Pascal's Wager is a "non-traditional" argument for belief in God; that is to say, it doesn't attempt to prove that there is a God, but that you should believe that there is. It is, thus, a sort of pragmatic argument.
Pascal begins by assessing the state of our knowledge on the matter of God. We know that there is an infinite, though Pascal claims we don't know its nature. For example, we know that there is an infinite number of numbers, but we don't know the nature of that infinite number, Pascal argues. Pascal's reasons here are a bit confused. He says we don't know if this even number is even or odd, but in fact, we would now say, we know that it is neither. Let that pass, however. Pascal's point here is that even if some infinities can be known to exist without knowing their nature, God is not like this. In the theoretical sense, we can neither know that God exists nor that God does not exist.
What about faith? Pascal thinks faith is fine, but some people might think that the rational choice is not to choose; neither to believe nor to disbelieve.
For reasons that are not clear to me, Pascal seems to regard agnosticism as not among the choices. He writes
...you must wager. It is not optional. You are embarked.Perhaps Pascal simly means that the real choice is between belief and lack of belief -- which includes agnosticism, but I doubt that it makes too much difference to the argument. That's because if Pascal is right, agnosticism would be a bad option. But what is the argument?
Pascal pictures our situation as one in which a coin flip is taking place at infinity, and we are offered the chance to bet. Initially, then, it's as though the odds are even. But what are the stakes? Pascal writes
If you gain, you gain all; if you lose, you lose nothing.After this, the argument gets hard to follow. Pascal imagines someone hearing this who says. "Yes, I must wager, but I may perhaps wager too much." The puzzle here is that we have just been told that if we lose, we lose nothing, which presumably means we are no worse off than we were. In other words, by betting "yes," we wager nothing. It's a free ticket to a cosmic lottery.
Pascal doesn't quite explain this, but he goes through a sequence of arguments that assume that one does risk. What one seems to risk, in the scenarios that Pascal discusses, is one's life. But Pascal assumes that a finite life is only of finite value. And from there he proceeds through a sequence of quasi-calculations that I will cheerfully admit I find quite confusing.
The source of the confusion is this. To calculate the rational course of action, we need to know what proposition we are betting for or against, we need to know what the odds are, and we need to know what we win or lose in each possible scenario. That is to say, we need to know what goes in each of the pay-off boxes in the following table:
God No God
__________________________________
| | |
Believe | gain = ? | loss = ? |
|________________|________________|
| | |
Don't believe | loss = ? | gain = ? |
|________________|________________|
Pascal never makes this clear. But what he does say is this:
God No God
__________________________________
| | |
Believe |gain = infinity | loss = n |
|________________|________________|
| | |
Don't believe | loss = ? | gain = ? |
|________________|________________|
If there is a God, belief in God promises infinite gain; if there is no God, we lose only some finite amount n by believing otherwise.But what if we don't believe?
It would be difficult to argue that we gain infinitely if there is no God and we are atheists. True, we believe the truth. But being right is only one among many values. Is being right about atheism (if it is right) really of infinite value? That's awfully hard to accept.
What about being wrong about atheism? Some people have read Pascal as assigning an infinite cost to this mistake. But nowhere in the essay does Pascal seem to argue in this way. Visions of hellfire and damnation don't enter the argument. And they needn't. All we need assume is that there is no infinite reward for believing there is no god when there is one. In that case, so long as there is some probability that there is a God, the rational thing to do is believe.
Let's look at this in a bit more detail, and in modern terms. Suppose we have a bet on a coin toss with the following "payoff matrix," as it is called:
Heads Tails
__________________________________
| | |
Bet Heads | $1.00 | -$1.00 |
|________________|________________|
| | |
Bet Tails | -$1.00 | $1.00 |
|________________|________________|
Is this a reasonable bet? It depends on the probabilities. Suppose the probability of heads is .5, and so the probability of tails is also .5. Here's how we calculate the "utility", as it is called, of betting heads: prob(Heads) x payoff - prob(tails) x loss = .5 x $1.00 - .5 x ($1.00) = 0.
This gives us a zero. But the same holds for betting on tails. So this is a game that is fair for both sides. Suppose, on the other hand, that the coin is biased, and that the chance of getting heads is .6. In that case, if the payoffs stay the same, the utility of betting heads is
.6 x $1.00 - .4 x $1.00 = $.20
whereas the utility of betting tails is
.4 x $1.00 - .6 x $1.00 = -$.20
This confirms common sense. We should bet "heads" because we can expect, over the long run, to average a twenty-cent gain each time we play.
Before we get to Pascal's argument, consider another. Suppose we are spinning a wheel with one hundred slots. One slot is red, and all the others are black; all are equally probable. If you bet on red and win, you win $1,000,000. If you lose, you lose $1.00. On the other hand, if you bet on black and win, you win only $10.00 and if you lose, you lose $1.00.
