March 2, 2011

Sobel on Pascalian Wagers

In the 13th and final chapter of his book, Sobel discusses Pascalian wagers. According to Sobel, there need not be anything wrong with the practical reasoning involved in a Pascalian wager. In addition to defending this controversial claim, Sobel must explain how, if the Pascalian reasoning is correct, he can be justified in holding on to his atheism. As the chapter unfolds, both contentions are defended as a package. In general, for reasons to be explained below, I disagree with Sobel's approach here. However, I do agree with him on one thing: religious faith is more a matter of practical than of theoretical reason. In this post I will explain Sobel's approach and my reasons for disagreeing with it, and in the next I will lay out my own view of the interplay of theoretical and practical reason in religious faith.

Pascal's original wager went something like this: if you believe in God and you are right, you gain eternal bliss. If you believe in God and you are wrong, you lose little or nothing. If you don't believe in God and you are right, you gain little or nothing. If you don't believe in God and you are wrong, things will go very badly for you. (According to Sobel, Pascal himself regards heaven as infinitely good, but hell as only finitely bad.)

Now, the first problem we face is that we can't just decide to believe things. For now, though, imagine we could. It seems, in Pascal's case, that it would then be practically rational to believe in God, as long as we think that there is even the slightest (epistemic) possibility of his existence.

The trouble is that it seems that it is very difficult, if not impossible, for a rational agent to get into a doxastic state that is this simple with respect to God. After all, most people are aware of many different religions, each of which claims that God has a different policy with respect to reward and punishment, and we can dream up even more possible policies a God might have. So we shouldn't just hold the simplistic view that if God exists he rewards those who believe in him and punishes those who disbelieve. (In fact, I should note, no such reasoning could ever get one to Christianity, since, according to the New Testament, even demons believe in God [James 2:19].) Furthermore, as Sobel notes, given the sort of character traditionally ascribed to God, it seems likely that he might frown on epistemic irresponsibility - that is, he might want us to believe according to the evidence.

To this sort of problem, Sobel adopts a three-pronged response. First, he adopts strict subjective Bayesianism, which has the consequence that perfectly rational individuals could differ radically in the credences (subjective levels of confidence) they attach to the same proposition, even if they have exactly the same evidence. Second, he applies the same principle to values - that is, he holds that two perfectly rational individuals could attach radically different values to precisely the same outcome. Finally, to come back to our worry about the involuntariness of belief, Sobel holds (with perhaps most philosophers) that it is possible for us to effect what we believe only indirectly, and that in order to include an alternative in a decision problem, we have to believe the option is open to us. That is, I have to believe that if I were to embark on a project of self-manipulation with the aim of bringing it about that, for example, I believe in a certain sort of God, I would succeed. Both beliefs about which options are open and the actual fact of which options are open will vary from person to person.

It should now be possible to see how there could be someone who was in a situation where Pascalian reasoning could recommend adopting a course of self-manipulation with the aim of bringing about religious belief. What is required is simply that the individual's values and credences be distributed among her options in such a way as to recommend that course. Sobel further recommends that, rather than standard Cantorian infinities, our decision theory ought to use hyperreal or surreal infinities. If it is possible for an agent to assign hyperreal infinimal (and/or infinitesimal) values to outcomes, then it will even be possible to compare different infinite values and disvalues without the math blowing up. (Incidentally, Sobel's appendix on the use of hyperreals in decision theory is surprisingly readable, given the difficulty of the subject matter.)

So why is Sobel an atheist? Well, he never says whether he believes that becoming a theist is among his options. However, he does say some other interesting things about his own position. The only point on which Sobel is quite clear about his own views is on pp. 525-526, where he indicates that, because he values theoretical rationality, he attaches a very significant (possibly infinite) disvalue to the sort of self-manipulation involved in the Pascalian scenarios. He also makes a couple of additional suggestions as to states atheists might be in which would lead to their rationally choosing not to believe, even where belief is an option for them. The first is that atheists may either attach only a finite value to heaven and finite disvalue to hell, or else may assign these hyperreal infinimal values/disvalues, while also assigning infinimal values/disvalues to some earthly goods and evils. Sobel writes, using the pronoun in scare-quotes to indicate the subject of the case under consideration, not necessarily himself,

'I' would trade away a small chance for eternal bliss for 'myself' in order that 'my' dog not be tortured or 'my' daughter mutilated. Indeed, leaving chances out 'I' would make a straight trade at least in the second case. So 'I' do not value eternal bliss incommensurably more than every personal good" (p. 527).

Second, the atheist might be convinced that, if God exists, he may reward "uncalculated, unstrategic faith," but not be a fan of Pascalian wagers, due to their selfishness, or some such (p. 528). Such an individual would be convinced that it would be better for him to believe, but only if it happens naturally, not if he manipulates himself into it. The Pascalian wagers would therefore not recommend a course of self-manipulation to him.

Sobel is thus in a position to conclude that the Pascalian reasoning could recommend belief to some, but not others.

My objection is to Sobel's radical permissiveness in the assignment of credences and values. In particular, I simply can't accept the view that it could ever be practically rational to be theoretically irrational: one always has most (subject and objective) reason to manage one's beliefs/credences properly. As a result, it could never be practically rational to engage in the kind of self-manipulation recommended by (Sobel's rendition of ) Pascalian wagers. This will further imply that, at least if it is always practically rational to obey decision theory, not just any distribution of values can be rational. This is because, as Sobel has shown, given some distributions of values, decision theory recommends self-manipulation.

Basically, the bottom line is that I, unlike Sobel, think that Clifford won the Clifford-James debate quite decisively: it is wrong always and everywhere to believe on insufficient evidence. Theoretical reason ought to be autonomous. Nevertheless, as I said, I do think that practical reason plays the major role in religious faith. In my next post, I will try to explain how this can be.

(Cross-posted at The Prosblogion)

Posted by Kenny at March 2, 2011 5:10 PM
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Comments

I think your excellent analysis leaves one with the very clear conclusion that the Wager is a matter of economics rather than theology.
If religion is reduced (...or magnified if one wishes) to game theory, then what we have is a satirical story about Nathan Detroit and Guys and Dolls... and Einstein's observation that God does not roll dice is shown to be very wrong.

In my opinion, the problem with the Wager is that the logic is capable of being extended to everything, not just God.
Hence, since there is a extremely small probability that I might fall off the edge of the Earth shaped like a flat pita bread, I ought to have a certain amount of credence invested in Flat Earth Theory just to be on the safe side.
(Unless we assert that all beliefs must be all-or-nothing... which is pretty hard to accept if we apply Bayesian probabilities to the question and always allow for future data to influence our judgments.)

Posted by: Montag at March 9, 2011 4:18 AM

Should gamers hold a race for faith-horse, rationalist,naturalist and skeptic and faith does not show up, she loses and then one of the others will win the race.So, Pascal's Wager can not even begin!
Why then posit the supernatural when first one has to give evidence for it. To claim absurdly the promise of Heaven or otherwise, then is irrational!
Pascal is trying to pull a fast one whilst we rationalists point to the crowd that faith is a no show!
One need not even bring in other religions and so forth to calculate this pseudo-query. No a priori but instead mere observation warrants crediting Pascal with this scam.

Posted by: Carneades of Ga. at February 6, 2012 1:25 AM

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