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Johnicholas comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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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