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What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel
Journal of Humanistic Mathematics 8 (1):108 - 119 (2018)
Abstract
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.Author Profiles
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Citations of this work
Infinite Lotteries, Spinners, Applicability of Hyperreals†.Emanuele Bottazzi & Mikhail G. Katz - 2021 - Philosophia Mathematica 29 (1):88-109.
Mathematische Wissenschaftsphilosophie im Marburger Neukantianismus.Thomas Mormann - 2019 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 11:55 - 75.
Dimitry Gawronsky: Reality and Actual Infinitesimals.Hernán Pringe - 2023 - Kant Studien 114 (1):68-97.
References found in this work
Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
Infinitesimals as an issue of neo-Kantian philosophy of science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
Toward a History of Mathematics Focused on Procedures.Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze & David Sherry - 2017 - Foundations of Science 22 (4):763-783.
Abraham Robinson. Non-standard analysis. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, vol. 64 (1961), pp. 432–440; also Indagationes mathematicae, vol. 23 (1961), pp. 432-440. - Abraham Robinson. Topics in non-Archimedean mathematics. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, edited by J. W. Addison, Leon Henkin, and Alfred Tarski, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 285–298. - Abraham Robinson. On generalized limits and linear functionals. Pacific journal of mathematics, vol. 14 (1964), pp. 269–283. - Alan R. Bernstein and Abraham Robinson. Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos.Pacific journal of mathematics, vol. 16 (1966), pp. 421–431. - Abraham Robinson. Non-standard analysis.Studies in logic and the foundations of mathematics. North-Holland Publishing Company, Amsterdam1966, xi + 293 pp. [REVIEW]Gert Heinz Müller - 1969 - Journal of Symbolic Logic 34 (2):292-294.
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