The Wager

The Wager (Taken from Section III of the Pensees)

Pascal begins this selection by giving us reason to think that even if God does exist, there will be no evidence for him. In virtue of the very nature of God, any argument for his existence is bound to fail.

If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is. This being so, who will dare to undertake the decision of the question? Not we, who have no affinity to Him.

Who then will blame Christians for not being able to give a reason for their belief, since they profess a religion for which they cannot give a reason? They declare, in expounding it to the world, that it is a foolishness, stultitiam; and then you complain that they do not prove it! If they proved it, they would not keep their word; it is in lacking proofs that they are not lacking in sense.

Because Pascal believes that no good argument for God’s existence is possible, he’s going to try to ground believe in God in prudential considerations, rather than truth or probable truth. Just like we buy health insurance because we think it’s a wise move, Pascal thinks we should believe in God because it’s wise to do so.

Pascal will give us three distinct arguments here, all designed to show that it’s prudent to believe in God, but he only intends the third to be taken seriously. The first two arguments are “starter arguments” designed to ease us into the last.

"Yes, but although this excuses those who offer it as such and takes away from them the blame of putting it forward without reason, it does not excuse those who receive it." Let us then examine this point, and say, "God is, or He is not." But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.

Do not, then, reprove for error those who have made a choice; for you know nothing about it. "No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all."

Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see.

Pascal has just claimed that we must choose, that we can’t avoid the issue of belief in God by opting to be agnostic. Of course, he’s not denying that agnosticism is a possibility, or that we can’t opt to be agnostic. His point is simply that we can’t avoid the issue of belief in God by choosing to be agnostic. This is because, by choosing to be agnostic, we choose not to believe that God exists. Of course, unlike atheists, we choose not to believe that God doesn’t exit, but nonetheless we don’t believe that God exists and that’s what Pascal thinks is the issue. Do you believe in God or not? That is a choice you can’t avoid making.

If you find that a bit confusing, just think about the decision to believe in God like the decision to get on the bus. A theist gets on the bus. An atheist has decided to never get on the bus. An agnostic isn’t sure whether or not she’ll get on the bus. Pascal’s point is that neither the atheist nor the agnostic are on the bus and that’s the issue because neither of them will have a chance of going where the bus would take them. Do you get on the bus or not? That’s a choice you can’t avoid making. Sure, you can put it off, but putting it off indefinitely is the same, practically speaking, as deciding to never get on the bus.

Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

Pascal has just given us the first argument for belief in God. We’ll call it Pascal’s “Nothing to Lose” Argument. Pascal’s point here is captured by the following decision matrix:

Pascal’s

“Nothing to Lose” Argument

God exists

God doesn’t exist

You believe in God

You gain everything

You don’t gain or lose anything

You don’t believe in God

You don’t gain anything and may lose something

You don’t gain or lose anything

Since you have nothing to lose and something to gain by believing in God, you should believe in God. It’s as though someone offers to give you a free lottery ticket. You have nothing to lose by taking the ticket and something to gain by taking it, so you should take it. Easy call.

"That is very fine. Yes, I must wager; but I may perhaps wager too much."

Here, Pascal acknowledges that belief in God isn’t as simple as the “Nothing to Lose” Argument makes it appear. In particular, religious belief isn’t free. Sacrifices of various sorts are usually required, so if we believe in God and he doesn’t exist then we will be out something. Of course, we’ll only be out a finite amount. No matter how miserable our religion might compel us to make ourselves, even if we sleep on nails, subsist on locusts, and wear hair shirts, all without any sense of spiritual comfort or satisfaction, eventually we’ll be embraced by the sweet oblivion of death.

(Note that Pascal does not appeal to any psychological benefit – such as a feeling of security or a sense of significance or meaning - that belief in God might give us. He’s running the worst case-scenario for belief in God in order to show that even if religious belief causes us nothing but grief in this life, it’s still worth it.)

