30",
journal = "Foundations of Science",
issn = "1233-1821",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms

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 M

PY - 2017/6/24

Y1 - 2017/6/24

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

UR - http://www.scopus.com/inward/record.url?scp=85021226787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021226787&partnerID=8YFLogxK

U2 - 10.1007/s10699-017-9534-y

DO - 10.1007/s10699-017-9534-y

M3 - Article

SP - 1

EP - 30

JO - Foundations of Science

JF - Foundations of Science

SN - 1233-1821

ER -