Journal of Logic, Language and Information (2019) 28:515–549 https://doi.org/10.1007/s10849-019-09289-0 Lewis’ Triviality for Quasi Probabilities Eric Raidl 1,2 Published online: 12 April 2019 © Springer Nature B.V. 2019 Abstract According to Stalnaker’s Thesis (S), the probability of a conditional is the condi- tional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following ques- tion: does (S) still lead to triviality, if the probability function in (S) is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and con- ditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: (1) Adams’ thesis, where the probability function on the left in (S) is replaced by a probability-like function, (2) abandoning conditionalisation, where probability condi- tionalisation on the right in (S) is replaced by another propositional update procedure and (3) the approximation thesis, where equality in (S) is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. Keywords Probability of a conditional · Conditional probability · Triviality · Plausibility measures · Conditional plausibility space · Stalnaker thesis · Adams’ thesis · Conditional valuation functions Funding for this research was provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Research Unit FOR 1614 and under Germany’s Excellence Strategy – EXC-Number 2064/1 – Project number 390727645. B Eric Raidl eric.3.raidl@uni-konstanz.de; eric.raidl@uni-tuebingen.de 1 Department of Philosophy, University of Konstanz, Postfach 9, 78457 Constance, Germany 2 Cluster of Excellence Machine Learning, University Tübingen, Maria-von-Linden Straße, 6, 72076 Tübingen, Germany 123