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  1. Infinite Lotteries, Spinners, Applicability of Hyperreals†.Emanuele Bottazzi & Mikhail G. Katz - 2021 - Philosophia Mathematica 29 (1):88-109.
    We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei–Shelah model or in saturated models. We argue that some of the objections to hyperreal probabilities arise from hidden biases that favor Archimedean models. We discuss the advantage of the hyperreals over transferless fields with infinitesimals. In Paper II we analyze two underdetermination theorems by Pruss and (...)
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  • (2 other versions)Mathematische Wissenschaftsphilosophie im Marburger Neukantianismus.Thomas Mormann - 2019 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 11:55 - 75.
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  • Dimitry Gawronsky: Reality and Actual Infinitesimals.Hernán Pringe - 2023 - Kant Studien 114 (1):68-97.
    The aim of this paper is to analyze Dimitry Gawronsky’s doctrine of actual infinitesimals. I examine the peculiar connection that his critical idealism establishes between transcendental philosophy and mathematics. In particular, I reconstruct the relationship between Gawronsky’s differentials, Cantor’s transfinite numbers, Veronese’s trans-Archimedean numbers and Robinson’s hyperreal numbers. I argue that by means of his doctrine of actual infinitesimals, Gawronsky aims to provide an interpretation of calculus that eliminates any alleged given element in knowledge.
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