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Probability, Regularity, and Cardinality

Published online by Cambridge University Press:  01 January 2022

Alexander R. Pruss
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Abstract

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 2 , April 2013 , pp. 231 - 240
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I would like to thank Trent Dougherty, Alan Hájek, Jonathan Kvanvig, and A. Paul Pedersen for discussions, comments, and encouragement and the anonymous readers for feedback that led to significant improvement of this article.

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