Because belief in God has a price, the decision matrix involved is actually more like this:

	God exists	God doesn’t exist
You believe in God	You gain everything.	You lose some finite good.
You don’t believe in God	You don’t gain anything and may lose something.	You don’t gain or lose anything.

This complicates the picture quite a bit. It’s no longer the case that you have nothing to lose by believing in God. It’s no longer as though someone is offering to give you free lottery ticket; you have to pay for it. Should you decide to play, or not? Obviously, if the price is low enough, the pot high enough, and the chances good enough, you should buy the ticket. But how can you tell how low the price, how big the pot, and how good the chances need to be in order to make it worth your while to enter? Not surprisingly, there’s a formula.

Consider, for a moment, the following Terribly Abstract Betting Game. “W” is how much you’ll net, if you win. “L” is how much you’ll forfeit, if you lose. “CW%” is your chance of winning and “CL%” is your chance of losing.

Now let’s suppose that you play 100 games.

Since you have CW% chance of winning and since you played 100 games, we can assume that you won CW times. Each time you won, you netted amount W. So, in all, you netted CW*W from your winning games.

But you didn’t just win. Since you have CL% chance of losing, and since you played 100 games, we can assume that you lost CL times. Each time you lost, you forfeited amount L. So, in all, you forfeited CL*L from your losing games.

Your total winnings or losings, after you play 100 games, is the sum of your winning games and your losing games, or CW*W – CL*L

If we wanted to see how much you won or lost, on average, per game, we’d divide this by the number of games you played, getting (CW*W - CL*L)/100. But now for a bit of math:

(CW*W - CL*L)/100 =

(CW*W) /100 - (CL*L)/100 =

(CW/100)*W - (CL/100)*L =

CW%*W - CL%*L

This is called your expected utility. If you play this game, you can expect to win, or lose, on average,

CW%*W - CL%*L

for each game you play. If this amount is positive, then you can expect to earn money in the long run and you should play the game. If this amount is negative, then you can expect to lose money in the long run and you shouldn’t play.

For example, should we bet $3 to win $10 if the chances of winning are 40%? Let’s see.

CW%*W - CL%*L =

0.40*7 - 0.60*3 =

2.80 – 1.80 =

We should play. On average, we can expect to win one dollar a game.

Should we play the same game if the odds of winning are 20%?

CW%*W - CL%*L =

.20*7 - .80*3 =

1.40 – 2.40 =

-1

This time we shouldn’t play. On average, we can expect to loose one dollar a game.

So, given that belief in God isn’t free, is it worth the risk? Let’s see what kind of game Pascal is giving us.

Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness.

This is Pascal’s second argument, which we’ll call Pascal’s “Something to Lose” Argument. He assumes here that the chances of God’s existing is 50%. (“Since there is an equal risk of gain and of loss.”) When he talks about gaining lives, he’s adopting the simplifying assumption that Heaven can be considered to be an infinite number of incredibly happy lives enjoyed consecutively. This gives us the following, much more sophisticated, decision matrix.

Pascal’s

“Something to Lose” Argument

Conse-quences

of God’s existing

Chances

of God’s existing

Conse-quences

of God’s not existing

Chances

of God’s not existing

Expected Utility

You believe in God

Infinite reward

50%

Finite loss

50%

Infinite

You don’t believe in God

Nothing or loss

50%

Finite gain

50%

Finite gain or loss

See how this works? It depends upon the fact that 50% of an infinite amount is still an infinite amount. (Don’t believe me? There are an infinite number of counting numbers, 1, 2, 3, 4, etc., right? Now just take the even numbers. How many are there?) And if you subtract a finite amount, however large, from an infinite amount, you still have an infinite amount left over. (Erase the first billion counting numbers. How many remain?) Infinity is like that.

So, according to this decision matrix, what should you do? It’s obvious! You should believe in God.

But this still isn’t Pascal’s final argument, because Pascal realizes that he may be presupposing too much when he assumes that the chances of God’s existing is 50%. Maybe the odds are with the atheist after all and the existence of God is unlikely. In allowing for this possibility, he gives us his third and final argument.

