Article ID: CBB672281990

Hermann Cohen’s Principle of the Infinitesimal Method: A Defense (2020)

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In Bertrand Russell’s 1903 The Principles of Mathematics, he offers an apparently devastating criticism of The Principle of the Infinitesimal Method and Its History (PIM) by the neo-Kantian Hermann Cohen. Russell’s criticism is motivated by a concern that Cohen’s account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum and thus threatens the idea of mathematical truth. This article defends Cohen against Russell’s objection and argues that, properly understood, Cohen’s views of limits and infinitesimals do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the article, of Cohen’s positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen’s views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals elements of what is at stake, both historically and philosophically, in Russell’s criticism of Cohen.

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Authors & Contributors
Katz, Mikhail G.
McCoy, C. D.
Vrhovski, Jan
Bair, Jacques
Marcelo E. Coniglio
Ely, Robert
Concepts
Philosophy of mathematics
Infinitesimals
Mathematics
Calculus
Logic
Geometry
Time Periods
20th century, early
19th century
17th century
20th century, late
21st century
20th century
Places
Germany
China
Great Britain
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