Richard at "Philosophy, et cetera" has an interesting post on Pascal's Wager. Richard interprets the wager as having the following form:
1) There is a non-zero possibility of receiving an infinite reward (everlasting joy in heaven) if and only if you believe in God.
2) Infinity multiplied by any non-zero real number is still infinite.
3) Since Expected utility = Reward * Probability, the expected utility of believing in God is infinite, whereas the expected utility of disbelief will be finite. [From 1 & 2]
4) As a matter of practical reason, you ought to act in such a way as to maximize your expected utility.
C) Therefore, you ought to believe in God (or act in ways that will help you to develop such a belief).
This is an interesting argument in itself; although it's worth noting that it's not a wager but a utilitarian ethical argument. I think, however, Pascal's Wager is rather different. So here are my current thoughts on the subject. A caveat before starting out: Pascal's Wager is found in the Pensées; since the Pensées are fragments, we face something of the same problem with interpreting Pascal's argument that we do with interpreting any fragmentary text. In particular, we have to guess the actual context and point of the argument from the other fragments. Further, the fragments we have are just notes - they are not fragments of a developed text but fragmentary notes for a text that was never written. (You can go here for the main texts.)
The Wager is expressed dialectically, so it needs to be broken down into its dialectical elements to be interpreted properly. (Indeed, it is virtually certain from the way the Wager fragments are organized that Pascal intended to write it as a dialogue; failure to recognize this has been one of the most common vitiating factors in attempts to interpret it.) Unfortunately, because we are dealing with fragmentary notes, we have to reconstruct a bit. Here's my rough-draft attempt at a reconstruction/paraphrase that stays close to Pascal's actual notes.
Let us now speak according to natural lights. (Context)
A: We cannot know if God is or what He is, for we have no affinity to the infinite and incomprehensible. If this is so, who will dare try to decide the question of whether God exists? Not us.
B: But if we can't decide the question, how could one blame Christians for not giving a reason for their belief? After all, they don't claim to be able to prove the mysteries of God; and yet, despite not considering the question decidable yourself, you blame them for not giving proofs!
A: Well, yes, they don't claim to be able to prove divine mysteries, so fair enough on that point. But this still doesn't excuse people who believe what Christians are claiming.
B: Let's look at this point. The question is whether God is or is not. But we are already presupposing that reason can't decide this issue. "A game is being played at the extremity of this infinite distance where heads or tails will turn up." So what will you wager? According to reason, there isn't any basis either way (according to our supposition). So you really have no right to reprove people for having made a choice without proof; you yourself admit that you don't know anything more than they do.
A: True; but I don't blame them for having chosen to believe that God exists, but for having chosen at all rather than suspending judgment. Whether you choose heads or choose tails, you are still in the wrong. "The true course is not to wager."
B: Ah, but that really doesn't seem to be an option. [Admitting a choice, you have already embarked on thinking through the wager, which involves considering what you might wager.] So what would you choose? On the assumption that you must choose, let's see what's less in your interest. You have two things to lose, the true and the good; two things to stake, knowledge (pertaining to reason) and happiness (pertaining to will); two things you are trying to avoid, error and misery. By our supposition, reason isn't shocked at either of the options available, and we have to choose anyway. Let us estimate the gain and loss of happiness in wagering whether God is. If you gain, you gain all. If you lose, you lose nothing. So wager that God is.
A: OK, let's go with that for the moment. Even then we are still faced with a problem, since gain and loss is not the only thing to consider in a wager. We also must consider how much we are wagering. Even if I must wager, I might end up wagering too much.
B: Let's consider that. Since by our supposition we have no particular reason to choose either side over the other, if we wagered one life of happiness for the possibility of gaining two lives of happiness, we still could wager. If we stood three lives to gain, however, on our supposition that we must play, and on our supposition that reason is indeterminate on the issue (which implies that for all we know the chance of gain on either side is equal), we would be stupid not to wager one life of happiness for the chance of gaining three lives of happiness. But suppose there are infinite lives of happiness on the table. Since we can be right to wager one life of happiness against two, and since it would be stupid to wager one life of happiness against three, what shall we say about wagering one life of happiness against infinite lives? What we stake is finite. What we can gain is infinite. So long as we don't stand an infinite to lose, the reasonable thing is to wager everything on the chance of infinite gain. And it doesn't seem that we have anything to lose.
A: But it isn't certain whether we will gain anything, whereas it is quite certain that we are risking something. There is, as it were an infinite uncertainty about our gain, and this cancels out any reasonableness in risking what we are certainly risking.
B: Not so. Everyone is staking something certain for something uncertain; but we are weighing a finite certainty (our stake) against a finite uncertainty of gain. Uncertainty of the gain is related to the chances of gain and loss; and this, on our previous supposition, is for all practical purposes even. Reason has not shown us any more chances on one side than on the other - this is what started us off. So our game is one of finite risk, equal risk of loss and gain, and infinite possible gain. "This is demonstrable; and if men are capable of any truths, this is one."
A: OK; but it would still be better if we could see the cards - get some sort of inside tip to help us make a better bet.
B: And so we can; we have things like Scripture and all the things to which Christians appeal.
A: Yes, but if I must wager, I'm in a bind. I simply am not made so that I can believe these sorts of things.
B: Then at least learn what's involved in your inability to believe. The issue is a matter of passion, emotion, rather than reason, for reason allows one to believe, but you cannot believe. This is a disease that can be cured. See if you can become convinced, not by piling arguments on top of each other, but by getting your passions under control. The remedy for unbelief is to do what others in your place have done. If you do what they have done, getting involved in the spiritual disciplines that abate the control of the passions over us - attending mass regularly, taking the holy water, or whatever - then this will fix your problem and bring you naturally to believe.
A: But this is what I'm afraid of.
B: Why? What do you have to lose? Your stumblingblocks here are your passions, not your reason; your emotions are getting in the way. And doing these sorts of things is precisely what will lessen your slavery to your passions.
[They continue to discuss this issue a bit, talking about what is really lost and won through these spiritual disciplines. We now come to the end.]
B: What harm will come from taking this side? Due to this spiritual discipline, "you will be faithful, humble, grateful, generous, a sincere friend, truthful." To be sure, you'll lose out on those poisonous pleasures of fame and luxury, but surely these other things more than compensate. By doing these things you will gain so much in this life, and you will see so great a certainty of gain at every step you take, and you will see that what you lose will be so worthless, that you will at last recognize that your risk is virtually nothing, whereas your gain was actually certain and infinite all along.
A: That is a very charming idea!
B: If this pleases you or seems impressive in any way, know that it is made by a man who, before and after, has knelt in prayer to that infinite Being before whom he lays all he has, asking that you in your doubts may be given such strength that you, too, can lay down before Him everything you have for your own good and His glory.
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