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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?

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  • 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.
    – Conifold
    Commented 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
    Commented Feb 7, 2019 at 23:55
  • as in i'm asking what i mean! always a bad start hah @Conifold
    – user35983
    Commented Feb 8, 2019 at 0:06
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    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".
    – Conifold
    Commented Feb 8, 2019 at 0:14

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Firstly, one would need to distinguish between a proposition being certain and a person being certain of it. All kinds of propositions might be certainly true (e.g. mathematical or logical theorems) but being certain of them requires sufficient competence on the part of a person to recognise it. Since you are contrasting certainty with knowledge, I assume you are interested in the latter. We should also make it clear that we are talking about an epistemically justifiable kind of certainty, rather than just a psychological condition. After all, people can be certain of all kinds of things, including things that most others would consider plainly false.

Some kinds of uncertainty (not all) can be represented as epistemic probabilities: we might call them credences or degrees of belief. The fact that credences obey the probability calculus can be justified on the basis of decision theory or on the basis of how credences behave inferentially when used in the context of deductive arguments. We could then say that a credence in A is certain if P(A) = 1. The problem is that we are hardly ever justified in claiming that something is absolutely certain. Indeed, in Bayesian theory there is a principle called the Cromwell Rule that we never assign probability zero or one to any proposition, because of the possibility of error.

This means the closest we can get to a certain credence is that P(A) > 1 - e, where e is some error threshold. In some circumstances this might work as a criterion of knowledge: we might say that a person knows A if their e is sufficiently small. But knowledge is a slippery concept and a great deal of ink has been spilled trying to analyse it. As various counterexamples due to Gettier and others have shown, even when there is strong justification for a credence in A, we tend to disallow that someone knows A if they just got lucky. So, knowledge and high degree of credence can come apart.

As to whether one can be certain about one's knowledge, this might be thought of as whether there can be degrees of uncertainty about one's level of uncertainty. We might try to represent this a meta level probability statement, such as P( P(A) > 1 - e1) > 1 - e2. This is possible, but rather clumsy. A simpler approach would be to treat the credence as having a range of values, or a probability distribution.

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  • +1 using e = 10^-82 (one divided by the number of particles in the universe) expresses as much certainty as we could possibly need for most problems, but still leaves the door open for conclusive evidence that the proposition is false.
    – user6527
    Commented Sep 5, 2023 at 15:56

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