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Eliezer_Yudkowsky comments on Demands for Particular Proof: Appendices - Less Wrong
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If this were the case, then what is to stop me from thinking of N>3^^^^^3 impossible methods of gaining evidence (aliens from Mars, or Planet X, or the past, or from Cygnus XJ45, or another dimension...), and then claiming that since these probabilities are mutually independent, summing up the positive probabilities, and claiming evolution (or any theory) to be unlikely to be true? I mean, aside from the thing about probability theory being invalid, which I haven't seen before.
Also, thank you Eliezer, for explaining why the argument about cryonics is logically rude. I've been banging my head on this exact topic with a friend for the past week and have been unable to get past that road block with her.
There are counterbalancing negative possibilities, you can't sum over just the positive ones. And since a prior probability distribution sums to 1, the contribution of even solely the positive possibilities must converge to a finite sum rather than diverging.