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August 2019 Conditionals and Conditional Probabilities without Triviality
Alexander R. Pruss
Notre Dame J. Formal Logic 60(3): 551-558 (August 2019). DOI: 10.1215/00294527-2019-0019

Abstract

The Adams Thesis holds for a conditional and a probability assignment P if and only if P(AB)=P(BA) whenever P(A)>0. The restriction ensures that P(BA) is well defined by the classical formula P(BA)=P(BA)/P(A). Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results (Lewis, etc.), any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on how far triviality results can go.

Citation

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Alexander R. Pruss. "Conditionals and Conditional Probabilities without Triviality." Notre Dame J. Formal Logic 60 (3) 551 - 558, August 2019. https://doi.org/10.1215/00294527-2019-0019

Information

Received: 3 August 2016; Accepted: 8 December 2017; Published: August 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07120755
MathSciNet: MR3985626
Digital Object Identifier: 10.1215/00294527-2019-0019

Subjects:
Primary: 60A10
Secondary: 60A99

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 3 • August 2019
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