Wednesday, September 5, 2007

Pascal's Wager


[taken from my forthcoming book for Quercus, Greatest Philosophers, out next month (and which, in my opinion, is a bargain at under £6 for a 200+ page, larger format, illustrated book. In fact I'm not sure it isn't too cheap.)]

According to Pascal, there are no rational grounds available to settle whether the Christian faith is true or false. Reason cannot settle the matter one way or the other. So should we believe, or not?

Pascal suggests we approach this question as if it involved placing a bet. We have two options: we can believe, or we can fail to believe. What do we stand to win or lose in each case?

Well, if I believe, and there is a God, then I win big. My reward will be eternal happiness. But what if there is no God? Then obviously I won’t receive that fantastic reward. But still, my loss is not so very great. Little more than those Sunday mornings I had to spend in church.

If, on the other hand, I fail to believe in God, and God exists, I lose big, for I face eternal damnation. Nothing could be worse. And if I fail to believe in God, and there is no God, then I win, but then I don’t win very much. Not much more, in fact, than those free Sunday mornings.

We can display these outcomes in a table, like so:

-------------------------------God exists-------------God does not exist

Believe in God-------------eternal bliss-----------small loss of worldly pleasures

Fail to believe in God-----eternal damnation---small gain in worldly pleasures

Now, assuming that we have no more grounds to suppose God does exist than to suppose he doesn’t, surely the rational bet to make is to believe in God. If I believe, then I will either win big or lose a little. If I fail to believe, then I either win small or lose big. Belief is therefore the more sensible wager, concludes Pascal.

Pascal claims belief in God is the rational choice even though there are no more grounds for supposing the belief is true than there are for supposing it is false. His claim sounds paradoxical, but, correctly understood, it is not. Consider an analogous case. You are diagnosed with a disease that will certainly soon kill you unless you receive treatment. There is only one treatment, and it has a 50% success rate. When the treatment doesn’t work, its side-effects are rather unpleasant. What should you do?

Clearly, the rational choice, assuming you want to live, is to undergo the treatment, despite the fact that you have no more grounds to suppose it will work than you have to suppose it won’t. Undergo the treatment and you will either win big or lose little. Fail to undergo the treatment, and you will either lose big or win small.

If Pascal is correct, the option of believing in God is similarly one it would be irrational not to embrace.

Objections to Pascal’s argument

Many have found Pascal’s argument persuasive, but it does run up against some well-known objections, including the following:

1. We cannot choose what we believe. First, some will respond, “But I can’t just choose to believe that God exists. It may be that, though I can see that belief in God is the rational bet, and so would very much like to believe it, I can’t manage it. Try as I might, belief eludes me.” Pascal acknowledges that we can’t usually choose what we believe. Certainly we can’t just make ourselves believe something directly, by a sheer act of will. However, he notes that even those who merely start off by going through the motions of religious belief often end up true believers. So if I also make myself go though the motions – if I regularly go to church and pray – I am likely to end up a true believer. This is exactly what Pascal recommends I should do.

2. Pascal’s wager is based on a dubious assumption. Pascal supposes that the arguments and evidence for and against God’s existence are evenly balanced. But are they? Most atheists would deny this. Many would say the arguments and the evidence overwhelming support the claim that there is no God. If they are right about that – if, say, the odds of God existing are not 50-50, but more than 99-1 against – then it is not quite so obvious that belief in God is the rational bet.

To illustrate, let’s return to the medical example outlined above. If you are told the probability that the treatment will succeed is not 50%, but much less than one percent, then it is not so clear that the rational choice is to opt for treatment. Especially as you know that you will almost certainly experience some nasty side-effects as a result. Under these circumstances, you might well calculate that you would be better off rejecting treatment.

3. Another dubious assumption. Third, we might question whether Pascal is right to assume all believers will be rewarded with eternal bliss and all disbelievers with eternal damnation. If I was God, I wouldn’t be particularly impressed by someone who believed in me purely on the basis of a self-interested calculation. Nor, if I had deliberately arranged the evidence for my existence to be equivocal, would I condemn to eternal agony someone who then failed to believe in me. Such punishment seems rather harsh, particularly from a God who is supposed to be supremely benevolent.

So Pascal’s estimation of how God, if he exists, will react to our belief or disbelief – that he will reward all believers with limitless bliss and punish all unbelievers with an eternity of hellfire – is certainly open to question.


Tony said...

I'm also not sure I agree that to 'Believe in God' entails only a 'small loss of worldly pleasures' if he does not exist. I would say that believing that the wonders of the universe and the Earth were created rather than that they evolved is to so diminish our existence that it renders life wholly meaningless.

The Barefoot Bum said...

