You're right. We don't really know how to handle uncertainty and fuzziness in logic properly (to avoid logical contradictions). There has been many mathematical

You're right. We don't really know how to handle uncertainty and fuzziness in logic properly (to avoid logical contradictions). There has been many mathematical attempts to model uncertainty (just to name a few - probability, Dempster-Shafer theory, fuzzy logic, non-monotone logics, etc.), but they all suffer from some kind of paradox. At the end of the day, none of these theoretical techniques prevailed in the field of AI, and we ended up with, empirically successful, neural networks (and LLMs specifically). We know they model uncertainty but we have no clue how they do it conceptually, or whether they even have a coherent conception of uncertainty. So I would pose that the problem isn't that we don't have the technology, but it's rather we don't understand what we want from it. I am yet to see a coherent theory of how humans manipulate the human language to express uncertainty that would encompass broad (if not all) range of how people use language. Without having that, you can't define what is a hallucination of an LLM. Maybe it's making a joke (some believe that point of the joke is to highlight a subtle logical error of some sort), because, you know, it read a lot of them and it concluded that's what humans do. So AI eventually prevailed (over humans) in fields where we were able to precisely define the goal. But what is our goal vis-a-vis human language? What do we want from AI to answer to our prompts? I think we are stuck at the lack of definition of that.