Philosophia Mathematica (forthcoming)

Abstract
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 show that they hinge upon parasitic external hyperreal-valued measures, whereas internal hyperfinite measures are not underdetermined.
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DOI 10.1093/philmat/nkaa032
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References found in this work BETA

Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.

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Citations of this work BETA

Weintraub’s Response to Williamson’s Coin Flip Argument.Matthew W. Parker - 2021 - European Journal for Philosophy of Science 11 (3):1-21.

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Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
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