We don’t have absolute certainty in ‘the Bayesian approach’. It would be counter-productive at best if we did, since then our certainty would be too great for evidence from the world to change our mind, hence we’d have no reason to think that if the evidence did contradict ‘the Bayesian approach’, we’d believe differently. In other words, we’d have no reason as Bayesians to believe our belief, though we’d remain irrationally caught in the grips of that delusion.
Even assuming that it’s a matter of word meanings that the four millionth digit of pi is 0, you can still be uncertain about that fact, and Bayesian reasoning applies to such uncertainty in precisely the same way that it applies to anything else. You can acquire new evidence that makes you revise your beliefs about mathematical theorems, etc.
We can be wrong about what the words we use mean.
What category error would that be?
We don’t have absolute certainty in ‘the Bayesian approach’. It would be counter-productive at best if we did, since then our certainty would be too great for evidence from the world to change our mind, hence we’d have no reason to think that if the evidence did contradict ‘the Bayesian approach’, we’d believe differently. In other words, we’d have no reason as Bayesians to believe our belief, though we’d remain irrationally caught in the grips of that delusion.
Even assuming that it’s a matter of word meanings that the four millionth digit of pi is 0, you can still be uncertain about that fact, and Bayesian reasoning applies to such uncertainty in precisely the same way that it applies to anything else. You can acquire new evidence that makes you revise your beliefs about mathematical theorems, etc.