I think what they mean is, “If an argument allows you to claim an unreasonably huge amount of utility from actions not seemingly capable of that, then you have a complex enough hypothesis that you can find others with the same complexity and opposite conclusion”.
PW-type arguments, then, refer to the class of arguments in which someone tries to justify a course of action through (following the action suggested by) an improbable hypothesis by claiming high enough expected utility. That class of arguments has the flaw that when you allow yourself that much complexity, you necessarily permit hypotheses that advise just as strongly against the action.
That is not something that you can salvage by using different numbers here and there, and so the argument and similar ones have bad (and unsalvageable) form.
“If an argument allows you to claim an unreasonably huge amount of utility from actions not seemingly capable of that, then you have a complex enough hypothesis that you can find others with the same complexity and opposite conclusion”.
That is still fine, because we know how to handle the hypotheses with negative utility. You just optimize over the net utilities of each belief weighted by their probabilities.The fact that there are positive and negative terms together doesn’t invalidate the whole argument. You just do the calculation, if you can, and see what you get.
That is not something that you can salvage by using different numbers here and there, and so the argument and similar ones have bad (and unsalvageable) form.
If you have the right numbers, and a simple enough case to do the computation, would you find PW an acceptable argument?
I’m still having trouble understanding your objection.
When you decide to have faith based on PW, you’re using some epistemology that allows you to pick out the “faith causes infinite utility” hypothesis out of the universe-generating functionspace, and deem it to have some finite probability. The problem is that that epistemology—whatever it is—also allows you to pick out numerous other hypotheses, in which some assert the opposite utility from faith (and their existence is provable by inversion of the faith = utility hypothesis elements).
In order to show net positive utility from believing, you would have to find some way of counting all hypotheses this complex, and finding out which comes ahead. However, the canonical PW argument relies on such anti-faith hypotheses not existing. You would be treading new ground in finding some efficient way to count up all such hypotheses and find which action comes out ahead—keeping in mind, of course, that at this level of complexity, there is a HUGE number of hypotheses to consider.
So you would be making a new argument, only loosely related to canonical PW. If you think you can pull this off, then go ahead and write the article, though I think you’ll soon find it’s not as easy as you expect.
And I would submit that any hypothesis that allows you to claim something has infinite utility (or necessarily more utility than the result of any other action) must itself be infinitely complex, thus infinitely improbable, canceling out the infinity claimed to come from faith.
As you know, I think the essence of Pascal’s wager is this:
If believing in X has positive utility, then you should believe in X.
I think there is enough to debate about in that statement alone.
But suppose that X = God exists. It seems to me that you are consistently writing that Pascal’s Wager fails because in this case the utility of X is impossible to compute due to the complexity of X. I don’t believe this makes the argument fail for two reasons:
Pascal’s Wager says, “If belief in X has positive utility, you should believe in X’. This argument doesn’t fail (in form) if the utility is negative or impossible to compute.
I disagree that the utility is impossible to compute, despite all your arguments about the complexity of X. My reason is straight-forward: atheists do calculate (or at least estimate) the utility of believing in God. Usually, they come up with a value that is negative. So it’s not impossible to estimate the average utility of a complex belief.
And I would submit that any hypothesis that allows you to claim something has infinite utility (or necessarily more utility than the result of any other action) must itself be infinitely complex, thus infinitely improbable, canceling out the infinity claimed to come from faith.
That’s not quite valid— there is some finite program that unfolds Permutation City-style into a universe that allows for infinite computational power, and thus (by some utility functions) infinite utility as the consequence of some actions. It would be wrong for a scientist living in such a universe to reject that hypothesis.
I think what they mean is, “If an argument allows you to claim an unreasonably huge amount of utility from actions not seemingly capable of that, then you have a complex enough hypothesis that you can find others with the same complexity and opposite conclusion”.
PW-type arguments, then, refer to the class of arguments in which someone tries to justify a course of action through (following the action suggested by) an improbable hypothesis by claiming high enough expected utility. That class of arguments has the flaw that when you allow yourself that much complexity, you necessarily permit hypotheses that advise just as strongly against the action.
That is not something that you can salvage by using different numbers here and there, and so the argument and similar ones have bad (and unsalvageable) form.
That is still fine, because we know how to handle the hypotheses with negative utility. You just optimize over the net utilities of each belief weighted by their probabilities.The fact that there are positive and negative terms together doesn’t invalidate the whole argument. You just do the calculation, if you can, and see what you get.
If you have the right numbers, and a simple enough case to do the computation, would you find PW an acceptable argument?
I’m still having trouble understanding your objection.
When you decide to have faith based on PW, you’re using some epistemology that allows you to pick out the “faith causes infinite utility” hypothesis out of the universe-generating functionspace, and deem it to have some finite probability. The problem is that that epistemology—whatever it is—also allows you to pick out numerous other hypotheses, in which some assert the opposite utility from faith (and their existence is provable by inversion of the faith = utility hypothesis elements).
In order to show net positive utility from believing, you would have to find some way of counting all hypotheses this complex, and finding out which comes ahead. However, the canonical PW argument relies on such anti-faith hypotheses not existing. You would be treading new ground in finding some efficient way to count up all such hypotheses and find which action comes out ahead—keeping in mind, of course, that at this level of complexity, there is a HUGE number of hypotheses to consider.
So you would be making a new argument, only loosely related to canonical PW. If you think you can pull this off, then go ahead and write the article, though I think you’ll soon find it’s not as easy as you expect.
And I would submit that any hypothesis that allows you to claim something has infinite utility (or necessarily more utility than the result of any other action) must itself be infinitely complex, thus infinitely improbable, canceling out the infinity claimed to come from faith.
As you know, I think the essence of Pascal’s wager is this:
I think there is enough to debate about in that statement alone.
But suppose that X = God exists. It seems to me that you are consistently writing that Pascal’s Wager fails because in this case the utility of X is impossible to compute due to the complexity of X. I don’t believe this makes the argument fail for two reasons:
Pascal’s Wager says, “If belief in X has positive utility, you should believe in X’. This argument doesn’t fail (in form) if the utility is negative or impossible to compute.
I disagree that the utility is impossible to compute, despite all your arguments about the complexity of X. My reason is straight-forward: atheists do calculate (or at least estimate) the utility of believing in God. Usually, they come up with a value that is negative. So it’s not impossible to estimate the average utility of a complex belief.
That’s not quite valid— there is some finite program that unfolds Permutation City-style into a universe that allows for infinite computational power, and thus (by some utility functions) infinite utility as the consequence of some actions. It would be wrong for a scientist living in such a universe to reject that hypothesis.