Lecture 6: Pascal's Wager

1.  Cognitive rationality and practical rationality

Generally we can distinguish cognitive rationality (what should I believe?) from practical rationality (what should I do?).  The answer to "what should I believe?" seems to be: proportion your belief to the available evidence.

    Given  that the evidence from design is ambiguous (would God really incorporate sickle cell anemia as worthy design feature?)  and that the argument from evil seems rather troubling, one would have to conclude on the basis of the evidence we have considered (and we have not considered it all—e.g. miracles or personal experiences) that the probability of God's existence seems low.

    However, if certain beliefs can be adopted at will, then those beliefs are like actions, and so can be assessed for their practical rationality as well as their cognitive rationality.  Sometimes we do think that a person should adopt a belief in the teeth of the evidence, simply because things could go better for them if they do.  ("You've got to believe you are going to get well even though 9 out of 10 people with your disease die within six months!  Believing you will get well is your only chance of survival.")
 

2. Probability and expectations: what is the rational thing to do under conditions of uncertainty?

    Sometimes we have to act when we are not certain what the outcome of our actions will be. When we are not certain we must take a weighted average of the values of the various possible outcomes of the action, where the weights are supplied by our own degrees of belief.  Suppose I'm rather thirsty and I think there is only one chance in ten that the liquid in the glass is s a lethal poison, and nine chances in ten that it is water, but I really really want to go on living after my next drink. Then it is clearly rational for me to forego the liquid, suffer my thirst.  The disvalue of dying - although fairly improbable (1/10) -  outweighs the value of probably quenching my thirst and living to tell the tale.  So it is rational for me to act   as though the glass contains the poison, even though I think it more likely that it doesn't.

The prize of belief if it tuns out God exists  is eternity in heaven.  This is infinitely valuable compared with the finite value of even the best possible finite life. What happens if I believe in God and he doesn't exist.  Well, I will have missed out on some of the benefits of the good life, but I will have led a life full of good (or so Pascal argues).  Whatever the trade-off here the life is either of finite value (or disvalue) compared with the infinite value of an infinity of blissful lives joined end to end in heaven.  Now e can calculate the expected value of belief:

Expected value of belief = probability that God exists x value of belief given that God exists
                                            + probability that God  doesn't exist x value of belief given that God doesn't exist.

                                        = p x infinite value + (1-p) x finite value.

                                           = infinite value                               provided only that p is not zero.

(Remember   1/1000 x infinite value = infinite value.  To be granted every 1000th day in paradise and to be comatose for the other 999 is still to experience an infinite amount of bliss.)

Thus the expected value of belief is infinite.

The expected value of disbelief if God exists is eternity in hell.  That is is infinitely disvaluable.  The expected value of disbelief is the same:

Expected value of disbelief = probability that God exists x value of disbelief given that God exists
                                            + probability that God exists x value of belief given that God doesn't exist.

                                        = p x infinite disvalue + (1-p) x finite value.

                                           = infinite disvalue.
 
(Remember   1/1000 x infinite disvalue = infinite disvalue.  To be granted every 1000th day in hell and to be comatose for the other 999 would still be an infinitely big bummer.)

So the expected value of belief is far greater than the expected value of disbelief.
 
 

3. Some objections to the Wager

A    It's too risky.  You have to give up the certainty of the good life for a possibly very low probability of the prize.

Replies:

Every choice involves a certain risk for an uncertain gain.  (We are certain only of death and taxes, and even then neither the date nor the amount is certain.)

You have to act in one way or the other.  ("There ain't no neutral  ground.")  You either have to act as though God exists, or act as though he doesn't.  So you are forced to choose a path here.

B    You can't just decide to believe.  If you are rational your beliefs are proportionate to the evidence and by assumption we don't have enough evidence to believe.

Reply:

As Pascal says:

Learn from those who were once bound like you and who now wager all they have ... They behaved just as if they did believe, taking holy water, having masses said, and so on. That will make you believe quite naturally, and will make you more docile. (Pascal Pensee L 418)

C    Maybe what works for me is Rasputin's method.  Rasputin taught his followers that the best way to come to  genuine faith is through repentance for really major sins, and you can only repent  really major sins if you first commit them.  So it seems that ,my best chance of salvation through faith lies in some serious initial   debauchery.

Reply:
 

  .....mmmmmm......There is in fact a serious objection lurking here.  There is always some small probability that I will end up believing after any course of action.  I may be less likely to believe after indulging in serious debauchery (although many preachers do claim to have been serious debauchers prior to their salvation) but even if I am less likely to end up believing after a night on the town than after a morning at church, provided there is some non-zero probability for each , they will both have the same expected value (an infinite amount).

Suppose some course of action (church-going, say) makes it 99% likely I will end up in heaven and another (serious debauchery, say) makes it only 1% likely.  Which should I choose?  Both have the same (infinite) expected value.  But the former seems like the more rational course of action.  It seems that now we should adopt a different principle of rationality. In addition to the principle of maximizing expected value we should add the following tie-breaker principle:

Tie-breaker:  if two actions both have infinite expected value, choose that action which makes the infinite payoff more likely.

D   There are many  possible Gods.  In which one should I place my faith in the hope of eternal reward?

Reply:

See article by Lycan and Schlesinger.

Here is the web address of an excellent online article, by Alan Hajek,  on Pascal's Wager in:

(Hajek has delved more deeply into Pascal's wager than any other philosopher.)