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In a well-known paper (2007), Tim Williamson claimed to show with a simple coin-tossing example that allowing hyperreal probabilities cannot save the principle of Regularity. A crucial step of Williamson's proof is that an equiprobability assignment to two infinitary events, one of which is a truncated version of the other, is justified by their isomorphism. But Howson (2017) argued that this step cannot be established because, he claimed, those events are not in fact isomorphic. There is a mapping from events to events which sends event-coordinates to their successors and which is provably measure-preserving. However, it is shown that even appealing to this similarity relation fails to salvage Wiliamson's argument.
