Blaise and Bayes

"Pascal's Wager " is something of a misnomer. In a single paragraph of his Pensées, Blaise Pascal in fact presents three wagers—three arguments for believing, or for at least taking steps to believe, in God—as Hacking has observed in his paper "The Logic of Pascal's Wager " (1972). Hacking reconstructs them using the apparatus of Bayesian decision theory. He also makes a point of granting that each of these arguments is valid. While he questions Pascal's premises, he is emphatic that Pascal's conclusion really does follow from those premises in each case. I will contend here, equally emphatically, that all three arguments are invalid. Hacking portrays the first wager as an ―argument from dominance‖, although as we‘ll see, he is somewhat unclear about what that means. He contends that an argument from dominance is automatically valid: if there is a dominating act, then rationality requires it to be performed. I demur, showing that such an argument is invalid without a further assumption about the relevant conditional probabilities. McLennen characterizes the first wager with a stronger sense of dominance, which he calls ―superdominance‖. But I show that even superdominant acts in his sense need not be performed. He understates th