There is a sense in which it is possible to have negative knowledge. This is the case when one is mistaken. For example: suppose a person reads that Virgil was the first emperor of Rome. A person who has no knowledge of who was the first emperor of Rome would know nothing; in order to get to the state of knowing nothing about who the first emperor of Rome was our hypothetical person would need to learn that Virgil was not the first emperor of Rome. That is, if one adds true information, our man arrives at ignorance. This is very similar to how negative and positive numbers behave. If we keep the analogy to positive and negative numbers, we can meaningfully say that a rock knows more about the Roman Empire than a man who only knows that the Virgil was the first emperor of it, since the rock has zero knowledge while the man who is mistaken has negative knowledge.

In like manner, it is possible for a fool to be less wise than a rock, since a fool has negative understanding, while a rock simply has no understanding.

Large Language Models (LLMs) are statistical text generators. There is nothing in them which is even analogous to understanding, and certainly nothing which is understanding. They are, with regard to understanding, like rocks.

And here we come to something that (I think) deceives many people into believing that LLMs are intelligent: there are a great many fools in the world, so LLMs have more understanding of the world than many people.