It seems to me that Wei Dai's argument is flawed (and I may be overly arrogant in saying this; I haven't even had breakfast this morning.)
He says that the probability of knowing an uncomputable problem would be evaluated at 0 originally; I don't fundamentally see why "measure zero hypothesis" is equivalent to "impossible;" for example the hypothesis of "they're making it up as they go along" having probability 2^(-S) based on the size of the set shrinks at a certain rate as evidence arrives; that means that given any finite amount of inference the AI should be able to distinguish between two possibilities (they are very good at computing or guessing vs all humans have been wrong about mathematics forever) unless new evidence comes in to support one over the other "humans have been wrong forever" should have a consistent probability mass which will grow in comparison to the other hypothesis "they are making it up."
Nobody seems to propose this (although I may have missed it skimming some of the replies) and it seems like a relatively simple thing (to me) to adjust the AI's prior distribution to give "impossible" things low but nonzero probability.
Wei Dai's argument was specifically against the Solomonoff prior, which assigns probability 0 to the existence of halting problem oracles. If you have an idea how to formulate another universal prior that would give such "impossible" things positive probability, but still sum to 1.0 over all hypotheses, then by all means let's hear it.
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