Sunday, November 07, 2004

Pascal's Wager

Pascal's Wager has got to be one of the worst philosophical arguments I've ever come across. It attempts to show that as a matter of practical reason, you ought to (try to) believe in God. (Note that it does not purport to be a proof of God's existence.) A basic sketch of the argument's logic follows:

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).

The first problem I want to highlight is that the formula in premise (3) should probably only apply to finite values. Strange and implausible things happen when you start playing with infinity, e.g. the St. Petersburg Paradox. [Update: more here.]

But the real problem is with premise (1).

I don't mean to suggest that it's impossible to receive an infinite reward, though that is one response that could be made - especially if one thinks theism is inconsistent and so could not possibly be true, or if one denies that infinity as such could actually exist. But those are not my complaints here. Rather, I think it is absurd for the theist to suggest that it's impossible for a non-believer to receive an infinite reward.

The problem is that they have set up a false dichotomy between atheism and Christianity. But of course there are all sorts of other theological positions one could consider here. For example, perhaps some god exists, but has a twisted sense of humour, causing it to send all believers to hell (for infinite suffering), whereas all non-believers will receive an infinite reward (heaven). This is extremely unlikely of course, but it at least seems possible (if traditional theism is). So, since it comes with a non-zero probability, we can run through an analogue of Pascal's argument which yields the opposite conclusion.

So premise (1) is false. This alone is enough to immediately refute Pascal's Wager, if treated as the deductive argument shown above. Perhaps one could modify it though, to form a slightly weaker version based on the premise that believing in God is more likely to yield infinite utility. I'm not sure how one would establish that though. Probably the best one could do here is try to offer an infinite-utility-involving scenario that sounds more plausible than any other. Consider the following from Jeremy Pierce (which I'm taking slightly out of context here):

What if God does exist and won’t reveal this to anyone with any certainty unless they’re genuinely seeking God through religious practices, and only then when they try hard enough and seek in the right ways (whatever those ways might be)? If this is true, then could a nonbeliever be innocent in not seeking God? One might argue that a nonbeliever needs to have pursued God through the worship, prayer, reading of scriptures, genuine efforts to see and evaluate oneself in the way a perfect God would want us to, entering into a community of faith to see life through the eyes of faith, and so on. Simply learning about religion isn’t enough, because that’s not what God is looking for in us. Only if we enter into religious practices, genuinely seeking God, would God give us this assurance. If this is possible, then it may be that the atheist or agnostic doesn’t have all the evidence that a theist has. This is an interesting possibility that should at the very least give pause to those who think the lack of convincing arguments for believing in God is a good enough reason for not believing in God.

It sounds vaguely plausible that God might want that. But I don't think a truly benevolent deity would impose an infinite punishment on honest non-believers. I don't find that even remotely plausible.

And consider this alternative scenario: What if God does exist, and happens to value epistemic integrity and rationality? He wants people to believe what they are epistemically justified in believing, rather than blindly embrace dogma. Perhaps some theists are justified in their beliefs, due to the 'special evidence' God reveals to them. But certainly many atheists are also justified in their beliefs, given the evidence that's available to them. So God is happy with all these epistemically responsible people, and rewards them all appropriately. However, he is repulsed by the opportunistic dogmatist who ignores the evidence and irrationally adopts faith hoping for salvation. So God does not reward such irresponsible people. Therefore, if this were true, one should follow the evidence and ignore all these 'pragmatic' arguments for belief.

I think my honest deity sounds at least as plausible as the traditional theistic one, and probably more so. So, as a matter of practical reason, you ought NOT believe in God (presuming this is what the evidence otherwise advises), lest ye suffer the wroth of mine honesty-besotted deity!

