Abstract
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.
Citation
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