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SilasBarta comments on The Fundamental Question - Less Wrong

43 Post author: MBlume 19 April 2010 04:09PM

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Comment author: SilasBarta 23 April 2010 07:34:02PM *  1 point [-]

There aren't many difficult steps in refuting Pascal's wager, and I dont' think there's be much disagreement on it here.

The refutation of PW, in short, is this: it infers high utility based on a very complex (and thus highly-penalized) hypothesis, when you can find equally complex (and equally well-supported) hypotheses that imply the opposite (or worse) utility.

(Btw, I was one of those who voted you down.)

Comment author: byrnema 23 April 2010 07:37:16PM *  1 point [-]

Again, is it the argument that is wrong, or Pascal's application of it?

(Can you confirm whether you down-voted me because it's off-topic and inflammatory, or because I'm wrong?)

Comment author: SilasBarta 23 April 2010 07:42:12PM *  0 points [-]

Again, is it the argument that is wrong, or Pascal's application of it?

It is always wrong to give weight to hypotheses beyond that justified by the evidence and the length penality (and your prior, but Pascal attempts to show what you should do irrespective of prior). Pascal's application is a special case of this error, and his reasoning about possible infinite utility is compounded by the fact that you can construct contradictory advice that is equally well-grounded.

(Can you confirm whether you down-voted me because it's off-topic and inflammatory, or just because I'm wrong?)

I downvoted you not just for being wrong, but for having made such a bold statement about PW without (it seems) having read the material about it on LW. I also think that such over-reaching trivializes the contribution of writers on the topic and so comes off as inflammatory.

Comment author: byrnema 23 April 2010 08:10:26PM 0 points [-]

It is always wrong to give weight to hypotheses beyond that justified by the evidence and the length penality (and your prior, but Pascal attempts to show what you should do irrespective of prior).

Are you saying, here, that it is wrong to factor in the utility of the hypothesis when giving weight to the hypothesis?

his reasoning about possible infinite utility is compounded by the fact that you can construct contradictory advice that is equally well-grounded.

If he didn't consider all the cases, his particular application of the argument was bad, not the argument itself, right?

I downvoted you not just for being wrong, but for having made such a bold statement about PW without (it seems) having read the material about it on LW. I also think that such over-reaching trivializes the contribution of writers on the topic and so comes off as inflammatory.

I have read the material, but I disagreed with it, and it's often not clear -- especially when the posts are old -- how I can jump in and chime in that I don't agree. Often it's just the subtext I disagree with, so I wait for someone to make it more explicit (or at least more immediate) and then I bring it up.

Thanks for your explanation about the down-voting.

Comment author: SilasBarta 23 April 2010 08:20:11PM 2 points [-]

Are you saying, here, that it is wrong to factor in the utility of the hypothesis when giving weight to the hypothesis?

No (assuming you mean the expected utility of the action given the hypothesis), just that you have to accurately weight its probability.

If he didn't consider all the cases, his particular application of the argument was bad, not the argument itself, right?

But his argument wouldn't somehow be improved by considering all the cases (not that it would be practical to even consider all the hypotheses of lengths up to that which implies high utility from faith in God!). Considering those cases would find hypotheses that assign the opposite utility to faith, and worse, some would be more probable.

To salvage the argument, one would have to not just consider more cases, but provide a lot more epistemic labor -- that is, make arguments that aren't part of PW to begin with.

Comment author: byrnema 23 April 2010 08:30:12PM 0 points [-]

All of your objections to PW seem to be about Pascal's application of the argument (the probabilities he inputted, the number of cases cases he considered) in which case we can agree that his conclusion wouldn't be correct.

When I read that Pascal's Wager is flawed as an argument, I interpret this as 'the argument does not have good form'. Did people just mean, all along, that they disagreed with the conclusion of the argument because they didn't agree with the numbers he used?

Comment author: SilasBarta 23 April 2010 08:40:14PM *  4 points [-]

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.

Comment author: byrnema 23 April 2010 09:09:52PM 1 point [-]

"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?

Comment author: SilasBarta 23 April 2010 10:17:03PM 3 points [-]

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.

Comment author: orthonormal 24 April 2010 01:08:00AM 2 points [-]

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.

Comment author: byrnema 23 April 2010 11:18:29PM *  2 points [-]

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:

  1. 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.

  2. 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.