Lecture 4 – Pascal’s Wager
22 Sept./05

Blaise Pascal (1623-62)
•	a famous mathematician by age 16 (cone geometry – Pascal’s theorem)
•	pioneer of probability theory and decision theory
•	Pascal’s method of infinitesimal analysis credited by Leibniz as inspiration for his own calculus
•	also achieved scientific fame for work on hydrostatics, and barometric experiments concerning the possibility of a vacuum
•	Pensées, 1670, fragments published posthumously
•	an influence on (Christian) existentialism
•	undermines possibility of demonstrative proof of God’s existence; so the question is – given that we can never be certain of God’s existence, ought we to believe in Him or not?
•	“If we must not act save on a certainty, we ought not to act on religion, for it is not certain.  But how many things we do on an uncertainty, sea voyages, battles!  I say then we must do nothing at all, for nothing is certain…” (52).  

The Wager
•	“A game is being played at the extremity of this infinite distance [between us and certain knowledge of God’s existence] where heads or tails will turn up.  What will you wager?” 
•	choice of rational action based on “expected value” – this value arrived at by “(1) assigning a value, s, to each possible outcome of the action, (2) subtracting the cost of the action, c, from this value, and (3) multiplying the difference by the probability of the respective outcomes and adding these products together” (Excerpted from “Blaise Pascal” in The Cambridge Dictionary of Philosophy, 2nd ed.  Robert Audi, Ed.  Cambridge:  Cambridge UP (1999), 649.
•	Or, P1(S1 - C1) + P2(S2 - C2) > 0  the wager is worth the risk
•	To put it another way:

	God exists	God doesn’t exist	
Believe
(Small cost)	HUGE win	small loss	
Don’t believe
(No cost)	HUGE loss	small win	

•	“If you gain, you gain all; if you lose, you lose nothing.”
•	“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.”
•	“I confess it, I admit it.  But, still, is there no means of seeing the faces of the cards?”   Yes, Scripture and the rest, etc.  “Yes, but I have my hands tied and my mouth closed; I am forced to wager, and am not free.  I am not released, and am so made that I cannot believe. What, then, would you have me do?”
	True.  But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe.  Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions.  You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it.  Learn of those who have been bound like you, and who now stake all their possessions.…  Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc.  Even this will naturally make you believe, and deaden your acuteness. 

•	“‘I would soon have renounced pleasure,’ say they, ‘had I faith.’  For my part I tell you, ‘You would soon have faith, if you renounced pleasure.’”

Problems with the wager
•	William James criticized it on the grounds that it is unable to dictate a decision for one faced with two religions, both offering infinite rewards.  However, elsewhere in the Pensées, Pascal goes to great length to show that Christianity, of all religions, offers superior explanatory power.  Therefore, he construed the choice as between Christianity and unbelief, not Christianity and (for instance) Islam.
•	Contemporary decision theory prohibits the introduction of infinite values because they skew the whole calculation, making even the slightest risk irrational (i.e., even if there is shown to be only a vanishingly small chance that God exists, according to Pascal, we still ought to belief that He does.).