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Alicorn comments on Ingredients of Timeless Decision Theory - Less Wrong
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Here is what I don't understand about the free will problem. I know this is a simple objection, so there must be a standard reply to it; but I don't know what that reply is.
Denote F as a world in which free will exists, f as one in which it doesn't. Denote B as a world in which you believe in free will, and b as one in which you don't. Let a combination of the two, e.g., FB, denote the utility you derive from having that belief in that world. Suppose FB > Fb and fb > fB (being correct > being wrong).
The expected utility of B is FB x p(F) + fB x (1-p(F)). Expected utility of b is Fb x p(F) + fb x (1-p(F)). Choose b if Fb x p(F) + fb x (1-p(F)) > FB x p(F) + fB x (1-p(F)).
But, that's not right in this case! You shouldn't consider worlds of type f in your decision, because if you're in one of those worlds, your decision is pre-ordained. It doesn't make any sense to "choose" not to believe in free will - that belief may be correct, but if it is correct, then you can't choose it.
Over worlds of type F, the expected utility of B is FB x p(F), and the utility of b is Fb x p(F), and FB > Fb. So you always choose B.
Saying that you shouldn't do something because it's preordained whether you do it or not is a very confused way of looking at things. Christine Korsgaard, by whom I am normally unimpressed but who has a few quotables, says:
(From "The Authority of Reflection")
I don't understand what that Korsgaard quote is trying to say.
I didn't say that. I said that, when making a choice, you shouldn't consider, in your set of possible worlds, possible worlds in which you can't make that choice.
It's certainly not as confused a way of looking at things as choosing to believe that you can't choose what to believe.
I should have said you shouldn't try to consider those worlds. If you are in f, then it may be that you will consider such possible worlds; and there's no shouldness about it.
"But", you might object, "what should you do if you are a computer program, running in a deterministic language on deterministic hardware?"
The answer is that in that case, you do what you will do. You might adopt the view that you have no free will, and you might be right.
The 2-sentence version of what I'm saying is that, if you don't believe in free will, you might be making an error that you could have avoided. But if you believe in free will, you can't be making an error that you could have avoided.
In the context of the larger paper, the most charitable way of interpreting her (IMO) is that whether we have free will or not, we have the subjective impression of it, this impression is simply not going anywhere, and so it makes no sense to try to figure out how a lack of free will ought to influence our behavior, because then we'll just sit around waiting for our lack of free will to pick us up out of our chair and make us water our houseplants and that's not going to happen.
What if we're in a possible world where we can't choose not to consider those worlds? ;)
"Choosing to believe that you can't choose what to believe" is not a way of looking at things; it's a possible state of affairs, in which one has a somewhat self-undermining and false belief. Now, believing that one can choose to believe that one cannot choose what to believe is a way of looking at things, and might even be true. There is some evidence that people can choose to believe self-undermining false things, so believing that one could choose to believe a particular self-undermining false thing which happens to have recursive bearing on the choice to believe it isn't so far out.