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A Summary and Critique of Pascal’s Wager

Blaise Pascal, Pascal

One of the most popular-in part because it’s one of the easiest to understand-arguments in favor of the existence of God is known as “Pascal’s Wager,” named after the 17th century French mathematician and philosopher Blaise Pascal who formulated one version of this argument.

Anyone who has ever taken an Introduction to Philosophy class is likely familiar with this argument, but for those who are not, here it is in its simplest, most straightforward form:

Consider the advantages and disadvantages of believing in a God who will reward those who believe in Him and punish those who do not after they die. There are four possibilities.

* You believe and you turn out to be right, in which case you get the reward.

* You believe and you turn out to be wrong, in which case nothing happens and you’re just dead.

* You disbelieve and you turn out to be right, in which case again nothing happens and you’re just dead.

* You disbelieve and you turn out to be wrong, in which case you get the punishment.

So basically if you believe, then you either get Heaven or nothing, and if you disbelieve, then you either get Hell or nothing. (You don’t even get the satisfaction of being right if you disbelieve and there’s no God, because you’ll be dead and thus won’t know you were right.)

Therefore, the rational choice is to believe.

On the surface, it certainly does seem wise to play it safe and believe “just in case.” But there are at least two major problems with this argument.

The first is that it uses a decision theory approach which only makes sense when applied to actions and not beliefs. I will illustrate with an analogy.

Let’s say you walk into a casino and are offered the following wager: One die will be rolled, and you must bet on either “even” or “odd.” If you bet on “even” and a 2, 4, or 6 comes up, you win a million dollars, whereas if a 1, 3, or 5 comes up, nothing happens. If you bet on “odd” and a 1, 3, or 5 comes up, nothing happens, whereas if a 2, 4, or 6 comes up, you get taken out back, tortured mercilessly, and killed.

Is there really any doubt which is the wiser wager? Of course you bet on “even,” in spite of the fact that an “odd” is just as likely to be rolled. Indeed, for that matter the probabilities need not be equal. If you replace “even” with “6,” and replace “odd” with “non-6,” then you should bet on the 6, even though you have only a one in six chance of being right. Heck, let’s go even farther. If it were a trillion-sided die, and you could bet on a “6” and get a million dollars or nothing, or bet that a non-6 will be rolled and get nothing or tortured and killed, then it’s a no-brainer to bet on the one in a trillion shot.

As long as there’s a non-zero chance of rolling an even number (or whatever the “million dollars or nothing” wager is), then that’s the only bet that makes sense. Not on “faith” or anything like that, but purely on the basis of a rational assessment of the costs and benefits of the various outcomes.

OK, so we’re fine so far.

But now consider an even more peculiar casino. The wager is the same as the original “even” or “odd” one, but with one important difference. This time you don’t “do” something to make your wager (such as place some sort of marker on a square that says “EVEN,” or declare “I hereby bet on ‘even,'”). Instead, the casino employs a mind reader with supernatural, infallible powers, and your wager is determined by what you believe. In order to wager on “even” for the million dollars or nothing, you have to in fact believe the next roll will be a 2, 4, or 6.

Well now you’re in a fine pickle. You have no idea what the next roll will be, and worse yet, you know that you don’t know. The mind reader will see that you believe an even is no more and no less likely than an odd, and thus you won’t be able to make the advantageous wager.

Therein lies the problem: you can’t “decide” to have a certain belief. You can say it, you can act like you believe it, but that’s different from believing it. And in this case, it’s believing it that matters.

Pascal’s Wager, alas, is analogous to our second casino, not the first. So even if the argument is correct that it would be advantageous to believe in God, knowing that doesn’t help you. By hypothesis in the argument, you’re in a state of uncertainty-you know that you don’t know if there is or isn’t a God, just like in the casino you know that you don’t know what the next roll will be.

Now, while this objection is an important one, it may not be a fatal one. Indeed, Pascal himself recognized this problem and attempted to deal with it.

If the only problem with Pascal’s Wager were this one, then the way around it would be to find some way to believe there is a God despite your present uncertainty. True you cannot simply will yourself to believe something, but perhaps there’s some more indirect way to achieve the same end.

