Graeme Dice wrote:But, since an eternal afterlife is an infinite reward, and you can't prove that there is a zero probability of it taking place, then the expected value of belief of any kind is infinite.
OK, you're right - I may have misinterpreted your argument slightly. However, your line of reasoning above is still invalid because it does not construct the decision matrix correctly - it fails to properly account for all of the possible outcomes. In fact, it appears to consider only 3 of the possible 9 outcomes (if one interprets it as covering only 2 of the possible outcomes, then it describes Pascal's Wager - obviously, this is the way I interpreted it intiially).
Let us assign annihilation on death a utility of zero (0). It's neutral - you're not around to care, so it isn't going to bother you. Let us assign an enjoyable eternal life a utility of infinity (+inf). Let us assign an eternal life of suffering an infinite negative utility (-inf). (Once the infinities get involved, considering any outcomes with finite, non-zero isn't particularly valuable - with one exception which I will describe later)
Now, we let us narrow ourselves to two options in life (we'll assume that what matters is actions not words - if you look at the way agnostics live, they've generally made a decision, but just refuse to admit it consciously):
1. Atheism
2. Faith (in something - we won't be specific here, since this decision matrix can be constructed to compare atheism to any arbitrary faith, or any two faiths to each other, for that matter)
Now, what are the possible outcomes?
1. No afterlife (annihilation for everybody)
Atheism: 0
Faith: 0
(This outcome is considered by your comment & Pascal's Wager)
2. Good afterlife for everyboy
Atheism: +inf
Faith: +inf
3. Bad afterlife for everyboy
Atheism: -inf
Faith: -inf
4. Good after life for atheists, annihilation for believers
Atheism: +inf
Faith: 0
5. Good after life for atheists, bad after life for believers
Atheism: +inf
Faith: -inf
6. Annihilation for atheists, bad after life for believers
Atheism: 0
Faith: -inf
7. Annihilation for atheists, good after life for believers
Atheism: 0
Faith: +inf
(This outcome is considered by your comment, but not Pascal's Wager)
8. Bad after life for atheists, good after life for believers
Atheism: -inf
Faith: +inf
(This outcome is considered by your comment & Pascal's Wager)
9. Bad after life for atheists, annihilation for believers
Atheism: -inf
Faith: 0
If we assume that all outcomes (with the possible exception of the first) have equal probability, then you will find that all of the positive infinities and negative infinities cancel out, and both faith and atheism end up with an expected utility of zero.
Since faith has the non-negotiable cost of requiring you to suspend rationality with respect to part of your life, an argument based purely on decision theory is going to favour atheism, not faith.
The only way to get the outcome to favour faith is to adjust the probabilities such that faith gives you a
better chance at an enjoyable eternal life (for example, assigning 0 probability to the powers that be choosing to annihilate or eternally torment believers in a particular faith - this is something both your comment and Pascal's Wager do). And what could possibly justify arbitrarily altering the probabilities like that? Why,
faith, of course!
Atheists distort the probabilities too - but we just assign outcome 1 a much greater probability than any of the other outcomes. And that doesn't have any real effect on the decision matrix, since the expected utility of that outcome is always 0. (The finite negative value of faith only has an impact because the other 8 outcomes cancel each other out whenever they are assigned equal priority - and this is the case regardless of how much more likely we consider outcome 1 to be).
"People should buy our toaster because it toasts bread the best, not because it has the only plug that fits in the outlet" - Robert Morris, Almaden Research Center (IBM)
"If you have any faith in the human race you have too much." - Enlightenment