Infinite Lotteries, Spinners, Applicability of Hyperreals

Emanuele Bottazzi, Mikhail G. Katz

Research output: Contribution to journalReview articlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)88-109
Number of pages22
JournalPhilosophia Mathematica
Volume29
Issue number1
DOIs
StatePublished - 1 Feb 2021

Bibliographical note

Publisher Copyright:
© 2020 The Authors [2020]. Published by Oxford University Press. All rights reserved.

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