Lastly, one might argue that - quite apart from the silly practical advice of Pascal's Wager - atheists have an epistemic obligation to seek out all the evidence for theism, including the special 'experiences' that we are told occur only to those 'inside' the worldview. To quote Jeremy again:

It's easy to find different perspectives that compete to explain our experience. The question becomes how to look at those different perspectives and judge between them about what we should believe. It may be that you can’t understand the theistic framework without having tried to live, think, and feel from that orientation. The claim would then be that someone who hasn’t done this hasn’t given oneself the opportunity to look at the evidence in a balanced way.

Given the vast variety of worldviews on offer these days, it would be absurd to suggest that one has an unconditional epistemic obligation to 'try them all out', just in case doing so might yield some new/unexpected evidence. Surely we should only go to such extreme lengths if we have some prior, independent reason to find the worldview plausible.

Suppose I believe that Santa Clause is real. Moreover, he is omnipotent (how else could he deliver all those presents on time?), omniscient (he knows whether you've been naughty or nice) and at least moderately benevolent too (he gives us presents!). Now, after you die, you get to turn into an elf and spend eternity in joyful union with Santa - but only if you believe in him! If you don't believe, your rotting corpse gets fed to the reindeer, and your soul's energy is captured within a special battery to help light up Rudolph's red nose. Now, I know this all sounds rather silly, from your limited worldview, but trust me: if you just take a leap of faith, and immerse yourself within my merry religion for a while, you too will see the light.

Presumably nobody feels any compunction to take me up on my offer. We have no epistemic obligation to try out a belief in omni-Santa. But I find Christianity no less implausible. (Really, I don't. I could go along with some sort of deism, perhaps, like the one I described earlier. But theism, with its revealed texts and lovingly vengeful God, really does strike me as ludicrous. No offence intended to any theists who might be reading this - your circumstances and evidence may, after all, differ from mine.) So, absent any compelling reasons to the contrary, the rational atheist surely has no epistemic obligation to take theism seriously. If anything, he's obliged not to. (See also Clayton's comments in the linked-to post.)

Update: What I'm here calling "Pascal's Wager" differs from Pascal's original argument. For a reconstruction of the latter, see Siris.

Update 5 Dec: John Holbo sums up (something like) my central objection here in a single sentence: "What are the odds that any one possible one true jealous God is the one true one true jealous God, after all?"

7 comments:

  1. I've been working on a little story about a society that was a lot like ours, but a little more rational. The people there were just a little bit better than us at figuring out what was best for them and acting on those beliefs. Since you and Brandon have brought up the topic, I've decided to rush my story into print. 

    Posted by Blar

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  2. Genius to the rescue

    You still haven’t sunk the argument.

    (3) Strange and implausible things happen when you start playing with infinity.

    The st petersberg paradox is not a paradox it just brings into the matter various issues of marginal utility of a dollar and "non repeatable bets".
    Surely you are not saying that infinity*1 is less than 5*1 the fact you cannot exactly place infinity is of no concequence at all since we only want to know which is greater.

    (1) I think it is absurd for the theist to suggest that it's impossible for a non-believer to receive an infinite reward.

    The issue I see here is not in relation to the magnitude of the “reward” offered after death it is more to do with the concept that the universe exists for much longer than a human lifetime. On earth your life will be fairly short if there is an afterlife there is no reason to believe it would ever end – thus you have your infinite (or just very large) difference even if afterlife offers no more than current life.

    “For example, perhaps some god exists, but has a twisted sense of humour, causing it to send all believers to hell (for infinite suffering), whereas all non-believers will receive an infinite reward (heaven). This is extremely unlikely of course, but it at least seems possible (if traditional theism is).”

    It’s very inconsistency allows us to write it off as “less likely” and thus playing the odds assume the opposite.

    “ So, since it comes with a non-zero probability, we can run through an analogue of Pascal's argument which yields the opposite conclusion.”

    But since the two arguments are offset against each other that argument is nonsense. UNLESS you think it is MORE likely or exactly as likely that god is “weird sense of humour” as not.

    “So premise (1) is false.”

    You failed to prove it you just shed doubt upon its perfection - classic but very weak form of attack.

