Timothy Williamson’s coin-flipping argument: refuted prior to publication

In a well-known paper, Timothy Williamson (Analysis 67:173–180, 2007) claimed to prove with a coin-flipping example that infinitesimal-valued probabilities cannot save the principle of Regularity, because on pain of inconsistency the event ‘all tosses land heads’ must be assigned probability 0, whether the probability function is hyperreal-valued or not. A premise of Williamson’s argument is that two infinitary events in that example must be assigned the same probability because they are isomorphic. It was argued by Howson (Eur J Philos Sci 7:97–100, 2017) that the claim of isomorphism fails, but a more radical objection to Williamson’s argument is that it had been, in effect, refuted long before it was published.