Betting Against Blaise

You know, I'd probably post more often if I didn't have this compulsion to make such long posts when I did. Maybe I should work on trying to come up with things to post about that I don't feel like going on about at such length...

Anyway, this particular post was belatedly inspired by a certain month-old post at Pooflingers Anonymous, and certain comments thereto. Essentially, I feel like writing something about Pascal's Wager.

Probably everyone reading this has heard of Pascal's Wager. In its original form, in Pascal's Pensées, it went as follows:

"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 ... you must wager. It is not optional. You are embarked. Which will you choose then? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is."

Pascal's Wager has since cropped up over and over again in different clothing (the Pooflingers post I linked to above, for instance, was basically about a variation on Pascal's Wager), but it all boils down to the same essential argument. Basically, either God exists or he doesn't. If you believe in God, then you have infinite gain if He exists, and lose nothing if He doesn't. If you don't believe in God, then you still lose nothing if He doesn't exist, but if He does exist, you don't gain anything either. So it's clearly to one's benefit to choose to believe in God.

As I said, everyone reading this has probably already heard of Pascal's Wager, and I doubt there's anything really new I can bring to the table on the subject. Still, though, I guess there's no harm in posting my feelings about the Wager. And my feelings are, in summary, that the arguments most often marshalled against Pascal's Wager don't really hold a lot of water--but there are other, much stronger, arguments that don't get raised as often, and that deserve more attention than they get.

(Actually, though, arguing against Pascal's Wager may be a bit pointless, in that I don't know that anyone really believes it to begin with. I doubt anyone truly holds to religious beliefs solely because of Pascal's Wager--including Pascal himself, who I'd bet already believed firmly in God before concocting this "wager" as a post hoc rationalization. Still, the human capacity for tortuousness of thought can be astounding, and I've been surprised before by discovering that people actually believed things I'd assuming nobody remotely sane could really give any credence to, so who knows?)

One of the most common objections to Pascal's Wager is that it would apply just as well to other religions besides Christianity. What if it's not the Christian god that exists and is doing the judging, but the Muslim god, or the Jewish god, or a Hindu god, or, heck, Ratu-mai-mbula, and choosing to believe in the Christian god gains you nothing at all? For that matter, what about the different Christian denominations, many of which believe that only members of their particular denomination of Christianity will be saved, and all others are going to hell? This objection, though, seems to me to be beside the point. Pascal's wager doesn't depend on the chances of Christianity--or any specific sect within Christianity--being true being precisely 50%, or any other particular value. Provided you accept the premises, and accept that there's some finite chance, however small, of the Christian God existing, it holds just as well if there are a number of other gods and potential valid belief systems out there. Of course, Pascal's Wager would give no guidance in choosing which god to believe in, but it would still seem to imply that choosing to worship some god is better than choosing atheism, even if you choose your god at random.

Then there's the objection that a belief based on a pragmatic argument like Pascal's Wager isn't true faith, and may not be sufficient for salvation. Closely related is the objection that you can't really believe in something by just deciding to do so. These, too, though, are rather beside the point. They require the assumption that God cares why you claim to believe in Him. That may seem like a reasonable assumption, but it's clearly not one that Pascal made--in fact, for Pascal's Wager to make any sense, one has to assume that he assumed just the opposite, that God doesn't care why you claim to believe in Him, as long as you do. If you want, you can easily make this assumption explicit--just replace "God" in the statement of the Wager with "a God who rewards those who profess belief in him, regardless of their motivations for doing so". There you go. A version of Pascal's Wager that's completely airtight--at least against these specific objections.

The fact is, it seems to me that if you accept the premises, Pascal's Wager is actually a pretty good argument.

I don't accept the premises.

For one thing, there's the implicit premise that the probability that God exists is finite--and not just any God, but the kind of God required for Pascal's Wager to work. Certainly that premise could be argued against; one could say that since there are infinitely many other equally unfounded possibilities out there, the probability could in fact better be regarded as infinitesimal. This argument could, perhaps, be countered by claiming that the possibility of the Christian God existing is stronger than that of some other arbitrary being, because after all some people claim to have had visions of the Christian God, and there's no such testimony regarding most of the rest of this infinite array of possibilities. The chain of counterarguments could be followed farther--or we could dismiss the whole business with the assertion that trying to define a probability for the existence of God is meaningless in the first place, which I'm not at all sure isn't true--, but I don't see a point in dwelling on this; the implicit premise of a finite probability for the existence of Pascal's God may have its weaknesses, but the two explicit premises are weaker.

