Either God is tricky, or maybe probability is.
Pascal’s Wager: Say there’s only a small chance God exists. If you are an atheist but God does actually exist, He will send you to hell for eternity. This is infinitely bad. Therefore you should believe in God on the off-chance he does exist, since a small chance of something infinitely bad is worse than the alternative.
Believe in Pascal’s Wager? Have I got a deal for you! says if you believe it, you should send Alex Tabarrok money because he will put in a good word to God for you. Hey, there’s a small chance he has a direct line to God, which yields infinite utility (or avoids hell’s infinite disutility).
FWIW, I’m thinking the paradoxes in this sort of arithmetic always happen when you start doing addition/multiplication distribution across those darn infinities. Like on the third page Tabarrok starts talking about p1*Inf – p2*Inf = (p1-p2)*Inf. That’s shady shit.
I don’t like the SEP entry on it, because there’s too much history and it talks too much about the boring stuff like the oddness of a decision to believe or disbelieve something.
I read (well, browsed) the Taddock and Osterdal papers earlier, having been referenced in Andrew Gelman’s post on one-sided bets.
It seems to me that Pascal was not so much trying to prove:
(1) It is irrational to disbelieve in God.
as trying to show:
(2) It is rational to believe in God.
Philosophers, et al., treat it as (1), of course, but I think Pascal may have been trying to give intellectual comfort to those who were wavering in their commitment to belief in God because of the social and intellectual pressures of French rationalism (including himself, natch).
But treating it as (2) removes silliness like Taddock and Osterdal’s (that is, it would be silly to send Taddock any money). (2) doeesn’t imply (1), and isn’t inconsistent with “It is rational to disbelieve in God.”
The SEP (in the boring bits you disliked) takes this up a bit, in its discussion of Pascal’s recommendation to those who have some measure of belief but are tempted to disbelieve. That is, take up the practices of belief in order to increase belief. But it’s ok to do so, it’s not irrational (says Pascal) because of the infinite value of belief.
I sort of preached a sermon on this (Ryan heard it), which I posted at The Child of Grace at the Infinite Café.
I think I did distribution across sums of infinity in Phil160A… Could explain why it was my worst grade in my entire Stanford career.
I once complained to Etchemendy (author of the class’s logic text and Provost at Stanford) that I was failing the less he created. He told me that, in fact, the class existed in a similar form when he was an undergrad, and he failed it too.
I still have nightmares about Phil160A.
Wow, this is the most commented-after Social Science++ post ever! Will, you are thinking far more reasonably about the topic than I. Andrew, thanks for the Etchemendy story; it somehow makes far too much sense.