According to Stalnaker’s Thesis (S), the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: 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 conditionalisation. 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 conditionalisation 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’.

中文翻译：

---

Lewis 对准概率的平凡性

根据 Stalnaker 的论文 (S)，条件的概率是条件概率。在一些温和的条件下，该论文将概率和条件变得无关紧要，正如大卫·刘易斯最初所展示的那样。本文提出以下问题：如果将（S）中的概率函数替换为类概率函数，（S）是否仍然导致平凡？文章考虑了 Friedman 和 Halpern 意义上的似真函数，它另外模拟了概率可加性和条件化。这些准概率包括 Friedman-Halpern 的条件似真空间，以及条件 doxastic 状态的其他已知表示。该论文证明了刘易斯对准概率的平凡性，并讨论了这对避免刘易斯的平凡性的其他三个突出策略有何影响：(1) Adams 的论文，其中 (S) 左边的概率函数被一个类概率函数代替， (2) 放弃条件化，其中 (S) 右边的概率条件化被另一个命题更新程序取代(3) 近似命题，其中 (S) 中的等式被近似替换。该论文还表明，刘易斯的平凡结果实际上是关于“可加性”和“条件性”的。