So what do you make of this argument then? Suppose I were of the opinion that 2 is an even prime. You come to me with an argument to the effect that I should not believe 2 to be prime because a randomly selected prime number is very, very unlikely to be even. Should I be convinced by that? I may be convinced that in some sense, 2 is unlikely to be even, but I don't think I should accept that 2 is not even, or that the evenness of 2 is questionable.
Similarly, suppose someone believes an argument to be universally compelling. It seems to me that EY's argument should be unmoving: granting that it is unlikely for a randomly selected argument to be UC, but theirs is no randomly selected argument. And on DaFranker's reading of this argument, the thesis that a given X is unlikely to hold for of all minds relies on the assumption that for most X's, there is (something like) a 50% chance of its being true of some mind. But certainly a UCMAist won't accept that this is true of UCMA's. UCMA's, they will say, are exactly those X's for which this is not true.
The burden may be on them to justify the possibility of such an X, but that fact won't save the argument.
As for your first paragraph, well, this is a straightforward application of Bayes' theorem. If you're sure that 2 is even, then learning that 2 was randomly selected from some distribution over primes should not be enough to change your credence very much.
As for your second and third paragraphs: Yes, the argument of Eliezer you're talking about doesn't refute the existence of universally compelling arguments; it merely means that you shouldn't believe you have a universally compelling argument unless you have a good reason for believing so. If you think yo... (read more)
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