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Beyond finite additivity

Published online by Cambridge University Press:  02 August 2024

Colin Howson
Colin Howson*
Affiliation:
Professor of Philosophy at the University of Toronto
*
Corresponding author: Peter Urbach; Email: [email protected]
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Abstract

There is a Dutch Book argument for the axiom of countable additivity for subjective probability functions, but de Finetti famously rejected the axiom, arguing that it wrongly renders a uniform distribution impermissible over a countably infinite lottery. Dubins however showed that rejecting countable additivity has a strongly paradoxical consequence that a much weaker rule than countable additivity blocks. I argue that this rule, which also prohibits the de Finetti lottery, has powerful independent support in a desirable closure principle. I leave it as an open question whether countable additivity should be adopted.

Type
Article
Information
Philosophy of Science , Volume 91 , Issue 3 , July 2024 , pp. 533 - 542
Copyright
© The Estate of Colin Howson and the Author(s), 2024. Published by Cambridge University Press on behalf of the Philosophy of Science Association

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Footnotes

This article was written by Colin Howson and submitted to the journal before his death. Peter Urbach graciously agreed to review and assist in the final publication of this article, and to serve as corresponding author during these final stages.

†

Deceased

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