Under what definitions of truth and knowledge (especially Bayesian) are 'definitely knowing' and 'certain' different

Under what definitions of truth and knowledge are 'definitely knowing' and 'certain' different? Apologies if too much of a semantic question, but I think we should agree that we can have a sense of definitely knowing, perhaps something to do with conviction, and certainty.

I don't think it's a matter of faith, that they are different when we have faith in something, not really, because I think 'faith' is belief in an unjustified proposition, rather than merely with-holding certainty from the proposition. Is the answer that I am, in fact, certain of my knowledge, if I definitely know it, but I can be certain without being certain that I am, unlike not knowing I know (the soi disant KK principle)?

But then wouldn't Bayesian probability suggest that uncertain certainty is just uncertainty? Apologies if I've misremembered what Bayes meat entirely.

So maybe there's some meaning 'absolute' that has bearing: there is such a thing as relative as opposed to absolute certainty. But then shouldn't we withhold absolute certainty from anything that is not vacuous?

• We do withhold absolute certainty from anything, including the "vacuous". But when the uncertainty is for all practical purposes minuscule one would hardly feel the difference. If you are hoping for a precise cutoff between "definite" and "not definite" in terms of probability you will be disappointed, I am afraid, no such thing exists. It is similar to how many grains make a heap, vague predicates, like heap or certainty, produce no sharp boundaries. Feb 7, 2019 at 23:35
• agreed @Conifold but is that all that phrase can mean. i guess it's a bad question actually...
– user35983
Feb 7, 2019 at 23:55
• as in i'm asking what i mean! always a bad start hah @Conifold
– user35983
Feb 8, 2019 at 0:06
• One does not have to measure uncertainty by probability, and in many cases that is either impossible or meaningless, or both. Hesitation about known answers is sometimes interpreted as knowledge without belief. One can also distinguish qualitatively between different levels of certainty, like mathematical vs empirical (the idea being that the former is "infinitely more" certain, because self-made). The old school term for the certainty of the "highest" degree was "apodictic". Feb 8, 2019 at 0:14