Foundations of Science

, Volume 22, Issue 1, pp 125–140 | Cite as

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

  • Piotr Błaszczyk
  • Vladimir Kanovei
  • Mikhail G. KatzEmail author
  • David Sherry


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.


Archimedean axiom Cauchy Felix Klein Horn-angle Infinitesimal Leibniz Ontology Procedure 



The work of V. Kanovei was partially supported by RFBR Grant 13-01-00006. M. Katz was partially funded by the Israel Science Foundation Grant No. 1517/12. We are grateful to the anonymous referees and to A. Alexander, R. Ely, and S. Kutateladze for their helpful comments. The influence of Hilton Kramer (1928–2012) is obvious.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Piotr Błaszczyk
    • 1
  • Vladimir Kanovei
    • 2
    • 3
  • Mikhail G. Katz
    • 4
    Email author
  • David Sherry
    • 5
  1. 1.Institute of MathematicsPedagogical University of CracowCracowPoland
  2. 2.IPPIMoscowRussia
  3. 3.MIITMoscowRussia
  4. 4.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  5. 5.Department of PhilosophyNorthern Arizona UniversityFlagstaffUSA

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