This paper is an attempt to Euler the reader.
See https://slatestarcodex.com/2014/08/10/getting-eulered/
> There is an apocryphal story about the visit of the great atheist philosopher Diderot to the Russian court. Diderot was quite the clever debater, and soon this scandalous new atheism thing was the talk of St. Petersburg. This offended reigning monarch Catherine the Great, who was a good Christian woman ... so she asked legendary mathematician Leonhard Euler to publicly debunk and humiliate Diderot. Euler said, in a tone of absolute conviction: “Monsieur, (a+b^n)/n = x, therefore, God exists! What is your response to that?” and Diderot, “for whom algebra was like Chinese”, had no response. Thus was he publicly humiliated, all the Russian Christians got an excuse to believe what they had wanted to believe anyway, and Diderot left in a huff.
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The brain is a physical object and governed by the same laws that govern any other machine. Therefore, AGI, whatever that is, is possible in principle. To argue otherwise is to just assert unfalsifiable Cartesian dualism, i.e. souls.
The argument in no way proves, "mathematically" or otherwise, any property of AGI. The author's comments on the thread are, charitably, dense and obscure --- but I'm not feeling charitable, so I'm going to say they're evasive and Euler-y.
I don't think it's worth anyone's time to understand or deconstruct the argument in detail without some explanation of why the brain can do something a machine can't that isn't just "because souls".
Agreed. To slightly nuance your last three paragraphs, if the brain exceeded the physical, and if this meant we could do something a computer cannot be made to do, then to prove AGI impossible "all" the proponents of such claims would need to do would be to prove that human brains can do a calculation that is not Turing computable.
Anything else short of disproving the Church-Turing thesis will come up short.
They could start by proving that computable functions outside the Turing computable is possible, because if they are not, their claims would fall apart.
But neither this paper, nor his previous paper, even mentions the Church-Turing thesis.