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

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...

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Bibliographic Details
Published in:Foundations of science 2018-06, Vol.23 (2), p.267-296
Main Authors: Bascelli, Tiziana, Błaszczyk, Piotr, Borovik, Alexandre, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kutateladze, Semen S., McGaffey, Thomas, Schaps, David M., Sherry, David
Format: Article
Language:English
Subjects:
Basic converters
Education
Epistemology
Mathematical Logic and Foundations
Mathematical research
Methodology of the Social Sciences
Philosophy
Philosophy of Science
Theorems
Theorems (Mathematics)
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Summary: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.
ISSN:1233-1821
1572-8471
DOI:10.1007/s10699-017-9534-y