Humans don't think logically (as in, formal logic where talking about axioms makes sense), so I don't understand your question.
So a math proof is evidence that mathematicians aren't human? You might want to back off from that statement. Humans don't always think logically.
It was an analogy -- prior beliefs in either informal reasoning or Bayesian probabilities are like axioms in that they're input to a procedure to determine conclusions. The analogy doesn't have to be instantiated precisely in humans to have a reasonable sense extractable.
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.