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Stephen_Cole comments on Open thread, Aug. 10 - Aug. 16, 2015 - Less Wrong Discussion
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Has there been discussion of Jack Good's principle of nondogmatism? (see Good Thinking, page 30).
The principle, stated simply in my bastardized version, is to believe no thing with probability 1. It seems to underlie Good's type 2 rationality (to maximize expected utility, within reason).
This is (almost) in accord with Lindley's concept of Cromwell's rule (see Lindley's Understanding Uncertainty or https://en.wikipedia.org/wiki/Cromwell%27s_rule). And seems to be closely related to Jaynes' mind projection fallacy.
There have been discussions on this topic, although perhaps not framed as nondogmatism. If you have not read 0 and 1 are not probabilities and infinite certainty, you might find them and related articles interesting.
Meeehhhh. Believe nothing empirical with probability 1.0. Believe formal and analytical proofs with probability 1.0.
Have you never seen an apparently valid mathematical proof that you later found an error in?
It's common sense to infer that someone is talking about valid proofs when they talk about believing in proofs.
That is the problem in a nutshell: how do you know it is a valid proof? All the time one thinks the proof is valid and it turns out one is wrong.
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.