[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; where-ever 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. And thus, when one is forced to play, he must renounce reason to preserve his life, rather than risk it for infinite gain, as likely to happen as the loss of nothingness…

This is the famous Pascal’s Wager! Here he concedes that the chances of God’s existing might not be 50%. As long as there is some finite chance, however small, that God exists, it’s still prudent to believe in God.

Pascal’s Wager	Conse-quences of God’s existing	Chances of God’s existing	Conse-quences of God’s not existing	Chances of God’s not existing	Expected Utility
You believe in God	Infinite reward	finite amount f	Finite loss	1-f	Infinite
You don’t believe in God	Nothing or loss	finite amount f	Finite gain	1-f	Finite gain or loss

This argument depends upon the fact that the smallest fraction of an infinite amount is still an infinite amount. (Once again, consider the counting numbers, 1, 2, 3, 4, etc. Now take every trillionth one. You’ll still have an infinite number of numbers.) And, as before, if you subtract a finite amount, however large, from an infinite amount, you still have an infinite amount left over.

Here is Pascal’s Wager in argument form:

1. You should believe in God.

2. The chance that God exists is positive and finite.

3. If you believe in God and he exists, you’ll get an infinite reward. If you believe in God and he doesn’t exist, you’ll have only a finite loss.

4. Believing in God has an infinite expected utility.

5. If you don’t believe in God and he exists, you’ll either win nothing or else you’ll lose something. If you don’t believe in God and he doesn’t exist, you’ll win only a finite gain.

6. Not believing in God has a finite gain or negative expected utility.

7. Believing in God has a much higher expected utility than not believing in God.

8. You should do that which has the higher expected utility.

2 + 3 2 + 5

A | B |

4 + 6

C |

7 + 8

D |

So, are you convinced? Would you believe in God on this basis? Actually, some people seem to. They talk about believing in God “just in case.” There are, nonetheless, some problems with Pascal’s Wager. I see four.

Problem I

One of the most glaring problems, probably, is with premises 3 and 5. Premise 3 says that if you believe in God and he exists, you’ll get an infinite reward. Premise 5 says that if you don’t believe in God and he exists, you’ll either win nothing or else you’ll lose something. But who’s say this any of this is true? Mightn’t God damn to Hell, or consign to oblivion, some people who believe in him – particularly people who believe in him solely on the basis of self-interested considerations of the type Pascal advances? And mightn’t God grant eternal bliss to some nonbelievers? What if God chooses to reward people for responsibly using the powers of reason that He’s given them, for example? What if God prizes thinking well over believing any particular thing. In this case, mightn’t God save people who don’t believe in Him because they’re convinced by reasonably strong arguments to the effect that He doesn’t exist, while damning people who do believe in Him without any real support for that belief?

Problem II

More to the point, even if premises 3 and 5 are true, by his own lights, Pascal shouldn’t believe them or ask us to believe them. He’s already stated that we aren’t in a position to know anything about God, which appears to be inconsistent with claiming to know what God would decide to do believers or nonbelievers after death.

(If you wish, we can think some more about Premises 3 and 5.)

Problem III

Premise 8, which says that you should do that which has the higher expected utility, might also be problematic. For one thing, it assumes that our belief should be guided by considerations of utility rather than truth, which – as we’ve seen in our study of epistemology – is not a position with which everyone agrees.

Problem IV

For another thing, premise 8 might be false in virtue of giving us advice that’s impossible to carry out. There’s a saying in ethics: “Ought implies can.” This means that if we can’t do something, then it can’t be the case that we ought to it. It must be possible for us to be ethical. But is it possible for us to pick and choose our beliefs on the basis of their utility? If it would be useful for you, right now, to believe that you’re next in line for the British throne, could you do it?

We’ve seen, therefore, that Pascal’s Wager is open to criticism at thee of it’s premises:

1. You should believe in God.

2. The chance that God exists is positive and finite.

3. If you believe in God and he exists, you’ll get an infinite reward. If you believe in God and he doesn’t exist, you’ll have only a finite loss.

