What is the practical difference you're imagining between "consistently correct guess" and "knowledge"?
LLMs aren't databases. We have databases. LLMs are probabilistic inference engines. All they do is guess, essentially. The discussion here is about how to get the guess to "check itself" with a firmer idea of "truth". And it turns out that's hard because it requires that the guessing engine know that something needs to be checked in the first place.
Knowledge has an objective correctness. We know that there is a "right" and "wrong" answer and we know what a "right" answer is. "Consistently correct guesses", based on the name itself, is not reliable enough to actually be trusted. There's absolutely no guarantee that the next "consistently correct guess" is knowledge or a hallucination.
Also, too, there are whole subfields of philosophy that make your statement here kinda laughably naive. Suffice it to say that, no, knowledge as rigorously understood does not have "an objective correctness".
The fact that you are humanizing an LLM is honestly just plain weird. It does not have feelings. It doesn't care that it has to answer "is it correct?" and saying poor LLM is just trying to tug on heartstrings to make your point.
Knowing it's correct. You've just instructed it not to guess remember? With practice people can get really good at guessing all sorts of things.
I think people have a serious misunderstanding about how these things work. They don't have their training set sitting around for reference. They are usually guessing. Most of the time with enough consistency that it seems like they "know'. Then when they get it wrong we call it "hallucinations". But instructing then not to guess means suddenly they can't answer much. There no guessing vs not with an LLM, it's all the same statistical process, the difference is just if it gives the right answer or not.
Knowledge is knowledge because the knower knows it to be correct. I know I'm typing this into my phone, because it's right here in my hand. I'm guessing you typed your reply into some electronic device. I'm guessing this is true for all your comments. Am I 100% accurate? You'll have to answer that for me. I don't know it to be true, it's a highly informed guess.
Being wrong sometimes is not what makes a guess a guess. It's the different between pulling something from your memory banks, be they biological or mechanical, vs inferring it from some combination of your knowledge (what's in those memory banks), statistics, intuition, and whatever other fairy dust you sprinkle on.
I love the convergence with philosophy here.
This is the second reply that's naively just asserted a tautology. You can't define "knowledge" in terms of "knowing" in the sense of the English words; they're the same word! (You can, I guess, if you're willing to write a thesis introducing the specifics of your jargon.)
In point of fact LLMs "know" that they're right, because if they didn't "know" that they wouldn't have told you what they know. Which, we all agree, they do know, right? They give answers that are correct. Usually.
Except when they're wrong. But that's the thing: define "when they're wrong" in a way rigorous enough to permit an engineering solution. But you really can't, for the same reason that you can't prevent us yahoos on the internet from being wrong all the time too.