A probability distribution is regular if it does not assign probability zero to any possible event. Williamson (Analysis, 67, 173–180, 2007) argued that we should not require probabilities to be regular, for if we do, certain “isomorphic” physical events (infinite sequences of coin flip outcomes) must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub (Analysis, 68, 247–250, 2008) responds that Williamson’s coin flip events differ in their inclusion relations to each other, or the inclusion relations between their times, and this can account for their differences in probability. Haverkamp and Schulz (Erkenntnis, 76, 395–402, 2012) rebut Weintraub, but their rebuttal fails because the events in their example are even less symmetric than Williamson’s. However, Weintraub’s argument also fails, for it ignores the distinction between intrinsic, qualitative differences and relations of time and bare identity. Weintraub could rescue her argument by claiming that the events differ in duration, under a non-standard and problematic conception of duration. However, we can modify Williamson’s example with Special Relativity so that there is no absolute inclusion relation between the times, and neither event has longer duration except relative to certain reference frames. Hence, Weintraub’s responses do not apply unless chance is observer-relative, which is also problematic. Finally, another symmetry argument defeats even the appeal to frame-dependent durations, for there the events have the same finite duration and are entirely disjoint, as are their respective times and places.

如果概率分布不为任何可能的事件分配概率为零，则该概率分布是规则的。Williamson ( Analysis, 67 , 173–180, 2007) 认为我们不应该要求概率是规则的，因为如果我们这样做，某些“同构”物理事件（硬币翻转结果的无限序列）必须具有不同的概率，这是难以置信的. 他的言论暗示了一个假设，即机会是由内在的、定性的环境决定的。Weintraub ( Analysis, 68 , 247–250, 2008) 回应说，威廉姆森抛硬币事件之间的包含关系不同，或者时间之间的包含关系不同，这可以解释它们的概率差异。哈夫坎普和舒尔茨 ( Erkenntnis, 76, 395–402, 2012) 反驳温特劳布，但他们的反驳失败了，因为他们例子中的事件比威廉姆森的更不对称。然而，温特劳布的论点也失败了，因为它忽略了内在的、质的差异以及时间关系和赤裸裸的身份之间的区别。Weintraub 可以通过声称事件在持续时间不同，在非标准和有问题的持续时间概念下来挽救她的论点。然而，我们可以用狭义相对论修改威廉姆森的例子，这样时间之间没有绝对的包含关系，除了相对于某些参考系外，两个事件都没有更长的持续时间。因此，除非机会是相对于观察者的，否则温特劳布的回答不适用，这也是有问题的。最后，另一个对称性论证甚至击败了对依赖于框架的持续时间的诉求，