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The basic problem is that it seems pretty clear that human intelligence is not anything like a Turing machine and no one has presented any computational system not equivalent to a Turing machine. Some might conclude this is a foundational problem.

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It does not follow, merely from noting that there are differences between human intelligence and a Turing machine, that no "merely" Turing-equivalent device could display human-level intelligence. Every attempt I have seen so far to carry through that argument either ends up begging the question or becoming an argument from incredulity.

Note that this is not an argument that it is possible, which certainly has not been conclusively established.

I think it is on those making the claim that a system equivalent to a Turing machine can have human level or superior intelligence. Humans are vastly more intelligent than any other organism we have encountered. I may be incredulous at the idea but the scale of difference between human intelligence and programs based on Turing machines is enormous.

The wholw point of turing machines is that they can emulate any computable system. You could have your a turing machine simulate every atom inside a human, and then you trivially have a turing machine that shows intelligence equivalent to a human.

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