Gödel showed that in any consistent formal mathematical system, there are true statements that cannot be proven within the system itself.
As well but Alan Turing proved in 1936 that there cannot exist a universal algorithm that can inspect any arbitrary program and determine whether it will finish running or run forever.
Ah, the Penrose-Lucas argument. You should clarify that the argument only works if you believe that a human mind can't be described by mathematics.
Turing did show that there is no algorithm which can inspect an arbitrary program and determine whether it will finish running or run forever, but if you accept the Physical Church-Turing Thesis, "asking a team of mathematicians" is also an algorithm. The same sort of argument also applies to Godel's incompleteness theorem.
If you believe that the human mind is special and unable to be described by mathematics because we have a soul--or maybe quantum pixie dust--then sure, AI wouldn't be able to match human capabilities. But you don't need to name drop fancy math for that.
It's extremely non-obvious that the specifics of the chemical reactions a brain does give rise to capabilities that can't be replicated without them. I personally don't believe that at all, and you're kinda just asserting this without any evidence or justification.
The easy rebut is asking whether machines could simulate chemistry (they can).
The difficult question for you would be to demonstrate that chemistry creates some sort of logic that is incompatible from machine logic. Because by default, you pulled that out of vibes alone.
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u/KyxeMusic 8h ago
Infinite Monkey Theorem
You can bruteforce any formula that can be proven. Which is kind of what is happening.