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The Borel-Kolmogorov Paradox Is Your Paradox Too: A Puzzle for Conditional Physical Probability

Published online by Cambridge University Press:  01 January 2022

Alexander Meehan  and
Snow Zhang
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Abstract

The Borel-Kolmogorov paradox is often presented as an obscure problem that certain mathematical accounts of conditional probability must face. In this article, we point out that the paradox arises in the physical sciences, for physical probability or chance. By carefully formulating the paradox in this setting, we show that it is a puzzle for everyone, regardless of one’s preferred probability formalism. We propose a treatment that is inspired by the approach that scientists took when confronted with these cases.

Type
Decision Theory and Formal Epistemology
Information
Philosophy of Science , Volume 88 , Issue 5 , December 2021 , pp. 971 - 984
Copyright
Copyright 2021 by the Philosophy of Science Association. All rights reserved.

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Footnotes

†

We are grateful to Jacob Barandes, David Builes, Eliya Cohen, Kenny Easwaran, Adam Elga, Hans Halvorson, Michele Odisseas Impagnatiello, Jim Joyce, Boris Kment, Kyle Landrum, Sarah McGrath, Chris Register, Laura Ruetsche, Alejandro Naranjo Sandoval, Haley Schilling, and audiences at the Harvard Foundations of Physics Series and Princeton and MIT for their very helpful feedback and advice. The title of this article is inspired by the similar title “The Reference Class Problem Is Your Problem Too” by Alan Hájek (2007).

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