Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 3 (2019), 551-558.
Conditionals and Conditional Probabilities without Triviality
The Adams Thesis holds for a conditional and a probability assignment if and only if whenever . The restriction ensures that is well defined by the classical formula . 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.
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 551-558.
Received: 3 August 2016
Accepted: 8 December 2017
First available in Project Euclid: 4 July 2019
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Mathematical Reviews number (MathSciNet)
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