You said you trivially proved something and made up nonsensical lines of reasoning to justify it. If your "proof" can't port to Humans then it's not proof. You are just rambling.
>Humans make such mistakes precisely because they are not perfect reasoning machines.
Nobody is calling LLMs perfect reasoning machines. Your "point" was that they don't reason at all which of none of your ramblings has been able to "prove".
>If these LLMs are not, as I claim, reasoning on language rather than the abstract model of the query, then how come they fail miserably in exactly the ways you would expect where that the case?
They don't. The idea that you must make no mistake reasoning before you can be considered to be reasoning has no ground.
>LLMs generalize to non linguistic patterns. Yes, congratulations, if you turn a problem into a linguistic one LLMs can deal with them.
Can you read ? Did you even bother looking at the link? LLMs don't need patterns to be linguistic to reason over them lol. None of those patterns are turned linguistic. Some of them are arbitrary numbers that resemble nothing like the data they've been trained on.