# Does Pascal's Wager contain any logical flaws or fallacies?

Blaise Pascal's famous wager was that even if the existence of God cannot be determined through reason, a rational person should wager as though God exists, because living life accordingly has everything to gain, and nothing to lose.

What logical flaws and/or fallacies (if any) are committed in making this argument?

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I wonder if the question would be a better example for the future if it did not take sides? Perhaps a better (though equivalent in meaning) question would be, "Is Pascal's Wager a valid and compelling argument?" – Jon Ericson Jun 8 '11 at 0:11
@Jon added "if any" and changed the phrasing of the question for a bit more neutrality. Good point. – jozzas Jun 8 '11 at 0:29
In addition, it might be better to quote Pascal rather than paraphrase. I think your formulation is somewhat inaccurate: the actual Wager is between infinite reward and finite loss. But I suppose this will be common and must be dealt with if and when the site goes public. But I enjoyed the question and enjoyed answering it. – Jon Ericson Jun 8 '11 at 0:54
Alan Hájek certainly thought so. – Seamus Jun 16 '11 at 10:54

1. He assumed that if God exists then

1a. humans are immortal (as a necessary condition for 1b)

1b. God decides whether they are tortured eternally or happy eternally (one of them is enough to profit infinitely, though)

1c. God bases his decision on whether they believe in him (if this is not the case, the wager does not work, because believing in God or believing in God because of the wager might cause infinite torture)

1d. God bases his decision on whether they follow religious law (again, the wager does not work if God does not like people following religious law)

1e. God is the Christian God and you have to believe in exactly the right doctrinal points and those are the points that Pascal was raised with (again, the wager does not work if God does not like people to follow a particular religious law)

2. It is not true that you have nothing to lose if there is no afterlife and you have spent all your life following the instruction of the religion even though you would have preferred to do something else.

3. He also assumed that he can rationally decide to believe.

Summary: The wager assumes that there is a positive probability for God rewarding a particular behaviour with eternal bliss and a zero probability for God punishing this very behaviour with denial of eternal bliss. There is no reason for this assumption.

If the probability for a reward is in fact zero, it does matter if you sacrifice all the life you have for a non-existing reward.

If the probability for God disliking the behavious is not zero, then you have to weigh more than one infinite expectance values.

Even if everything works fine, you would have to be able to believe or disbelieve just because you want to. (Like, say, an atheist who reads a study that believers have a better healing chance for a particular cancer and decides to become a believer as a therapy.)

It's logically fine if someone believes all the assumptions and then says that it is a good idea to believe. But this person believes in the first place, they do not believe because of the assumptions, they are just happy with their belief because of what they believe.

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and I must add that this is one particular view of what God may be like. There have been many Gods in the past, and there is no particular way to think that God is supposed to like what Pascal had in mind. – Bob Jun 7 '11 at 22:46
Hey, Pope... you listening? ;-) – Jez Jun 7 '11 at 22:46
@Bob Some interpretations of the Wager argue that it could be suggested that believing in a generic God, or a god by the wrong name, is acceptable so long as that conception of God has similar characteristics of the conception of God considered in Pascal's Wager. I think that "many religions" is a valid flaw, as most Gods aren't tolerant of other religions, but I'm sure there are many other flaws :) – jozzas Jun 7 '11 at 22:52
@thei This is a good answer, but I think that there is more wrong with the wager than just this. You cover inauthentic belief well, but are there any other logical fallacies in the wager? Perhaps an argument from inconsistent revelations? And are any of the assumptions Pascal made false? – jozzas Jun 7 '11 at 23:22
In item 1b, the infinite reward is sufficient. Pascal did not mention eternal torture. 1a and at least 1e are also superfluous. But then all of item 1 is simply an attempt to rephrase the Wager and I don't see how it is a fallacy at all. Item 2 misunderstands the Wager&mdash;Pascal concedes the potential loss exists, but that it's finite. Perhaps you are looking for the false dilemma fallacy? – Jon Ericson Jun 8 '11 at 0:08

Here's my problem with it:

• Choose a group of self-described Christians and call them Group A.
Group A believes that Jesus was the son of God, he died on the cross for our sins, and only through him can we go to heaven.

• Choose another group of self-described Christians and call them Group B.
Group B believes that Jesus was the son of God, he died on the cross for our sins, and only through him can we go to heaven.

Given: for every Group A, there is a Group B that firmly believes that Group A is going to hell.

As a result, the statement "a rational person should wager as though God exists" is meaningless, unless you first define to which group you're referring.

