# 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?

• 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?" Jun 8 '11 at 0:11
• @Jon added "if any" and changed the phrasing of the question for a bit more neutrality. Good point. 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. Jun 8 '11 at 0:54
• Alan Hájek certainly thought so. Jun 16 '11 at 10:54

## 15 Answers

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.

• 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
• @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 :) 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? 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? Jun 8 '11 at 0:08
• You missed one. He also assumed that there was only one God. Jul 1 '11 at 7:20

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 beliefs 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.

• Exactly, Pascal's wager is something akin to 'the beginning of wisdom' not the end all convincing argument. Jul 1 '11 at 14:10
• Do I understand you right that Pascal's Wager wasn't really meant as an airtight logical argument, but rather a strategy to get people to join his belief? His goal was not intellectual point-scoring, but simply persuasion, even if it involved some logical slight of hand? Feb 26 '15 at 21:14
• @JonofAllTrades: Because Pascal's thoughts were organized posthumously, it's hard to tell what he planned to do with the Wager. However the translation I have, it comes right after a series of thoughts on how we avoid contemplating our own mortality and seek any distraction. Pascal implies that we owe it to ourselves to take the possibility of life after death seriously if only because of the relative payouts. Not contemplating eternal things turns out to be a bad bet even if the odds such thing exist is very low. Feb 26 '15 at 23:58
• Well put. And you convince me to read or, at least, finally acquire a copy of Pensee. I take the wager to be the original use of probability as refutation of skepticism, as Berkeley used "materialism." And today, since thermodynamics, science has been forced to defend its body of knowledge through statistical mechanics and "probability" as well. Dec 2 '15 at 2:17

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.

• 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. ;-) Jun 8 '11 at 0:35
• @Dori: Isn't that a form of begging the question? The argument sets up a dichotomy between the monotheistic God and the possibility of no god. You are free to reject the argument because the dilemma it presents is false, but you are not free to reject it because it's false. (Unless there is some flaw you have not mentioned.) To a monotheist, there is one God and some (or rather all) people have false beliefs about Him. Diversity of belief results from a defect in humanity (i.e., sin). Please see my answer. Jun 8 '11 at 16:36
• @Dori: I think not. Suppose I offered my guests vanilla ice cream with their pie or just the pie. One of them replies, "Well, I'll have Neapolitan." In this context, the answer is a non sequitur. You can't have Neapolitan since the only available option is vanilla. That might be a valid answer in an ice cream shop, but it's not at a dinner party with limited flavors. My criticism of your answer is that Pascal has invited you to his dinner party and you are treating it like an ice cream shop. (Again, my answer to this question may be useful to you.) Jun 8 '11 at 19:33
• @Jon - ① I removed the parenthetical from my post since it really was just a throwaway. ② I think your analogy is flawed; my perception is that the situation is closer to that of multiple ice cream vendors, all of whom are telling me to buy their vanilla and that every other vendor is fraudulent. I can't buy them all, and saying I just want "vanilla" still means rejecting n-1 vanillas.
– Dori
Jun 8 '11 at 19:58
• @Dori: It saddens me that you seem unwilling to engage the question with your answer. Let's hear from Pascal himself: "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...." So none of the vendors sell the correct vanilla--all are wrong in one way or another. But that's entire beside the point. Jun 8 '11 at 20:18

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.

• 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". 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.
– user20
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.) Jun 8 '11 at 20:07
• Forth option: There are several gods. Why do everyone forget that option? 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. Jul 5 '12 at 15:46

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.

• 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. 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. 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. Jul 5 '12 at 15:51
• @philosodad: That's an interesting suggestion. Jul 6 '12 at 23:36

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.

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.

• The idea of "nothing to lose" isn't a huge problem, since the wager still works with "a finite amount to lose". Jun 7 '11 at 22:43
• 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.
– user20
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.

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.

• 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. 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. Jun 7 '11 at 23:59

Avoiding purpose-built problems, there is one basic error of context.

As a Christian, he buys into the monotheistic tradition. The wager ignores the potential disapproval of all the other gods for believing in the wrong one.

If believing in Baal is worse than not believing in the Lord, in the Jewish world, and vice versus in the Samaritan world, and you live between them, you might be best off ignoring them both.

Even if your god's aren't jealous, they are likely to place different and opposing requirements upon you, which you don't have to reconcile if you simply avoid the concept of worship altogether.

