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Infinitesimals as an Issue of Neo-Kantian Philosophy of Science

Thomas Mormann and Mikhail Katz
HOPOS: The Journal of the International Society for the History of Philosophy of Science
Vol. 3, No. 2 (Fall 2013), pp. 236-280
DOI: 10.1086/671348
Stable URL: http://www.jstor.org/stable/10.1086/671348
Page Count: 45
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Infinitesimals as an Issue of Neo-Kantian Philosophy of Science
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Abstract

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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