[This may not be true, and even if it is true it’s not something that Pascal has any right to claim.]

4. Believing in God has an infinite expected utility.

5. If you don’t believe in God and he exists, you’ll either win nothing or else you’ll lose something. If you don’t believe in God and he doesn’t exist, you’ll win only a finite gain.

[This may not be true, and even if it is true it’s not something that Pascal has any right to claim.]

6. Not believing in God has a finite gain or negative expected utility.

7. Believing in God has a much higher expected utility than not believing in God.

8. You should do that which has the higher expected utility.

[Maybe we shouldn’t adopt beliefs on the basis of utility. And maybe it’s impossible to do so, anyway.]

2 + 3 L 2 + 5 L

A | B |

4 + 6

C |

7 + 8 L

D |

"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?"

Here, Pascal anticipated the last of the objections we saw – the concern that it might be psychologically impossible for us to decide to believe things, and he’s about to address it by advocating a particular type of voluntarism.

Voluntarism is the claim that we can, in fact, decide to believe things. There are many different kinds of voluntarism, but for our immediate purposes the interesting distinction is between direct voluntarism, which maintains that you can, right now, believe anything you want to at will and indirect voluntarism, which maintains that although you can’t just decide to believe whatever you want, you can decide to take actions that will tend to bring about that belief.

Direct voluntarism is not a plausible psychology of belief, as you probably discovered when considering whether you could, right now, decide to believe you were heir to the British throne. Indirect voluntarism, however, might be feasible, and that’s the kind of voluntarism Pascal recommends in the next paragraph.

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. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. 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…

So, according do Pascal, it might be impossible for you to decide to believe in God right now, but if you associate with believers, go to church regularly, and generally act as though you believe, eventually you’ll find that you really do.

Whether or not Pascal is right about this is a matter for psychology, not philosophy, to determine. It’s an empirical question to be settled by studying how beliefs change in circumstances like those recommended by Pascal.

But assuming, for the moment, that Pascal is right and that we can consciously adjust our beliefs in the direction of utility, we still have to consider whether or not we should adopt beliefs because we have reason to think that they’ll serve us well in the end. Is it really the best thing to “fool ourselves” into belief in God, as Pascal recommends?

Pascal anticipates that some of his readers might have qualms about this. Here’s what he says to them.

[Even this will naturally make you believe] and deaden your acuteness. "But this is what I am afraid of." And why? What have you to lose?

But to show you that this leads you there, it is this which will lessen the passions, which are your stumbling-blocks.

In other words, if you don’t believe in God, the problem is that you’re too acute (in other words, too sharp). By acting as if you believe, you’ll deaden your acuteness (i.e. make yourself duller). Not surprisingly, Pascal has no problem with this. Is it better to be bright and damned to Hell, or dim and go to Heaven?

Questions for Consideration:

· What if you could take a pill that would make you believe in God by lowering your IQ 20 points. Would Pascal counsel you to take the pill? What would you decide to do? Why?

Optional Material:

· Two other varieties of voluntarism are “weak” and “strong.” Weak voluntarism says that we can believe something even if there’s no evidence for it. Strong voluntarism says that we can believe something even if there’s compelling evidence against it. Does Pascal appear to be advocating weak or strong voluntarism? Think about it, then see if you agree with me.

· Pascal’s theological imagination is notoriously limited. He appears to assume that if we decide to believe in God, this religious belief could assume only one form: belief in the God of Christianity. But even if we grant him this (and it’s a lot to grant) it’s not clear that there is a single God of Christianity. If you hear a conservative preacher and a liberal preacher talk about God, they sometimes appear to be talking about completely different beings. So, assuming that we have a choice between believing in a vengeful God and a forgiving God, which belief should we choose if we think about the decision along Pascal’s lines? Think about it, then see if you agree with me.

Let’s summarize Pascal.