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+1 for using set theory and enumeration! – Arjang Jun 8 '11 at 0:11
But surely there aren't multiple deities allowed by the original Wager. I belief you are suggesting the Wager is an example of the false dilemma fallacy. Also Pascal would be amused to know that critics seem to assume he was unfamiliar with divisions within Christianity. The existence of Group A and Group B seems entirely irrelevant since Group B is clearly mistaken. ;-) – Jon Ericson Jun 8 '11 at 0:35
@Dori, they need not neccesserily be christians, any dogmatic belivers would do, no need to drag Jesus into it either. – Arjang Jun 8 '11 at 9:07
@Arjang - My understanding is that Pascal was wagering on Christianity, and the rest follows. But sure, go ahead and swap in any other faith whose followers believe that they alone go to heaven and all others go to hell. – Dori Jun 8 '11 at 10:09
@Jon - Wouldn't followers of other faiths be, by definition, believers in a different god? Can't be the same one, because after all, they're doing it wrong! ;-) – Dori Jun 8 '11 at 10:11

The logical flaw is that he ignored a third possibility. Essentially he assumed that either there is no God, or there is a God who will do something good for you if you do some set of positive actions or, at worst, will do nothing. The third possibility is that God is evil or just backwards, and does good only for those who disrepect him or don't believe in him or spend their lives convincing people to hate him, etc., and punishes everyone else. "Bad God" is just as probable as "Good God" without any other assumptions, so it makes no sense to believe that one or the other exists.

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Although I agree with your line of reasoning I'm not sure this is a "logical flaw" so much as a flaw in imagination. Pascal's conception of God likely precludes "Bad God". – Mike Howsden Jun 8 '11 at 19:51
@Mike I suppose it could go either way. The other answers have argued that precluding "Bad God" is a mistake. – Matthew Read Jun 8 '11 at 19:53
For the record, I believe this answer amounts to: "Pascal's Wager is a false dilemma". That's a valid critique, but it does not require the idea of a "Bad God". A lenient God, who rewards people regardless of their actions would be sufficient. (But I think this line of reasoning misunderstands what Pascal was trying to accomplish in the Wager.) – Jon Ericson Jun 8 '11 at 20:07
Forth option: There are several gods. Why do everyone forget that option? – Lennart Regebro Jul 1 '11 at 7:21
"Bad God" is a symptom of a larger problem: the problem with Pascal's wager is that it applies to every conceivable route to heaven simultaneously. So if non-belief is a conceivable route to heaven, it's the logical option. As is believing in the FSM, or Thor, ad infinitum. – philosodad Jul 5 '12 at 15:46

There are a great many logical fallacies in how the Wager is applied. Often the Wager is suggested as some sort of proof or last-ditch argument for God. But since it was embedded in the Pensées, which was Pascal's life project to defend Christian thought, it seems unlikely he intended for the Wager to stand alone. Whether anyone would be convinced by such an argument seems not to be the main thrust of Pascal's formulation of the Wager.

The very introductory statement to his argument shows that Pascal concedes that God cannot be proven in the Aquinian sense:

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.

It makes more sense to view Pascal's Wager as a precursor to Alvin Plantinga's Warranted Christian Belief. In contradiction to Cartesian skepticism, we are free (even compelled) to act on believes that we cannot prove from first principles. Any reasonable reading of Pensées would conclude that Pascal is not trying to take the risk out of choosing the Christian faith. Rather, he was defending the faith from the charge that it is irrational.

The Wager takes on added weight when you consider that Pascal himself made a bet and took up an ascetic lifestyle near the end of his life. It was this time that the Wager was formulated and it was not published in his lifetime. It's difficult to ignore the possibility that Pascal took the Wager quite seriously. He summarized the argument by making this precise point:

The end of this discourse.—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, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognise that you have wagered for something certain and infinite, for which you have given nothing.

"Ah! This discourse transports me, charms me," etc.

If this discourse pleases you and seems impressive, know that it is made by a man who has knelt, both before and after it, in prayer to that Being, infinite and without parts, before whom he lays all he has, for you also to lay before Him all you have for your own good and for His glory, that so strength may be given to lowliness.—Pensée 233

And I suppose that is the primary fallacy of Pascal's Wager: it can mean little to nothing to people who have not thrown themselves into the pattern of thought that Pascal himself followed. It is unpersuasive since it builds on uncommonly held premises.

On a personal note, I find the Wager touching, even though or perhaps because, it is flawed. I love T. S. Eliot description of Pascal: "a man of the world among ascetics, and an ascetic among men of the world." A normal Christian considering the sacrifice he made would be content to contemplate the words of Jesus in Mark 8:34-38 (ESV):

And calling the crowd to him with his disciples, he said to them, “If anyone would come after me, let him deny himself and take up his cross and follow me. For whoever would save his life will lose it, but whoever loses his life for my sake and the gospel's will save it. For what does it profit a man to gain the whole world and forfeit his soul? For what can a man give in return for his soul? For whoever is ashamed of me and of my words in this adulterous and sinful generation, of him will the Son of Man also be ashamed when he comes in the glory of his Father with the holy angels.”

But not Blaise Pascal, mathematician. Instead, he converted Jesus' idea into an example of the relatively new field of probability. And while the problem was setup in a way that it is easily rejected as an apologetic of Christianity, it is still valid and useful as a mathematical puzzle.

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Exactly, Pascal's wager is something akin to 'the beginning of wisdom' not the end all convincing argument. – Peter Turner Jul 1 '11 at 14:10

He assumes that God would accept the sort of cold, calculating faith able to make such a wager seriously.

