Conditions for probabilities of conditionals to be conditional probabilities
Conditions for probabilities of conditionals to be conditional probabilities
复制标题
条件概率成为条件概率的条件
作者：
W. Rehder
斯托纳克的命题指出，一个条件的概率等于一个条件的概率。乍一看，这句话听起来像是一个无害的双关语：“如果我扔出一个偶数，扔出一个6的概率是多少？如果我扔出一个偶数，扔出一个6的概率是多少？”他接着讨论了大卫·刘易斯（David Lewis）令人惊讶的证明，他的论点是错误的或微不足道的：假设这个论点，刘易斯（Lewis）表明，不可能有超过四个不同的值。在续集中，van Fraassen重新提出了斯塔纳克的论点，理由不在这里讨论。取而代之，我们将给出斯托纳克命题的充分必要条件，条件是：（A .1）给定事件A得到，事件“/3”的条件概率i定义为
Stalnaker 's Thesis states that a conditional probabil i ty is the same as the probabil i ty of a conditional. At first sight, this s ta tement sounds like a harmless pun: "Wha t is the probabil i ty that I throw a six if I throw an even number , if not the probabil i ty that: if I throw an even number , it will be a six?" in van Fraassen ' s suggestive phrasing [7]. He goes on to discuss David Lewis ' s surprising demonstra t ion [3] that the thesis is wrong or trivial: assuming the Thesis, Lewis showed that no probabil i ty ass ignment can have more than four distinct values. In the sequel, van Fraassen revives Sta lnaker ' s Thesis on grounds which will not be discussed here. We shall instead give necessary and sufficient conditions for the Stalnaker thesis provided that: (a.1) the conditional probabil i ty of an event "/3, given that the event A obtains, is defined by