A probability distribution is regular if it does not assign probability zero to any possible event. Williamson argued that we should not require probabilities to be regular, for if we do, certain “isomorphic” physical events must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub 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 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. (shrink)

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)