    “ This alone is enough to immediately refute Pascal's Wager”

    ermm heh your claims are getting stronger - you need A LOT more proof to refute something than that.

    “It sounds vaguely plausible that God might want that. But I don't think a truly benevolent deity would impose an infinite punishment on honest non-believers. I don't find that even remotely plausible.”

    There is no need to assume true benevolence – true benevolence would by definition result in good things for everyone no matter what and thus its probability would become a non issue for the purpose of this debate.

    “What if God does exist, and happens to value epistemic integrity and rationality?”

    Being religious does not mean that you are being irrational or embracing dogma or doing anything other than potentially accepting Pascal’s wager and probably accepting some basic principles. One could argue that those principles are the things that god hates 9for example if god hated people believing in Jesus or saying they are a Christian then the Christians would have trouble or if he hated them praying or visiting Mecca the isalmists would have trouble but it seems somewhat irrational that he would have a particular hatred for such things even if the religion was wrong. And that is what it would take for your argument to have weight.

    “So, as a matter of practical reason, you ought NOT believe in God (presuming this is what the evidence otherwise advises), lest ye suffer the wroth of mine honesty-besotted deity!”

    hehe… I’ll take that under consideration.

    One of the other pieces of logic is that god might vaguely favour the existence of the correct religion. If he does indeed have an effect on earth – if that is the case you can assume that one of the major religions is probably at least slightly related to the truth – giving them a statistical advantage over something you might make up on the spare of the moment.

    >“Lastly, one might argue that - quite apart from the silly practical advice of Pascal's Wager - atheists have an epistemic obligation to seek out all the evidence for theism, including the special 'experiences' that we are told occur only to those 'inside' the worldview.”

    Go atheists... good for them. You are welcome to make the sacrifice. Religion has all sorts of twisted implications for example if people are saved only if they repent beating a person until they repent and killing them before they change their mind might be “a good thing” for them – even if it damns the person who actually did it to hell.
     

    Posted by GeniusNZ

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  3. Genius, thanks for your comments. I think some of them are rather confused, however.

    For example, you say: "You failed to prove [premise 1 false] you just shed doubt upon its perfection - classic but very weak form of attack."

    Your objection simply isn't true. Recall that premise 1 says "There is a non-zero possibility of receiving an infinite reward if and only if you believe in God". But I showed that there is a non-zero possibility of infinite reward even if you don't believe in God. It logically follows (from the meaning of "only if"!) that premise 1 is false. This is no "weak form of attack". This is a counterexample - an outright refutation of the premise in question.

    Also, your selective quotations lead you to attack a straw man of my claims. You quote "This alone is enough to immediately refute Pascal's Wager", and then complain: "you need A LOT more proof to refute something than that". But you cut me off mid-sentence. What I really said was: "This alone is enough to immediately refute Pascal's Wager, if treated as the deductive argument shown above." And my claim there is quite correct. If a deductive argument is shown to have a false premise, then it is shown to be unsound. I showed that premise 1 is false. It immediately follows that the argument containing it is unsound. Nothing more is needed.

    You then talk about "offsetting" the various alternative scenarios against each other. This is pretty much what I said myself; we can "form a slightly weaker version based on the premise that believing in God is more likely to yield infinite utility." Perhaps you just didn't read my post closely enough. It certainly seems odd that you would object on the basis of something that I discuss myself later in the post!

    "There is no need to assume true benevolence"

    The usual definition of 'God' includes not only omnipotence and omniscience, but also moral perfection. This brings up the problem of evil, of course, as you note. But that's a problem for another day. You seem to be suggesting that theists believe in an evil/malicious deity who unjustifiably punishes those who don't believe in him. I've never met anyone who believes in a God they consider evil (or even imperfect). While this isn't a logical objection to your point, it does suggest some reason to doubts its practical import (since it doesn't really seem to fit into the usual dialetic of the argument). But usual dialectic aside... well sure, such a malicious God is possible - but still doesn't strike me as plausible.

