(b) all of classical physics is computable therefore
(c) thinking relies on non-classical physics.
(d) In addition, he speculatively proposed which brain structures might do quantum stuff.
All of the early critiques of this I saw focussed on (d), which is irrelevant. The correctness of the position hinges on (a), for which Penrose provides a rigorous argument. I haven't kept up though, so maybe there are good critiques of (a) now.
If Penrose is right then neural networks implemented on regular computers will never think. We'll need some kind of quantum computer.
> If Penrose is right then neural networks implemented on regular computers will never think.
I disagree that that is necessarily an implication, though. As I said before, all that it implies is that computational tech will think differently than humans, in the same way that airplanes fly using different mechanisms from birds.
Part of Penroses's point (a) is that our brains can solve problems that aren't computable. That's the crux of his brains-aren't-computers argument. So even if computers can in some sense think, their thinking will be strictly more limited than ours, because we can solve problems that they can't. (Assuming that Penrose is right.)
I wonder if LLM's have shaken the ground he stood on when he said that. Penrose never worked with a computer that could answer off the cuff riddles. Or anything even remotely close to it.
(a) doesn't hold up because the details of the claim necessitate that it is a property of brains that they can always perceive the truth of statements which "regular computers" cannot. However, brains frequently err.
Penrose tries to respond to this by saying that various things may affect the functioning of a brain and keep it from reliably perceiving such truths, but when brains are working properly, they can perceive the truth of things. Most people would recognize that there's a difference between an idealized version of what humans do and what humans actually do, but for Penrose, this is not an issue, because for him, this truth that humans perceive is an idealized Platonic level of reality which human mathematicians access via non-computational means:
> 6.4 Sometimes there may be errors, but the errors are correctable. What is important is the fact is that there is an impersonal (ideal) standard against which the errors can be measured. Human mathematicians have capabilities for perceiving this standard and they can normally tell, given enough time and perseverance, whether their arguments are indeed correct. How is it, if they themselves are mere computational entities, that they seem to have access to these non-computational ideal concepts? Indeed, the ultimate criterion as to mathematical correctness is measured in relation to this ideal. And it is an ideal that seems to require use of their conscious minds in order for them to relate to it.
> 6.5 However, some AI proponents seem to argue against the very existence of such an ideal . . .
Penrose is not the first person to try to use Gödel’s incompleteness theorems for this purpose, and as with the people who attempted this before him, the general consensus is that this approach doesn't work:
(a) brains do things that aren't computable and
(b) all of classical physics is computable therefore
(c) thinking relies on non-classical physics.
(d) In addition, he speculatively proposed which brain structures might do quantum stuff.
All of the early critiques of this I saw focussed on (d), which is irrelevant. The correctness of the position hinges on (a), for which Penrose provides a rigorous argument. I haven't kept up though, so maybe there are good critiques of (a) now.
If Penrose is right then neural networks implemented on regular computers will never think. We'll need some kind of quantum computer.