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Pascal’s Wager Lecture

Pascal’s Wager.

Blaise Pascal (1623-1662).  French mystic and mathematician.  After work on conditional probability decided to avoid gambling.  Moved on to other questions: is it rational (logos) to believe in the existence of God.

The way Pascal reasons becomes influential not only among philosophers of religion but also as the founder of the modern theory of expected value/probabilistic decision theory.


I. Beliefs: Evidence vs. prudence.

The case of the briefcase:

I have briefcase with $1million dollars.  Another briefcase with loaded machine gun.  To Leo I say “I know you have no evidence that President Obama is juggling candy bars at this very moment.  Nevertheless, I want you to get your yourself to believe that’s true (with conviction).  You can use any psychological means possible (brainwashing, hypnosis, little colored pills, whatever).  Here’s the deal: if you succeed then I’ll give you $1million.  Otherwise, I use my machine gun.”

Leo’s situation: he has no evidence that President Obama is juggling candy bars at this very moment.  Nevertheless he has GOOD REASON to believe it.  That good reason is not evidential (obviously) but “prudential” (because he values money and his life).

Pascal’s question: even if we have no evidence that God exists do we have other reasons to determine whether we should believe?  Answer, yes, prudential reasons…

II. There sometimes reasons to bet even when the outcome is improbable.

Motivation: Pascal believes there is very little evidence that God actually exists.  Nonetheless, is it reasonable to believe in his existence?

Answer: yes, when the payoff is big enough.

The case of the gambling game.

Sheng finds $1 on the floor.  Decides to play a game that Jenny devised.

Game: pay $1 to play.  If you draw ace of spades, you get $1mill.  If you do not, you lose $1.
Odds of winning are small, 1/52.  Should Sheng still play?  Yes, of course.   How do we tell?

Expected Monetary value (p. 303-304).  (I’ll call it “expected utility” for this case)

= (the probability of winning) x (the net gain in utiles of winning) – (probability of losing) x (the net loss in utiles of losing)

Sheng’s case = 1/52 x $999,999 – 51/52 x $1 = $19,229

Question for later: how to interpret this result.

Pascal’s Wager (in sum): Asks, suppose I have little evidence that God exists.  Nevertheless do I have any “good reasons” to be believe that God exists?  Answer: yes.  a. I have prudential (as opposed to evidential reasons.  b. payoff is so big.

Pascal’s wager:

The pay-off heavily favors believing in God because the reward is so good and the punishment so bad.

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