One of the key features of Pascal's Wager is that the reward for correct belief is infinite, but the reward for correct disbelief is finite. Therefore, belief is statistically warranted no matter how small the actual probability is. Therefore we don't have to establish the actual probability at all; we need merely establish that it's not zero.

Of course, this argument ignores the possibility that the probability might be infinitesimal.

Pascal's Wager is noteworthy because it fails at every step: Each and every one of its premises is suspect, and its logic is invalid. It's the Worst. Apologetic. Ever.

cagliost said...

I think the best criticism of Pascal's wager is your number three: dubious assumptions of what merits heaven and hell.

People often miss it because they focus on god rather than heaven and hell. I find the following helps to illustrate it in believers' minds.

The important thing about Pascal's Wager is hell, not god. Belief in god could be substituted for belief in anything and the argument would still stand. But hell cannot be substituted because the argument depends on a large (to say the least) punishment. (I reckon you could get rid of the infinite reward and the argument wouldn't lose much force.)

"I don't know whether God exists."
"You might as well believe because otherwise you might go to hell."
"How do you know that hell exists?"

Pascal (and Christians who use the argument) are just asserting that we should believe without evidence or we'll go to hell. But what evidence do they have for hell?

Pascal's wager can therefore be used to justify belief in anything: reductio ad absurdum.

"My cult claims that you should believe the moon is made of cheese or you'll go to hell."
"Why should I believe that I'll go to hell if I don't believe the moon is made of cheese? Why should I even believe hell exists?"

Essentially: "part of my doctrine says that if you don't believe other parts of my doctrine, you'll go to hell."
"Why should I believe any of your doctrine?!"

I said Pascal's wager can be used to apparently justify belief in anything. Well, almost anything. It can't be used to justify belief in hell. "You might as well believe hell exists, because otherwise you'll go to hell"!

cagliost said...

(Perhaps there would also be a good point to mention to whoever you're trying to deconvert, that some atheists consider belief in god without evidence to be just as ridiculous as belief that the moon is made of cheese. It helps to illustrate what some believers don't realise: quite how ridiculous some people think their beliefs are.)

jikel said...

What about belief in the wrong god? After all, right at the top of the ten commandments, it says how jealous the Judeo-Christian god is. Maybe other gods are equally jealous (or worse!). Maybe not believing in any god is not nearly as bad as believing in the wrong god. And, if there are many (perhaps infinitely many) to choose from, but no way to tell which one is right, the likelihood of choosing wrong is very high (perhaps 1).

Psiomniac said...

I agree with those who have pointed out that for all we know, god has reserved a special circle of hell for those who hedge their bets.

I do struggle with this distinction between epistemic and ontological probability though. Is the boundary that clear? I would have thought that probability on the macro-scale is always an epistemological affair.

jeremy said...

I agree with cagliost that the third of the objections is the most fatal to Pascal's Wager. In this vein, take a look at can P.Z. Myers' hillariously cutting take on the the same subject. "Ah, the Argument from Imaginary Improbabilities. That's a dangerous game to play, because any fool can invent them, including me." It's really funny (I thought, anyway...)

Stephen Law said...

Many thanks for the link to P Z Myers. Mind you, I don't agree with you applying Myers' point to Pascal, 'cos the thing about Pascal's wager is that it only comes into play, according to Pascal, when reason cannot settle whether or not x exists. There's pretty good evidence that Myer's God doesn't exist, and none that he does, so Pascal would insist the wager does not apply.

The same would go for Cagliost's invented gods.

Paul C said...

From the Pensees:

"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."

From the top of my head:

"So, Mr Pascal, let me get this straight - you want me to believe in something, but you're incapable of knowing what exactly it is that you want me to believe in?"

I'll give that wager a miss.

jeremy said...

Fair point; I agree it doesn't quite apply. Of course, on what grounds Pascal could claim that Myers' god doesn't exist, but his god's existence is 50/50, I don't know. But you've already covered that objection.

cagliost said...

Ha ha, Paul C. I always find it amusing when, after someone rebuts the classical arguments for god, other people say "god is beyond reason" or "god is outside the universe". If it's beyond reason, then we don't need to bother rebutting arguments for god because they must already be unsound!

I disagree with Pascal's "[God] is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us." It would be possible for a god to have neither parts nor limits, but still be able to affect the universe with his magic powers, e.g. making bushes burn and talk. He could then explain who he was etc (and prove it with magic tricks), therefore not being "infinitely incomprehensible".

"the thing about Pascal's wager is that it only comes into play, according to Pascal, when reason cannot settle whether or not x exists." According to Pascal! I don't see why not. Even if there was very good evidence one way or another, one could still threaten the chance of hell if you believe the evidence.
Say there is an issue which the evidence is very clear about: is the moon made of green cheese? There is lots of evidence that it is not, and none that it is. My version of the wager still applies: "You should believe that the moon is made of green cheese, even though all the evidence says not, because you might go to hell if there happen to be magical forces which control the universe and send people to hell if they don't believe the moon is made of green cheese, regardless of the evidence of their own eyes, and despite this being rather improbable, infinite torture outweighs the improbability." I don't see how this is logically different from Pascal's wager: questionable premises (that hell exists, that non-believers in god go to hell, that non-believers in cheesy moons go to hell).

