4.While it may be better to understand the acts as bringing about belief, and remaining
within nonbelief, for convenience, I will formulate the acts as simply Believe and
(Believe).
5.The expression X >> Y should be understood as X greatly exceeds Y.
6.Clearly enough, the acts in this case have no propensity to bring about the states.
7.While objective probabilities are standardly used in calculating expected utility,
subjective (or epistemic, or personalist) probabilities can be employed as well. The wager
can accommodate either objective probability assignments or subjective ones.
8.By “nonstandard deity” I mean the gerrymandered fictions of philosophers. See, for
instance, Saka (2001, 321–41).
9.Even though it is possible to imagine any number of deviant gods, any extension
beyond a 3 x 3 matrix is logically redundant given that F2 exceeds the “this world”
outcomes of the deviant deities, and given that the best cases and worse cases are on a
par.
10.For additional detail on James, consult Bird (1986, 161–81).
11.See Wainwright (1995, 84–107).
12.I do not suggest that this brief argument is an adequate summary of Gale's detailed
objection to James.
13.Proposition (J) is modeled on a proposition discussed by Mills (1998, 34–35).
WORKS CITED
Bird, Graham. 1986. William James. London. Routledge and Kegan Paul.
Clifford, W. K. 1879. Lectures and Essays. Vol. 2. London: Macmillan.
Gale, Richard. 1991. On the Nature and Existence of God. Cambridge, England:
Cambridge University Press.
Hacking, Ian. 1972. “The Logic of Pascal's Wager.” American Philosophical Quarterly 9:
186–92.
Hick, John. 1990. Philosophy of Religion. 4th ed. Englewood Cliffs, N.J.: Prentice Hall.
James, William. 1956. “The Will to Believe.” In The Will to Believe and Other Essays in
Popular Philosophy. New York: Dover.
Macrae, Norman. 1992. John von Neumann. New York: Pantheon.
Martin, Michael. 1990. Atheism: A Philosophical Justification. Philadelphia: Temple
University Press.
Mills, Eugene. 1998. “The Unity of Justification.” Philosophy and Phenomenological
Research 58: 27–50.