philh comments on This is why we can't have social science - Less Wrong
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The amusing thing is that Mitchel's argument proves much more than he wants it to prove.
Notice that the above argument applies just as well to the original experiment being replicated.
My interpretation is that he's saying false positives are unlikely but false negatives are common. If that's the case, then getting a positive result should greatly affect your beliefs; but a negative replication shouldn't shift them much.
(I can't actually justify this interpretation by reading the text, but it does make the text seem fairly reasonable.)