It seems plausible that you should play and bet on red. The utility of betting on red, even with the bad odds, is
.001 x $1,000,000 - .999 x $1.00 = $999.001
The utility of betting on black is
.999 x $10.00 - .001 x $1.00 = $9.9901
Both bets have a positive utility; in both cases, you can expect to win "over the long run." But betting on the red space still makes sense even though the odds are against winning the bet. The reason is that the potential payoff is so great and the potential loss very small.
We will come back to this.
What, then, of God? The point is that no matter how small the probability is that God exists, as long as it isn't zero, the utility of belief in God is infinite, because a finite number, however small, times infinity is still infinity:
prob(God exists) x infinity = infinity.
And since we are only considering a finite cost if you bet on God and are wrong, infinity minus a finite number is still infinity
prob(God exists) x infinity - prob(God doesn't exist) x n = infinity.
So Pascal's point is that you stand to gain infinity by believing in God, and stand to lose at most a finite amount if you are wrong. It is therefore rational to believe in God.
What if you can't believe? Then Pascal's advice is to begin by acting as though you believe. As a Catholic, his advice was rather specific: go to mass, take holy water. Or as we might say, "Fake it until you make it." Walk the walk and talk the talk. This may not be guaranteed to work, but it has a fair chance.
There are other problems, however, and we pointed them out in class. What if you back the wrong God, or at least the wrong understanding of God? Although Pascal doesn't talk about it, the view of the Catholic Church in his day was that if you don't believe in Jesus as the Son of God and the Christ, you are damned. In particular, belief in a pagan religion was a recipe for damnation. That might seem to be a reason to play it safe and become a Christian, but what if the God who really exists is ot hte God of Christianity, but disapproves of false belief? Then believing in the Christian God is a recipe for eternal disaster.
In some ways, this argument is embarrassing. Although Christianity may not be completely unique in claiming that it offers the sole road to salvation, it is at least unusual among world religions in this respect. The origins of this bit of theological mischief are found in the way that some of the words of Jesus in the Gospels -- especially the Gospel of John -- have been interpreted.
I do not want to spend a lot of time on this issue, but two comments seem to be in order. The first is that this idea of eternal damnation for wrong belief is not very flattering to God. There is no serious likelihood that someone who lives and dies in a non-Christian culture (say, in Pakistan), born to non-Christian parents, will end up becoming Christian. If that is reason for God to damn them, then we might well think that God is a vain, egotistical cosmic tyrant.
The second point, however, is that the idea is dubious as Christian theology. This is a large topic, but leaving aside for now what other religions have to say about salvation, and assuming simply for the moment that Christianity is correct, there is a difference between saying that salvation is through Christ and saying that it requires conscious, explicit belief in Christ. If it required that, then those who die as infants, or those who are mentally incapacitated are beyond the pale of salvation, and that's at least as unflattering to God.
The philosophical/theological issue is best illustrated by another example. Suppose I take a medicine that contains two compounds, One is believed to be medically inert; the other is thought to effect the cure. Suppose in fact that it is the other way around. The supposedly inert substance is medically active; the "medicine" isn't. I believe I am cured by one thing. And I am cured. But what cured me was not what I think.
How does this apply to religion? A person might in fact be in touch with the source of salvation, and receive the benefits of that Source, without knowing Its name nor understanding it aright. I don't need to understand aspirin for it to cure my headache I don't need to understand love for it to heal. And, so the argument would go, I don't need to understand the inner nature of God for God to save my soul.
This argument, or a version of it, has been proposed by various theologians, most notably the great Catholic theologian Karl Rahner. Rahner believed that salvation is through Christ, but that one need not be able to name the source to benefit from it.
Of course, the same would hold if Christianity is wrong but there is a merciful God nonetheless. Receiving God's grace would be one thing; giving it the proper name would be another.
But this is a sideline from our central focus, which is Pascal's argument.
The specifics of the argument are suspect. They assume that we know more about what the alternatives are than we can really claim to know. But the general idea is interesting all the same: it might be better to be religious because one than has a chance of getting a benefit that would otherwise not be open to one. Still, it might seem, there is a cost. To become religious, one will have to adopt a life that is very different from the life one might otherwise choose to lead. And while we could rehearse once again Pascal's argument about infinite rewards, there is a different point that he makes towards the end of his essay: the religious life has intrinsic rewards. Pascal writes:
Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life and that, and that at each step you take on this road, you will see so great a certainty of gain, so much nothingness in what you risk, that you will at last recognize that you have wagered for something certain and infinite, for which you have given nothing.In other words, even within this life, it will become evident to you that the rewards of belief outweigh the costs to the point of rendering them utterly insignificant.
And there we might as well leave the argument. There are technical issues about the formal details, and they have a certain abstract interest. My own view is that an infinite gain that is highly improbable is not worth a finite but ruinous risk. But so what? Even if this is true, the risk of false belief in God is not even close to ruinous for most people. So the point is chiefly academic. When we come to William James, we will see an argument for a rather similar conclusion developed in a different way.