Foundations of Science 20 (1):1-25 (2015)

The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history
Keywords Errett Bishop  Abraham Robinson  Infinitesimals  Hyperreals  Intuitionists  Petard
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DOI 10.1007/s10699-013-9340-0
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References found in this work BETA

Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge and London: Cambridge University Press.
Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
Intuitionism an Introduction.Arend Heyting - 1956 - Amsterdam, Netherlands: North-Holland.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.

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Citations of this work BETA

Leibniz Versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.

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