To me this would seem to be a significant problem. I'm definitely not an expert on Pascal, so you may wish to take this with a grain of salt.

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Any religious tradition promising infinite good or infinite bad to the individual would be desirable according to the wager - not just Chrisianity. At this point, a reasonable person needs to examine the religious traditions that meet this definition to determine which infinite reward is most plausible, and they may reach different conclusions than Pascal.

There is also the issue of this being a very weak, fake faith. Would God accept it? The reasonable response would be that a person recognizing both the value of Christian faith, and their inability to believe such a ludicrous idea, would pray fervently for Christian faith. A merciful God would grant faith to anyone who seeks it, and the once-disbeliever would receive the infinite reward for finite effort anyways. A lack of a merciful God would mean the unbeliever might (a) convince himself falsely to believe - finite loss, finite reward or loss depending on if you believe that believing is its own reward; or (b) waste a bunch of time praying and never come to believe, finite loss, finite loss or reward depending on if you believe that believing is its own punishment.

You can modify Pascal's wager to suggest a course of action for people coming from a different understanding of religion (e.g., non-Christian) than his: A rational person would act according to whichever set of different religious traditions that promise infinite consequences and do not conflict with each other, weighted by which set he thinks is most likely to contain a religion that will actually deliver the hoped-for reward (which religions are most plausible), and also weighted by how attainable those rewards are for someone who takes this approach (e.g., can a person starting from unbelief end by attaining the rewards?). I think it's a little more complicated than this, since you also have to weigh in punishments, but hopefully you get the idea. Obviously, defining this set of religions would take a lot of thought, research, and reasoning. It is also likely that reasonable people could come to very different conclusions about the "best" religion using a generalized form of the wager like this.

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On the issue of weak faith, Jesus didn't exactly set the bar high: "For truly, I say to you, if you have faith like a grain of mustard seed, you will say to this mountain, 'Move from here to there,' and it will move, and nothing will be impossible for you." I don't know if the sort of belief that the Wager might produce would be even that large, however. – Jon Ericson Jun 8 '11 at 0:18
Which is why (considering Christianity only) a prudent Wagerer would ask God to give them faith. He's merciful and all-powerful, right? He can give me whatever evidence I need to believe, or He can just "touch my heart" in some mystical manner and make me believe. The unbeliever prays something like, "I don't believe in You, God, but I don't want to go to Hell. If I am wrong and You exist, please give me enough faith that I can go to Heaven instead." If God is irked, I'm still going to Hell. If He's pleased, I may get rewarded. If he doesn't exist, I wasted a few seconds. – Ethel Evans Jun 8 '11 at 0:31
@JonEricson there's actually a bit more to the mustard seed than size: a mustard seed is quite robust, very spicy, and of course, you can plant it and grow mustard. – philosodad Jul 5 '12 at 15:51
@philosodad: That's an interesting suggestion. – Jon Ericson Jul 6 '12 at 23:36

I think his premise has at least one fault: `living life accordingly has everything to gain, and nothing to lose` I personally think that are lots of things to lose, like the freedom to think beyond the dogma and many others. However if we assume all the sentences correct, the conclusion is correct, no pure logic flaws I think.

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The idea of "nothing to lose" isn't a huge problem, since the wager still works with "a finite amount to lose". – Ethel Evans Jun 7 '11 at 22:43
You speak true, will rethink the matter – Valentin Radu Jun 7 '11 at 22:48
I don't think one necessarily loses freedom to think beyond the dogma. The fact that some refuse to is sad, but not the same thing. – Matthew Read Jun 8 '11 at 15:18

The logical flaw is the premis itself, starting with a false promise reaching any conclusion is logically crrect.it has two parts

1)A god exists AND

2)God that exists has set of rules to award points for some types of behavious and deduct points otherwise.

The way he viewed god is the same as the sheep would view a shpered. They would do as they were told to meet the end just as the same as the non-behaving sheep, yet they all end up tasting same to the sheperd.

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Suppose someone tells you that it has been revealed to him that there's an omnipotent being who is very secretive and wants to be completely ignored, and that if you live your life as if there's no God you'll be given an infinite reward after you die, but if you outwardly show any religiosity, you'll be eternally punished? This equally unprovable assertion is subject to Pascal's own argument, and thus cancels it.

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 Not entirely true. There are valid reasons to consider existing religions more plausible than the convenient theory of Joe on the street; this argument just requires the savvy philosopher to consider which religion is more reasonable. However, if this belief were to be argued for and evidence for it provided until it were equally well supported compared to existing religions promising infinite good or infinite bad, then it would cancel Pascal's wager as a logical argument for Christianity. – Ethel Evans Jun 7 '11 at 22:51 Pascal does not himself address the point of eternal punishment. Rather he suggests the infinite reward on offer makes betting on God worthwhile. Your novel definition of God may have problems if you use it for other purposes than to refute the Wager. It reminds me of René Descartes' evil demon. – Jon Ericson Jun 7 '11 at 23:59