I takes guts to claim that Penrose is clowning himself, after all we are talking about one of the most accomplished mathematicians/physicist of our time. Penrose's argument in it's essence is that human thought/understanding has non-computable/non-algorithmic aspects and hence can not be replicated by a digital computer. His argument is based on the very theory that defines what digital computation is and as far I know has not been refuted to this day, that is over 40 years since Penrose first formulated it.
Penrose is wrong because he misinterprets Gödel's incompleteness theorem. Hence, it is not about refuting the theorem. Gödel's incompleteness theorem is true and nobody disputes that.
Nobody has formally refuted Penrose's argument because it is not a formal argument. As simple as that. The best we can do is explain why his interpretation of Gödel's incompleteness theorem is wrong.
Recall that to formally refute an argument, said argument has to be formally stated first—including axioms/assumptions and rules to manipulate those axioms/assumptions. Every formal theory of anything has those. Penrose's does not.
I don't think Penrose or anyone else claims that Penrose presents a formal argument. The idea of a formal system that contains statements about humans is a curious conception to begin with. People who claim that Penrose misinterprets Gödel's theorems should at least be able to point out how he does so. In fact Gödel himself drew very similar conclusions to Penrose's from his theorem: "My incompleteness theorem makes it likely that mind is not mechanical, or else mind cannot understand its own mechanism. If my result is taken together with the rationalistic attitude which Hilbert had and which was not refuted by my results, then [we can infer] the sharp result that mind is not mechanical. This is so, because, if the mind were a machine, there would, contrary to this rationalistic attitude, exist number-theoretic questions undecidable for the human mind."
I think that is mostly a matter of mathematical training. Well but then I have not really tried to make an LLM generate human levels of nonsense - that might convince me maybe.
I takes guts to claim that Penrose is clowning himself, after all we are talking about one of the most accomplished mathematicians/physicist of our time. Penrose's argument in it's essence is that human thought/understanding has non-computable/non-algorithmic aspects and hence can not be replicated by a digital computer. His argument is based on the very theory that defines what digital computation is and as far I know has not been refuted to this day, that is over 40 years since Penrose first formulated it.
Penrose is wrong because he misinterprets Gödel's incompleteness theorem. Hence, it is not about refuting the theorem. Gödel's incompleteness theorem is true and nobody disputes that.
Nobody has formally refuted Penrose's argument because it is not a formal argument. As simple as that. The best we can do is explain why his interpretation of Gödel's incompleteness theorem is wrong.
Recall that to formally refute an argument, said argument has to be formally stated first—including axioms/assumptions and rules to manipulate those axioms/assumptions. Every formal theory of anything has those. Penrose's does not.
I don't think Penrose or anyone else claims that Penrose presents a formal argument. The idea of a formal system that contains statements about humans is a curious conception to begin with. People who claim that Penrose misinterprets Gödel's theorems should at least be able to point out how he does so. In fact Gödel himself drew very similar conclusions to Penrose's from his theorem: "My incompleteness theorem makes it likely that mind is not mechanical, or else mind cannot understand its own mechanism. If my result is taken together with the rationalistic attitude which Hilbert had and which was not refuted by my results, then [we can infer] the sharp result that mind is not mechanical. This is so, because, if the mind were a machine, there would, contrary to this rationalistic attitude, exist number-theoretic questions undecidable for the human mind."
I will reply with a bit of humor.
Let Coq be a formal prove verifier.
Let Coq verify the proof for Gödel's incompleteness theorem.
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Conclude Coq has the microtubules necessary for consciousness.
Hint: Look up "Essential Incompleteness of Arithmetic Verified by Coq".
Indeed it is very difficult to imagine how humans could be machines given their almost endless capacity of self deception and irrationallity.
By the same token, it must be hard to imagine how language models could be machines huh?
I think that is mostly a matter of mathematical training. Well but then I have not really tried to make an LLM generate human levels of nonsense - that might convince me maybe.