Notre Dame Journal of Formal Logic

Conditionals and Conditional Probabilities without Triviality

Alexander R. Pruss

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 551-558.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1562205627

Digital Object Identifier
doi:10.1215/00294527-2019-0019

Mathematical Reviews number (MathSciNet)
MR3985626

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
Secondary: 60A99: None of the above, but in this section

Keywords
conditionals probability measure theory measure algebra conditional probability

Citation

Pruss, Alexander R. Conditionals and Conditional Probabilities without Triviality. Notre Dame J. Formal Logic 60 (2019), no. 3, 551--558. doi:10.1215/00294527-2019-0019. https://projecteuclid.org/euclid.ndjfl/1562205627


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