    "Being religious does not mean that you are being irrational"

    I never suggested that it (necessarily) does. Indeed, in that very same paragraph I wrote: "Perhaps some theists are justified in their beliefs, due to the 'special evidence' God reveals to them. But certainly many atheists are also justified in their beliefs, given the evidence that's available to them."
    The point is that if you are justified in your atheistic beliefs, and have no reason to think that God exists, then it would be epistemically irresponsible for YOU (in *that* situation) to try to believe in God against all the evidence. So a God who values epistemic responsibility might well punish such an opportunistic atheist-turned-'believer'.

    "god might vaguely favour the existence of the correct religion"

    Yeah, not a bad point that one. But I don't think such a 'statistical advantage' can really win out over the 'conceptual advantage' of an honest deity that actually makes more sense. ;)
    Also, why only 'vaguely'? I would expect him to favour his 'true religion' hugely, or not at all. No religion seems to be receiving any overt divine aid, so the latter looks more likely to me! 

    Posted by Richard

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  4. Also, you cannot explain away the St. Petersburg Paradox by appealing to diminishing marginal utility, for the reasons explained in the linked-to encyclopedia article. (In short, you can alter the game so that the award money increases exponentially, to match the 'marginal utility' effects.)

    "Surely you are not saying that infinity*1 is less than 5*1 the fact you cannot exactly place infinity is of no concequence at all since we only want to know which is greater."

    I'm not sure I understand that sentence or its relevance to this discussion. Of course I am not saying infinity is less than 5. What I am saying is that it could be pragmatically rational to forego a high-stakes game with an extremely small chance of winning an infinite reward. The "expected value" of such a case is perhaps best not described as infinite after all. (Economic models are, after all, just that - models.) Perhaps you're better off keeping your finite utility of living a happy atheistic life, rather than paying the costs of believing in a God you are almost (but not quite) certain does not exist. If I'm correct in this, then it removes the motivation for Pascal's wager. 

    Posted by Richard

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  5. I don't think you generally destroyed Pascal's Wager (Pascal didn't, I think, suggest that you were staking very much -- after all, you only have to go to church from time to time and do the occasional good deed, well, okay, and it seems adopt conservative politics, a rigid morality and a rather unpleasant attitude to everyone who disagrees with you, and even if the reward were not infinite, it would still be very much greater than what you would have to forego to gain it) but I did like your honesty-seeking deity. That's the sort of thing I was hinting at on the evangelical outpost. Pascal's Wager only works if there is only one God and he is precisely as the evangelical outpost guy suggests. So you have to take *two* wagers.

    How does Pascal choose a God from those possible, if several or all of them offer infinite rewards? What if God is wicked and will reward the wicked? Pascal ignored that the gamblers must gamble that God is in fact benevolent.
     

    Posted by Dr Zen

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  6. Well, if I were to gamble on any God, it would be a benevolent one. But the problem is, the Christian God is not benevolent. Rather, Pascal assumed that gamblers must gamble on a petty, insecure, self-absorbed God. (Why would anyone believe God has such unbecoming characteristics?) I think the 'honest deity' I proposed sounds much more moral than the Christian one. (Of course, a perfectly benevolent deity would reward everyone, so there'd be no need to 'gamble' at all!) 

    Posted by Richard

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  7. Pascal: "It is incomprehensible that God should exist, and it is incomprehensible that He should not exist[...] But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions."(Pensees 230-33)

    I know you said you aren't dealing with Pascal's actual argument, but isn't some context concerning what he felt the situation man finds himself in necessary in order to charitably approach his argument?

    His wager is not aimed by any means to someone who has no concern for religion, but to those who cannot make up their minds, for those who see both sides as compelling and yet still not convinced either way. For someone in such straits isn't such a wager maybe slightly pragmatic? He says, "Seeing too much to deny and too little to be sure, I am in a state to be pitied." (Pensees 229)

    Thank you.

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