Repelling a Prussian charge with a solution to a paradox of Dubins

Abstract

Pruss (Thought 1:81–89, 2012) uses an example of Lester Dubins to argue against the claim that appealing to hyperreal-valued probabilities saves probabilistic regularity from the objection that in continuum outcome-spaces and with standard probability functions all save countably many possibilities must be assigned probability 0. Dubins’s example seems to show that merely finitely additive standard probability functions allow reasoning to a foregone conclusion, and Pruss argues that hyperreal-valued probability functions are vulnerable to the same charge. However, Pruss’s argument relies on the rule of conditionalisation, but I show that in examples like Dubins’s involving nonconglomerable probabilities, conditionalisation is self-defeating.