> The mugger argues back that for any low but strictly greater than 0 probability of being able to pay back a large amount of money (or pure utility) there exists a finite amount that makes it rational to take the bet.
This is a basic logic error. It ignores the very obvious fact that increasing the reward amount decreases the probability that it will be returned.
E.g. if the probability of the reward R being returned is (0.5/R) we get "a low by strictly greater than 0 probability", and for that probability there is a (different) finite reward that would make it rational to take the bet, but it's not R.
This is even simpler and more stupid than the "proofs" that 0=1. It does not change my opinion that philosophers (and lesswrong) are idiots.