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

Foundations of Science 23 (2):267-296 (2018)

Authors
Alexandre Borovik
University of Manchester
David Sherry
Northern Arizona University
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.
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DOI 10.1007/s10699-017-9534-y
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
Ontological Relativity.W. V. Quine - 1968 - Journal of Philosophy 65 (7):185-212.

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