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Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. / Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre et al.

In: Foundations of Science, Vol. 23, No. 2, 01.06.2018, p. 267-296.

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

Harvard

Bascelli, T, Błaszczyk, P, Borovik, A, Kanovei, V, Katz, KU, Katz, MG, Kutateladze, SS, McGaffey, T, Schaps, DM & Sherry, D 2018, 'Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms', Foundations of Science, vol. 23, no. 2, pp. 267-296. https://doi.org/10.1007/s10699-017-9534-y

APA

Bascelli, T., Błaszczyk, P., Borovik, A., Kanovei, V., Katz, K. U., Katz, M. G., Kutateladze, S. S., McGaffey, T., Schaps, D. M., & Sherry, D. (2018). Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. Foundations of Science, 23(2), 267-296. https://doi.org/10.1007/s10699-017-9534-y

Vancouver

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. 2018 Jun 1;23(2):267-296. doi: 10.1007/s10699-017-9534-y

Author

Bascelli, Tiziana ; Błaszczyk, Piotr ; Borovik, Alexandre et al. / Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. In: Foundations of Science. 2018 ; Vol. 23, No. 2. pp. 267-296.

BibTeX

@article{b5dea339ec804b6a9dcdb1b154561f8a,
title = "Cauchy{\textquoteright}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{\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, DEFINITION, Cauchy's infinitesimal, DIFFERENTIALS, EPSILON",
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",
note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media B.V.",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s10699-017-9534-y",
language = "English",
volume = "23",
pages = "267--296",
journal = "Foundations of Science",
issn = "1233-1821",
publisher = "Springer Netherlands",
number = "2",

}

RIS

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

N1 - Funding Information: 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. Publisher Copyright: © 2017, Springer Science+Business Media B.V.

PY - 2018/6/1

Y1 - 2018/6/1

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

KW - DEFINITION

KW - Cauchy's infinitesimal

KW - DIFFERENTIALS

KW - EPSILON

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

U2 - 10.1007/s10699-017-9534-y

DO - 10.1007/s10699-017-9534-y

M3 - Article

AN - SCOPUS:85021226787

VL - 23

SP - 267

EP - 296

JO - Foundations of Science

JF - Foundations of Science

SN - 1233-1821

IS - 2

ER -

ID: 9048993