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Alejandro1 comments on LINK: Infinity, probability and disagreement - Less Wrong
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Agreed with everything you say, but I don't think it addresses the main question. Suppose the angel does not say your (2), but the original (2): there is an actual countable infinity of copies of you. If I understand correctly, you are saying that probability theory breaks down under this information and cannot even address the question of how likely is your die to be 1/6. If this is so, isn't a serious problem for multiverse theories, as suggested in the next-to-last quoted paragraph?
(Argh, see edit. Of course I forgot to include the actual argument.)
Well it's certainly a hint that there is something we are confused about. If you are talking about quantum many-worlds, then we can at least prevent our heads from exploding by using the notion of measure to talk about the probability of a world, which even applies to the supposedly uncountably many worlds. (I'm out of my depth here but I think we would then be talking about physical quantum amplitudes in configuration space, rather than subjective probabilities... which mysteriously correspond.)
If you are talking about a single spatially infinite universe... then yeah I don't know how to deal with that. Although I'd at least note that it is a very strange epistemological state that I am in, if I think that I somehow came to have accurate, meaningful beliefs about infinitely many, spatially infinite objects. How did that information get to me?
When N=infinity, N/2=N/6, so Tsvi's version goes through with no changes :P
And as for how to resolve it - take limits. The end.
I always wonder why people do things like say N/2=N/6 "Because it's infinite" then act surprise when it implies something weird. It is only very slightly more impressive than the trick from highschool algebra that makes 1=2 because someone divided by zero.