Another flaw that hasn't been pointed out yet is that there is a 50% chance that god exists. Pascal bases this on the fact that we can never know the probability.

Consider a lotto. There are two outcomes, win or lose. If you had no idea of the odds of this particular lotto, you wouldn't assume that the odds are exactly 50-50.

The same principle can be applies to Pascal's Wager. For those who believe that there is only a remote chance that god exists, the wager does not apply.

• I think this objection is confused about the purpose of the wager. And actually the odds wouldn't matter the way he structures it, because the benefits on one side are infinite and the costs of making the wager are low (all on his view of course). Dec 2 '15 at 2:28

If this life is all you have and will ever have it is unique and therefore has infinite value. The choice, assuming you accept the imaginary celestial side of the argument, is balanced: one infinity versus another. Moreover, there is no doubt that your current life does actually exist, and no evidnce whatever for the "infinity" of heaven. Pascal's actual wager would, then, have a person restrict the actions and pleasures of your one real, infinitely valuable life for the sake of a contradictory delusion, life after non-life.

One point that no one has mentioned but that I make use of in the following paper:

https://doi.org/10.4236/ojpp.2019.94030

Pascal came before the introduction of infinite sets. This is important because one can hold that there's no ultimate proof against God's existence, and also hold that the probability that God exists is zero. To do so, however, one must embrace the existence of infinite sets. Thus Pascal thought that zero probability implied impossibility. This fact about zero probability not implying impossibility is important to the Wager. For if we hold a position with zero probability, the expected payout for belief isn't necessarily infinite. Thus we could possibly have a finite expected payout for belief, but not be tied to an absolute proof against God's existence.

Myself I hold such a position - that the probability for God's existence (at least certain types of Gods) is zero, but there's no absolute proof against these Gods existing. It is also true that Richard Dawkins made the same mistake as Pascal in his "Spectrum of Theistic Probabilities". I won't go into large detail here, as you all can follow the link if you're interested in my work.

If one doesn’t believe that God exists then one doesn’t necessarily believe/ can affirm that God will punish (or forgive) people who don’t believe in him. If he exists he may be so forgiving that all of us we’ll live blessed ever after. But if he doesn’t exist then people who believed in him may have lost opportunities along the way. In other words you have nothing to lose by not believing.

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– J D
Dec 30 '19 at 17:15

There are a few fundamental problems with Pascal's wager.

(1) Which version of God one conceives of matters. The so-called Professor's God, instead of rewarding belief for belief's sake, rewards rationality. If you think you have sufficiently strong reason to think that God exists as to justify rational belief, then rationally, you should believe that he does; if you think you don't have sufficiently strong reason to think that God exists as to justify rational belief, then rationally, you should withhold belief. And that's what the Professor's God wants from you: believe or not according to the reason you have, or don't have, to think that God exists. And as it turns out, the usual game-theoretical result of Pascal's wager--that you're better off believing than not believing--gets reversed, if you don't think you have sufficiently strong reason to think that God exists as to justify rational belief that he does. In that case, if you do believe you lose out, while you gain if you don't believe. But...what would an actual God be like? Would he want you to believe in him no matter what? Or would he want you to believe in him only if it were rational to believe in him? You don't know--so you also don't know which way Pascal's wager militates. (2) Pascal's wager is an expected-value argument. (And, I will note, it does not matter whether the probability of Pascal's God's existence is 0.5 or is 0.000000000000000000001; as long as it's nonzero, Pascal's wager goes through.) But we know that expected-value arguments involving infinitudes--game-theoretic arguments involving infinitudes--have serious problems with them, and relying on one seems highly dubious. (3) We know that the form of the argument isn't one that we would normally rely on. If I said that there were powerful aliens who would destroy the Earth in a week unless you said to yourself, and meant it, "I submit to your [the aliens'] will." But suppose I further said that they would not only spare the Earth but would give you an elixir of immortality (and eternal youth and eternal good health--let's not forget the example of Tithonos) if you simply submitted yourself to their will (and they're telepathic, so they'll know). Nobody would do that unless he had really good reason to think that those aliens really existed! And nobody should rely on Pascal's wager unless he thinks he has really good reason to think that God exists already--which rather defeats the purpose of Pascal's wager in the first place.