Tuesday, August 16, 2011

The Dominance Form of Pascal's Wager

Blaise Pascal was a 17th Century French philosopher, mathematician and physicist.  He was also a Christian.  At the time of his death, he was working on a treatise on Christian apologetics, but he had only gotten so far as to compile a series of notes.  Still, these notes were published posthumously as his Pensees.  Note 233 contained his famous wager:
But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. It is all divided; wherever the infinite is and there is not an infinity of chances of loss against that of gain, there is no time to hesitate, you must give all...

There has been disagreement among philosophers as to how to properly interpret Pascal’s comments.  Ian Hacking, Professor of Philosophy at the University of Toronto, suggests that Pascal was making an argument from “dominance.” [1]  According to Hacking, Pascal proposes a dichotomy between the potential effects of wagering on God’s existence versus wagering against it.  If God does not exist, then neither belief nor unbelief bears any potential bad effects.  However, if God exists then wagering for him brings salvation whereas wagering against him entails damnation.  Because salvation is certainly superior to damnation, people should wager on God’s existence.  The “wager ‘God is’ dominates the wager ‘he is not.’”[2]
However, if this is indeed what Pascal meant, then he smuggles in some hidden assumptions.  “Belief in God,” for example, does not by definition entail salvation nor does unbelief by definition bring about damnation.  Mere belief in a “god,” without more, does not logically mandate salvation.  It is only because of the connection between belief and salvation borne through Christian theology that Pascal draws this conclusion.  The dominance form of the wager, therefore, is really contrasting “belief in the Christian God” versus “no God.”  Seen this way there are clearly other alternatives, such as the Islamic “Allah” or any god from the Hindu pantheon.  Thus, the wager does not exhaust all possibilities.
Rephrasing the wager as “belief in the Christian God” versus “not believing in the Christian God” would at least exhaust all logical possibilities (the latter category encompassing both atheism and other divine beliefs), but the “Christian God” side of the wager no longer clearly dominates (based solely upon potential effects).  For example, the Islamic “Allah” is now on the opposite side of the equation from the Christian “Yahweh.”  Which side of wager dominates now clearly appears to depend upon which of these two alternatives is factually true, as both carry damnation for non-believers if they are correct.
 Despite these deficiencies, the dominance form of the wager may still hold value to certain people depending on the options being explored.  Ultimately, this formulation of the wager is an existential argument.  It does not claim to prove the truth or falsehood of either alternative.  It simply illustrates the existential benefits of belief in the Christian God versus the acceptance of atheism.  If a person is examining only those two alternatives (because they have already discarded other worldviews), then the wager can have some efficacy in illustrating the dominance of the potential effects inherent in theism over those of atheism.

[1] Ian Hacking, “The Logic of Pascal’s Wager” in Philosophy of Religion: A Reader and Guide, ed. William Lane Craig (New Brunswick, NJ: Rutgers University Press, 2002), 17-24.
[2] Ian Hacking, “The Logic of Pascal’s Wager,” 21.

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