(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:
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 . . .
Source:
https://journalpsyche.org/files/0xaa2c.pdf
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:
https://plato.stanford.edu/entries/goedel-incompleteness/#Gd...