Ok. perhaps I need another tack here. You seem to be projecting onto me a steadfast desire to attribute abilities to LLMs. I am engaging in this conversation because it is a conversation and it is reasonable to respond to being directly addressed.

My initial point simplified down:

    M = makes the wrong move, while knowing the rules.
    A = AI Behavior
    H = Human Behaviour
    R = Resoning Ability

    Assertion Q: if there exists an instance of M from X  then X => !R

So if there exists an instance of a Game Mistake from an AI then it shows an AI cannot reason, but if assertion Q is true it would also follow that an instance of a Game Mistake from a human would show Humans cannot reason.

From this point down, no part of this reasoning involves Large Language models or an other aspect of AI.

    Stipulation:  H => R      Humans can reason
    Assertion Q where X is H:  If there exists an instance of M from H then X=>!R   
    Lerc's premise L:   There exists an instance of M from H

    Therefore given the Stipulation either Assertion Q is false or Lerc's premise is false.

At this point you asserted !L and ask for a Citation. I provided a link. You contested that since 1,2,3,4 does not show L that the citation does not demonstrate L.

I agree that 1. does not show L but that did not matter since 5. did show L. The other points were not addressed. I also offer other examples of L that I have observed from my own experience. When I had the thought of books about chess being written by people who have made illegal moves, I actually had in mind Levy Rozman who would freely admit that he has occasionally played illegal moves.

Then you seem to want an apology for 1,2,3,4 not meeting the criteria? I'm a bit confused as to what's going on by now. One instance of L is all that is needed when L is a claim of existence. If the citation does not meet your criteria then you can simply say so, you allude to motivations regarding LLM as motivation as if you think that LLMs are still relevant to L.

You don't have to win conversations, you can just work to clarify ideas. Your request for apology, and passive aggressive sign-offs suggests you feel like this is some sort of fight. As an attempt to resolve this I have written this extended post to make as clear as possible what my position and motivations are.

I don't want to assert abilities or lack of abilities onto AI models, my concern is with whether people making such assertions are well founded. This stands for arguments saying that AI has a capability, Arguments saying AI does not have a capability, and Arguments saying AI will never have a capability.

To go back to the very beginning where someone suggested an anthropomorphic fallacy, the comparison to humans was not a suggestion of a similarity of similar function. Humans provide and example of a set of properties that are generally accepted. It is valid to apply the implications of any of those properties equally to Humans and AI. Implying the existence of a property in an AI may be anthropomorphism, evaluating the implications of the property should it exist is not.