Pascal’s wager is a pragmatic argument for belief in the existence of God. What is commonly misunderstood about it, however, is that it is only meant to be taken once certain preconditions are met.
Suppose somone tosses a coin into the air, and you are forced to make a guess between heads or tails. Since there’s an equal chance of it landing on either, pure reason cannot make a decision between either. But even though reason cannot decide, that doesn’t mean either choice is irrational. You know that it is going to be one or the other. In fact, it is precisely because each choice appears to be equally rational that reason cannot make the final decision.
In a similar way, Pascal only intends the wager to work in situations where one finds that their pure reason cannot make a decision between belief and unbelief. This is why the wager is so often misunderstood and criticized. Many people accuse the wager of trying to get people to “force” themselves to believe something they find inherently irrational; but it’s not. If one finds Christianity irrational, then reason has already made the decision, and the wager cannot be made. The wager only works where one finds that reason cannot decide, either in principle or in fact.
So, says Pascal, when pure reason cannot decide, something else must be the determining principle. And in this case, he thinks the best course is to utilize a pragmatic calculus which weighs potential risks and benefits. Here’s how the actual wager goes:
“Every gambler takes a certain risk for an uncertain gain” , writes Pascal. The question is, is the uncertain gain worth the certain risk?
Let V stand for the overall expected value of a choice, after all factors have been weighed. Let B stand for belief, and U for unbelief. If V of B is higher than V of U, one ought to choose B over U. But if V of U is higher than V of B, one ought to choose U.
How do we determine overall value? The basic formula Pascal uses is the odds of winning multiplied by potential benefit/payout, and then potential cost subtracted from the result. We can write the formula thus: (O * P) – C = V.
As we’ve already discussed, the odds of belief or unbelief being the right choice are equivalent. The probability is 50/50. Let’ examine potential cost next. This number can legitimately vary among different rational agents, because there is a subjective component involved. For some people, perhaps those who desire religious beliefs to be true, living a life of faith is not a real cost at all. For others who aren’t very fond of religious faith, this could be something of a heavy burden. But whatever number one assigns to potential cost, Pascal notes that it will necessarily be a finite number, because you are only making finite, temporal sacrifices.
Similarly, if you choose unbelief and win, whatever number you assign to the potential benefit/payout, it too will necessarily be fininte, since there is only this life to chash in on. On the other hand, if you choose belief and win, the benefit/reward is infinite; but the potential cost for choosing belief is still only finite, since if you’re wrong, you can only possibly have wasted one finite lifetime.
So here’s how the formulas play out:
- Belief: (.50 odds * infinite potential payout) – finite potential cost = infinite overall value
- Unbelief: (.50 odds * finite potential payout) – finite potential cost = finite overall value
An number multiplied by infinity is still infinity, and when any number is subtracted from infinity the result is still infinite. Meanwhile, any two finite numbers multiplied will always get a finite number, and if any number is subtracted from a finite number, the result will always be finite.
In short, no matter what numbers you plug in for potential payout or potential cost, one should always choose belief over unbelief.
So, is Pascal’s wager a good argument? In all honesty, I’m not completely sure. It’s certainly more plausible, and more defensible, than it is usually made out to be. One of my concerns is about how the odds actually affects the equation as a whole. Pascal is pretty adamant that the wager is only meant to be taken where reason cannot decide. And yet, suppose one thinks the odds are not 50/50, but 49/51 in favor of unbelief. The actual math would still turn out in favor of belief. In fact, even if the odds were 1/99 in favor of unbelief, the math would support belief.
But perhaps Pascal might respond that where reason can decide, reason ought to decide. If the odds are 1/99, then reason has decided. The math of the equation is only meant to be used when the odds have been established to be 50/50.
It seems to me that if one were in a situation where after a long period of in depth thinking and studying, they legitimately cannot decide between belief and unbelief, and legitimately think a case can be made for both, that both are rationally plausible and defensible, then it seems to me that the wager would be justified.
Pascal quote from: Blaise Pascal. Pensees and Other Writings. Edited by Anthony Levi. Translated by Honor Levi. Oxford University Press. July 15, 2008.
My understanding of the “equation” of the wager comes from one of my philosophy professors.