Sure, but if we label the text as “factually accurate” or “logically sound” (or “unsound”) etc., then we can presumably greatly increase the probability of producing text with targeted properties
What on Earth makes you think that training a model on all factual information is going to do a lick in terms of generating factual outputs?
At that point, clearly our only problem has been we've done it wrong all along by not training these things only on academic textbooks! That way we'll only probabilistically get true things out, right? /s