Blaise and Bayes

Pascal presents at least three 'wagers' for believing in God. Hacking provides three reconstructions of them using the apparatus of Bayesian decision theory - dominance reasoning and calculations of expected utilities - contending that each is valid. The argument of this chapter is that each is invalid. The chapter canvases McLennen's reconstruction of the first wager as an argument from 'superdominance', it then shows how it can be strengthened in two respects that are faithful to Pascal's original text; yet the resulting argument is still invalid. The chapter then turns to the second and especially the third wagers, offering two new ways of reformulating them with valid arguments. In the process new decision rules for comparing acts of infinite and indeterminate expected utility are suggested and defended.