Maudlin, Tim (2020) Credence—and Chance—Without Numbers (and with the Euclidean Property). [Preprint]

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Abstract

Accounts of both rational credence and of objective chance have always confronted difficulties associated with events that are assigned “probability zero” by the usual Kolmogorov probability function used to model the situation. One sort of solution recommends extending the number field used to represent credences and chance to the surreals or hyperreals. But the correct solution—the solution that always respects the Euclidean property—is to eliminate numbers from the fundamental representation of credence and chance altogether in favor of a system of relations. This solution also sheds light on other paradoxes, such as the Banach-Tarski paradox and the St. Petersburg paradox.

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Item Type:	Preprint
Creators:	Creators Email ORCID Maudlin, Tim timmaudlin@JohnBellInstitute.org 0000-0001-8394-7264
Keywords:	objective chance, credence, Euclidean property, regularity, St. Petersburg paradox, Banach-Tarski paradox
Subjects:	Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Probability/Statistics
Depositing User:	Prof. Tim Maudlin
Date Deposited:	11 Nov 2020 05:07
Last Modified:	11 Nov 2020 05:07
Item ID:	18382
Subjects:	Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Probability/Statistics
Date:	10 November 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/18382

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