Perhaps there are hallucinogenic drugs that render people more likely to have this belief. Perhaps some lobotomy-like surgical procedure. Perhaps some kind of brain-washing program. Perhaps associating exclusively with people who already believe and shunning those who don’t. Perhaps reading only books and other material written by believers and avoiding any other reading.

It’s at least possible that empirical investigation will show that the belief in question is more likely to be held under certain circumstances than others, so in order to give yourself the best chance to believe, you would want to put yourself in those circumstances. You can’t choose the belief directly, but you can make choices that indirectly maximize your chances of believing down the road.

(I can hear believers shouting objections. Never mind all that ‘brain-washing’ and such; if you want to believe, just open your mind and heart. The evidence of God is abundant, both in nature and internally in the way we feel when we open ourselves to him.” But the problem with that is, if such evidence is indeed available and does indeed justify a belief in God, then Pascal’s Wager is superfluous. You should believe based on that evidence if it exists, not on the basis of Pascal’s Wager. Pascal’s Wager is only relevant in cases of uncertainty, where you do not know, and realize you do not know, if there is a God or not.)

So “choosing” the more advantageous belief turns out to entail a lot more than just checking a box to “be on the safe side.” It means possibly altering your brain or your circumstances significantly to overcome your realization that you don’t know if there’s a God or not. It means finding some way of “tricking” yourself out of uncertainty, with no guarantee you’ll even succeed.

Still, if Pascal’s Wager is correct, presumably it’s worth doing anything and everything to bring about that advantageous belief in ourselves (and others if we care about them), because remember that payoff-basically a value of positive infinity or nothing if you believe, and negative infinity or nothing if you don’t.

But it turns out the second of the two major objections to Pascal’s Wager is a fatal one.

Unfortunately for Pascal’s Wager, if it justifies believing there’s a God who rewards those who believe in him and punishes those who don’t, it equally justifies believing anything and everything else that there is a non-zero chance will have the same sort of payoffs, including some that contradict each other.

For example, what if we were to use the same approach as Pascal, but to the question of what to do if we are in a state of uncertainty as to whether there exists a God who provides an infinite reward to people who wear hats and an infinite punishment to those who don’t? You don’t know for certain that such a God exists or doesn’t, so shouldn’t you wear a hat just in case?

How about a God who’s gung ho about rationality, and who has contempt for people who believe things on “faith”? He might reward all the people who were intellectually honest and simply admitted that they didn’t know one way or the other, and punish all the people who bought into Pascal’s Wager and tried to find some way to believe in spite of the uncertainty. Should you be an agnostic to “be on the safe side”?

What about a jealous non-Christian God, who rewards all believers in all other religions, and even non-believers for that matter, and only punishes Christians? Should you hasten to dump all your Christian beliefs “just in case”?

Do you know for sure that there isn’t a race of alien superbeings about to arrive on Earth who will provide limitless unimaginable benefits to all virgins, and massacre everyone else? Maybe you should think twice about having sex, you know, just to be safe.

The point is there are an infinite number of things you can potentially believe or do based on there being some non-zero chance they’ll turn out to be the key to some great reward. But you can’t do all of them.

If your response is that those are all quite silly things, and the belief in the conventional God differs from those in there being sound evidence and arguments in its favor, then again you’re missing the point of Pascal’s Wager. Pascal’s Wager only applies in situations of uncertainty. You’re not saving it by citing other evidence and arguments; you’re bypassing it. By all means if there is evidence and sound arguments for your preferred theological beliefs, then have at it. But Pascal’s Wager can have no use for those considerations.

In summary, there are two main flaws that prevent Pascal’s Wager from being cogent. One, it uses a decision theory that’s applicable to actions and not (except possibly in a very indirect, convoluted way) to beliefs. Two, it commits the fallacy of false dilemma by claiming uncertainty yet positing that the only two possibilities are a God who rewards believers and punishes non-believers or nothing at all, when in fact there are an infinite number of other possibilities that have some non-zero likelihood.