A person can have good practical reasons for believing in God even if he is convinced that he does not have good intellectual reasons for doing so. Whether a person does have good practical reasons for believing in God depends on his probabilities and values for consequences of that believing, in which probabilities and values persons can vary. Pascalian wagers founded on a variety of possible probability/value profiles will be examined from a Bayesian perspective central to which is the idea that states and options are pragmatically reasonable only if they maximize subjective expected value. Attention will be paid to problems posed by infinite values. Part One explains the distinction between intellectual and practical reasons, and presents Pascal's Wager as cast by William James. Part Two comments on characteristics of belief options in Pascalian wagers to be studied. Part Three contains discussions of several wagers. It explores the variety of probabilities and values that can be brought to the betting table, and sets out wagers determined thereby as problems in Bayesian decision theory. A series of notes and an appendix bring to our subject a theory of ‘hyperreal’ numbers.

GROUNDS FOR BELIEFS

1 Theoretical and practical reasons. What is the proper response of a person who is convinced that there are no good arguments for or against the existence of God, that on balance his evidence and experience testify sufficiently neither way, and that he cannot decide the issue of God's existence on intellectual grounds?