> Probabilistic prediction is inherently incompatible with deterministic deduction.

Human brains run on probabilistic processes. If you want to make a definition of intelligence that excludes humans, that's not going to be a very useful definition for the purposes of reasoning or discourse.

> What if 1 + 2 is 2 and 1 + 3 is 3? Then we can reason that under these constraints we just made up, 1 + 4 is 4, without ever having been programmed to consider these rules.

Have you tried this particular test, on any recent LLM? Because they have no problem handling that, and much more complex problems than that. You're going to need a more sophisticated test if you want to distinguish humans and current AI.

I'm not suggesting that we have "solved" intelligence; I am suggesting that there is no inherent property of an LLM that makes them incapable of intelligence.