An LLM creates a high fidelity statistical probabistic model of human language. The hope is to capture the input/output of various hierarchical formal and semiformal systems of logic that transit from human to human, which we know as "Intelligence".

Unfortunately, its corpus is bound to contain noise/nonsense that follows no formal reasoning system but contributes to the ill advised idea that an AI should sound like a human to be considered intelligent. Therefore it is not a bag of words but a bag of probabilities perhaps. This is important because the fundamental problem is that an LLM is not able, by design, to correctly model the most fundamental precept of human reason, namely the law of non-contradiction. An LLM must, I repeat must assign nonvanishing probability to both sides of a contradiction, and what's worse is the winning side loses, since long chains of reason are modelled with probability the longer the chain, the less likely an LLM is to follow it. Moreover, whenever there is actual debate on an issue such that the corpus is ambiguous the LLM becomes chaotic, necessarily, on that issue.

I literally just had an AI prove the forgoing with some rigor, and in the very next prompt, I asked it to check my logical reasoning for consistency and it claimed it was able to do so (->|<-).