Foundations of Science 22 (1):125-140 (2017)

Foundations of Science recently published a rebuttal to a portion of our essay it published 2 years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy’s use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy’s mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno’s flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz.
Keywords Archimedean axiom  Cauchy  Felix Klein  Horn-angle  Infinitesimal  Leibniz  Ontology  Procedure
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DOI 10.1007/s10699-015-9473-4
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Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1983 - British Journal for the Philosophy of Science 34 (1):57-70.

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