Article ID: CBB001320796

Infinitesimals as an Issue of Neo-Kantian Philosophy of Science (2013)

unapi

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely, the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position toward the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals nor Whiggishly subscribed to the new orthodoxy of the great triumvirate of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen's lead, the Marburg philosophers sought to clarify Leibniz's principle of continuity and to exploit it in making sense of infinitesimals and related concepts.

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Authors & Contributors
Edgar, Scott
McCoy, C. D.
Augusto J. Franco Oliveira
Simon Truwant
Eduardo Noble
Davide Gullotto
Concepts
Infinitesimals
Mathematical analysis
Mathematics
Calculus
Philosophy of science
Philosophy of mathematics
Time Periods
20th century, early
19th century
18th century
20th century, late
20th century
17th century
Places
Germany
Spain
France
China
Berlin (Germany)
Great Britain
Institutions
Berlin Group (Philosophy)
Vienna Circle
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