"There's pretty good evidence that Myer's God doesn't exist, and none that he does, so Pascal would insist the wager does not apply. The same would go for Cagliost's invented gods."
I didn't postulate any gods; indeed my point was that one doesn't need to. As for PZ Myers, there is indeed no evidence that PZ is god. But I disagree with you that there is pretty good evidence that he is not. I think there is no evidence either way. What evidence did you have in mind that PZ is not god?
Since there is no evidence either way (I think) it is okay (according to Pascal) to invoke the wager,
Should we be agnostic about whether or not PZ Myers is god? The atheist would say no: the onus to provide evidence is with the believers. The Pascalian wagerers would say we might as well. I think my green cheese example shows them wrong (and if Pascal's proviso of no evidence either way is fulfilled, then there is no evidence to encourage belief).

cagliost said...

The wager cannot work because of questionable premises, and questioning them exposes it. There's a simple formula: if someone uses the wager to try to justify belief in x, use it to justify belief in not-x. Person A asserts "non-believers in god go to hell, so you should believe" or "it might be the case that non-believers in god go to hell, so you might as well believe." Reply: "believers in god go to hell, so you should not believe" or "it might be the case that believers in god go to hell, so you might as well not believe."

Pascal's wager can therefore be used to justify belief in something, and belief in its negation. Contradiction!
Of course, while both sides assert that hell exists, believers would say that their assertion of what it takes to get in to hell is true, and the opposite one false. Believers typically just take it as read that belief is what it takes to get into heaven, just as they typically assume that god is good. Alternative versions of the wager involving cheese and whatnot help to illustrate that we have no grounds for believing these questionable assumptions.

Stephen Law said...

Hi Cagliost

You might be right that, whatever Pacal might say, his wager should work even with respect to Myer's God, if it works at all.

Not sure about that, though (need to think further...)

On your other point - that there's no evidence Myers isn't God, only an absence of evidence that he is. Well, I would have thought the following is evidence that Myers isn't God -

He isn't omnipotent, omniscient etc. Indeed, he's fallible (though smart!) and no doubt shows a great many human frailties. We also have very, very strong evidence that he's mortal, etc.

There's also indirect evidence - e.g. there's a case for saying the very notion of God is incoherent, in which case there's a case for saying that Myer's claim that he is God is incoherent. And so on...

You may say - well, this is not conclusive evidence, is it? - maybe he just pretends to have these human frailties, etc.

But that's not to say it's not strong evidence.

jeremy said...

Yes, I think Cagliost's point is that the criterion "There are no rational grounds available to settle x" is superfluous to the substance of Pascal's actual argument. I agree with this.

But if this criterion is removed, it obviously technically ceases to be "Pascal's Wager", since Pascal certainly thought the criterion necessary. This was the point that you correctly pointed out to me.

And the revised version of the Wager (Scott Adams' Wager!) only avoids objection (2). Objection (1) remains, but (3) is still the killer.

jeremy said...

Stephen: You certainly provide good evidence the P.Z. Myers is (alas) not a god.

Just a thought... What if I bypassed this objetion by claiming to believe in a God of exactly P.Z. Myers' description? He would appear fallible (but smart!), and no doubt seem to have a great many human frailties. However, I believe that he has the requisite magical powers, and omniscience and omnipotence too. It's just that they are hidden; his facade is a ruse.

In this new situation, there is now no evidence in either direction - for or against. So, Pascal would be forced to donate to P.Z. Myers, by his own logic.

Either that, or he'd have to deny one of the premises, such as P.Z. Myers is a god, P.Z. Myers will send Christians to a (worse) hell, etc.

And that is precisely the road left open to atheists with respect to the Wager. What's more, it's an easy road, since there really isn't any convincing evidence that Pascal's own theological assumptions are true.

amy said...

I think when Pascal meant God;s existent, you can even include the Polytheists religion. When you look at those religion there is always a main God(a supreme from the other gods)It is kind of like monothesists but difference is they have many gods for things. I think monothesists worships the same God but has different perspectives. It comes down either you believe you are in control of your life events (coincidence)or an external force (God) is influencing and has put to you to this earth for a purpose. for example I believe in God have you studied the biology? I mean God or Gods made all the little cells in our body to work together and it has defenses it seems God thought of every little thing, for me that's proof that God exists. I may biased but i support all the people who believe in something because it all comes down to faith and not wagering if God exists.