Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts

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• 作者：Piotr Błaszczyk ; Vladimir Kanovei ; Mikhail G. Katz ; David Sherry
• 关键词：Archimedean axiom ; Cauchy ; Felix Klein ; Horn ; angle ; Infinitesimal ; Leibniz ; Ontology ; Procedure
• 刊名：Foundations of Science
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：22
• 期：1
• 页码：125-140
• 全文大小：
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Philosophy of Science; Methodology of the Social Sciences; Mathematical Logic and Foundations;
• 出版者：Springer Netherlands
• ISSN：1572-8471
• 卷排序：22

文摘

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.