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Stephen_Cole comments on Open thread, Aug. 10 - Aug. 16, 2015 - Less Wrong
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Meeehhhh. Believe nothing empirical with probability 1.0. Believe formal and analytical proofs with probability 1.0.
I get your point that we can have greater belief in logical and mathematical knowledge. But (as pointed out by JoshuaZ) I have seen too many errors in proofs given at scientific meetings (and in submitted publications) to blindly believe just about anything.
That wasn't quite my point. As a simple matter of axioms, if you condition on the formal system, a proven theorem has likelihood 1.0. Since all theorems are ultimately hypothetical statements anyway, conditioned on the usefulness of the underlying formal system rather than a Platonic "truth", once a theorem is proved, it can be genuinely said to have probability 1.0.
I will assume by likelihood you meant probability. I think you have removed by concern by conditioning on it. The theorem has probability 1, in your formal system. For me that is not probability 1, I don't give any formal system full control of my beliefs/probabilities.
Of course, I believe arithmetic with probability approaching 1. For now.