They can if they've been post trained on what they know and don't know. The LLM can first been given questions to test its knowledge and if the model returns a wrong answer, it can be given a new training example with an "I don't know" response.
“Hallucination” is seeing/saying something that a sober person clearly knows is not supposed to be there, e.g. “The Vice President under Nixon was Oscar the Grouch.”
Harry Frankfurt defines “bullshitting” as lying to persuade without regard to the truth. (A certain current US president does this profusely and masterfully.)
“Confabulation” is filling the unknown parts of a statement or story with bits that sound as-if they could be true, i.e. they make sense within the context, but are not actually true. People with dementia (e.g. a certain previous US president) will do this unintentionally. Whereas the bullshitter generally knows their bullshit to be false and is intentionally deceiving out of self-interest, confabulation (like hallucination) can simply be the consequence of impaired mental capacity.
> Frankfurt understands bullshit to be characterized not by an intent to deceive but instead by a reckless disregard for the truth.
That is different than defining "bullshitting" as lying. I agree that "confabulation" could otherwise be more accurate. But with previous definition they are kinda synonyms? And "reckless disregard for the truth" may hit closer.
The paper has more direct quotes about the term.
You're right. It's "intent to persuade with a reckless disregard for the truth." But even by this definition, LLMs are not (as far as we know) trying to persuade us of anything, beyond the extent that persuasion is a natural/structural feature of all language.
LLMs can not reliably tell whether they know or don't know something. If they did, we would not have to deal with hallucinations.