"If you gain, you gain all." All what? What does this mean? Pascal himself went on later in the Pensées to define "all" as "an eternity of life and happiness," and as "an infinity of an infinite life to gain". But that's a bit misleading. The implication seems to be that an infinite existence of bliss is, well, infinitely longer than a mere earthly life, and therefore worth infinitely more. So the value of what you potentially get by belief in God is literally infinite. But that only makes any sense if unbelievers get only their earthly life, and nothing beyond it. Even then, one could argue that there's a point of diminishing returns, that an infinitely long existence isn't really infinitely better than a few decades, just as someone with an infinite supply of money wouldn't be infinitely better off than someone who earns ten thousand dollars a year--he'd be much better off, sure, but there's not really any functional difference between having as much money as you want and having, say, five quadrillion dollars. I'm not sure I'm convinced that there is such a point of diminshing returns in regards to length of existence, but in any case it doesn't matter, because that's not what most religions really believe anyway. The Jehovah's Witnesses may say that only believers will be resurrected, and that infidels will be left to death and oblivion, but as far as I know they're pretty much alone in their belief. Most Christian denominations, certainly including the Catholicism Pascal followed, believe that everyone, believer and unbeliever, will live forever, as a spirit if not in the flesh--but that the former will live in Heaven and the latter in Hell. Most people might agree that living in bliss in Heaven would be better than eternal torment in Hell (though there are always the wags who insist that they'd prefer the company in the latter establishment). But even if Heaven is far better than Hell, is it really infinitely better? Is that even a meaningful question?

Still, regardless of how much or how little one might have to gain by believing in God, Pascal's Wager would still work as long as there was anything to potentially gain--as long as you accept his other premise that you don't have anything to lose.

That premise is the one I have the biggest problems with.

We lose nothing by believing in God? Well, maybe not, if all "believing in God" means is saying "I believe in God", and thereafter living your life however you want to. Heck, I can do that now. Look: "I believe in God." Woo hoo! I'm saved!

But I don't think that's what Pascal really meant by "wagering that God is", and it's certainly not what modern proponents of Pascal's Wager have in mind. Some of the utterances of the more evangelical branches of Christianity may seem to imply that all you have to do is say some special prayer to verbally accept Jesus Christ and that's that, but in general I'm pretty sure the kind of belief in God most Wager proponents have in mind involves a little more than that. It involves acting according to your belief. Going to church. Living your religion's commandments. Following the dictates of your ecclesiastical leaders.

And that can certainly mean a lot of loss. Loss of time, in attending pointless religious meetings. Loss of opportunity, in things and circumstances avoided solely because of religious dictates, that might have led to pleasureable and/or valuable experiences. Loss of personal growth and progress in directions forbidden by the church but with no other good reason to avoid. I certainly don't consider all that "nothing".

Now, to be fair, sometimes Pascal's Wager is stated in less absolute terms, and it's admitted that one may have something to lose by believing in a nonexistent God--it's just asserted that the small amount a mistaken believer loses is far outweighed by what a justified believer gains. But losing a little isn't good enough. For Pascal's Wager to work, either what we have to win must be infinite, or what we have to lose must be nothing. Otherwise, if the probability of God existing is small enough, it completely washes out the greater magnitude of the potential reward versus potential loss for believers--and, with all the other religions out there, and the lack of evidence for any of them, let alone one that happens to include a God who rewards people just for professing belief in him regardless of their motives, there are good grounds for regarding that probability as really, really small. Besides, I'm not so sure that what's lost is all that little. If we only get one chance at life, and we're throwing away some of what we could do with that one chance, and losing those possibilities forever...well, I'd say that's a pretty big loss after all. In fact, if we're really willing to talk about infinite gains for justified believers, it could arguably be just as valid to refer to the waste of a unique lifetime as an infinite loss--which would be enough to offset even that infinite gain, especially since the gain seems to have a much lower probability of coming about.

Hmm...I said earlier in this post that if one accepts the premises, Pascal's Wager is a good argument, and that the existence of other possibilities besides those of the Christian God or no god doesn't really matter much. Actually, now that I think about it, that's not quite true. The existence of other religions, and the potential existence of other gods (that is, if one concedes the potential existence of the Christian god), really doesn't matter, but there is another possibility that wreaks havoc with the Wager. What if God exists, but he punishes believers and rewards disbelievers?

Again, this isn't something I claim to be wholly original; I have seen this possibility raised before, but only briefly and apparently as a joke. I think it deserves more attention, though, because it really does demolish Pascal's Wager, even if you accept the premises. If there's a God that punishes the believers and rewards unbelievers--let's call him Cranky God--then Pascal's Wager falls apart entirely. Because then the unbelievers have the same potential gain as the believers, and unbelievers have a chance of "gaining all" just as the believers do.

But Cranky God is silly. Nobody really believes in Cranky God, do they? Well, no, of course they don't. So what? We have exactly as much evidence for Cranky God as we do the God of Christianity. If one accepts that there's a chance the Christian God might exist, there's no reason not to accept that there's a chance Cranky God exists. Even if one insists that the Christian God is more likely to exist than Cranky God, as far as the raw expectation values of reward go it doesn't really matter. As long as both probabilities are finite, either believing in Christian God or believing in no god (and thus being potentially rewarded by Cranky God) gives you an infinite expectation value for a reward, since infinity times any finite number is infinity.

And heck, disbelief gives a chance of reward from Cranky God without all the losses that belief in Pascal's God would accrue. Sounds to me like that's the better deal.

So there you go. All hail Cranky God!

No, wait, don't. After all, He'll punish you if you do.

Blaise, ol' buddy, you may have been a brilliant mathematician, and you deserve a lot of credit for your pioneering contributions to probability theory and all that...but I don't think I'll be taking your wager.

Nothing personal.