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Johnicholas comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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I see it, somewhat. But this sounds a lot like "I'm Omega, I am trustworthy and accurate, and I will only speak to you if I've predicted you will not imagine a pink rhinoceros as soon as you hear this sentence".
The correct conclusion seems to be that Omega is not what he says he is, rather than "I don't exist".
When the problem contains a self-contradiction like this, there is not actually one "obvious" proposition which must be false. One of them must be false, certainly, but it is not possible to derive which one from the problem statement.
Compare this problem to another, possibly more symmetrical, problem with self-contradictory premises:
http://en.wikipedia.org/wiki/Irresistible_force_paradox