Well, one clear thing about GPT4 that isn't intelligent is that it doesn't learn in situ. Knowledge has to be added to it via an external process. The prompt does allow it to condition further output based on "new" information but that isn't learning. Another thing GPT4 has trouble with is generalizing knowledge. While it is certainly able to generalize to a degree (more or less it is able to apply patterns in the training data from one domain to other domains) if you ask it to generalize to things not well represented in the training data but nevertheless obvious from the conceptual underpinnings thereof it fails. I see this frequently with complicated functional/function level programming. GPT4 gets hopelessly confused when you ask it about non-trivial functions which return or manipulate other functions, even though conceptually there is nothing confusing about it and, in fact, if you ask it about functions as first class objects, it can answer with reasonable text.
Thus, GPT4 can appear to have knowledge in the sense of generating text indicating such, but fail to use that knowledge. This is the most compelling indication to me of limited or total lack of intelligence. I believe that the vast majority of GPT4's "capabilities" amount to memorization and permutation, not the formulation of accurate models of things.
