[btilly]

I can't speak to the general opinion among philosophers about his argument. But my opinion about philosophy is such that their opinion would not sway mine in either way.

I can speak to the general opinion of his logical arguments among logicians. And it is not just widespread consensus against. It is a widespread consensus that the argument is filled with basic logic errors that render it absolutely wrong.

As Hilary Putnam points out, Penrose's arguments are even worse than Lucas'. In particularly Penrose argues that no program that we can know to be sound, can simulate all our human mathematical competence. But our brains do not use a sound thinking process. Therefore a sufficiently good simulation of our brains that it can do mathematics, would also not be sound. Gödel's theorem is entirely silent on the potential capabilities of such unsound systems.

Furthermore LLMs provide a convincing demonstration that unsound simulations of us can have surprising levels of competence. ChatGPT regularly demonstrates both its competence and unsoundness. Sometimes at the same time!

The potential for unsound systems to demonstrate competence far beyond what most expected, is demonstrated by LLMs. Admittedly the current error rate is unacceptably high. But it demonstrates that what Penrose claimed to be mathematically impossible, may plausibly become real within our lifetimes. (Though, given how old Penrose is, not his.)

[sarchertech]

I replied to your other post. His proof is much subtler than that and if it has flaws that isn’t it.

https://calculemus.org/MathUniversalis/NS/10/01penrose.html

[btilly]

I replied to you there.

But in section 4.5 of this "rebuttal", he admits to the flaw that I just pointed out, and dismisses it as logically possible but absurd. The fact that he grants that it is logically possible, demonstrates that his attempted logical demonstration is broken.

Also his opinion on absurdity has to be weighed against the unlikeliness of his conclusion that the known laws of physics will not suffice to explain the operation of the brain. Clearly that question is not as cut and dried as he believes.

[sarchertech]

responded to your other reply.

[btilly]

I am amused that my unintended repetition in the last two paragraphs demonstrates how unsound my absolutely human brain is.

(Unless I'm an LLM. I'm certainly unfunny enough to be one.)