Weintraub's Response to Williamson's Coin Flip Argument

A probability distribution is regular if it does not assign probability zero to any possible event. Williamson (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 (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 (2011) 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