[Chronos]

A while ago I wrote up my objections to the Penrose-Lucas argument: https://chronos-tachyon.net/essays/penrose-objections/ . I'm not super proud of how it turned out (way too meandering), but it boils down to:

1. Let's suppose for sake of argument that humans really can see the inherent truth of "Peano Arithmetic is consistent". That doesn't mean humans violate Gödel's Incompleteness Theorem: it could just mean that humans use axioms stronger than PA.

2. Gödel's Incompleteness Theorem only applies to systems that are perfectly logically consistent. Not sure how Penrose didn't notice, but humans... aren't.

3. When scientists proposed Quantum Mechanics as a replacement for Classical Mechanics, it was on them to explain how Quantum Mechanics simplified to Classical Mechanics in the common case. "Penrose Mechanics" is an even more radical departure — especially from a physics of computation standpoint, as Penrose Mechanics by definition would allow solving at least some of the problems in (ALL - R) in ~polynomial time. Penrose needs to explain how Penrose Mechanics reduces to Quantum Mechanics in the common case.

4. Penrose proposes that (a) there exist new physics, (b) that evolution has learned to computationally exploit the new physics via microtubules, and yet (c) that humans are the only lineage to make use of this feature of microtubules, even though microtubules are found in all eukaryotic cells (from mushrooms to amoebae). From a predator-prey standpoint alone, it would seemingly be a huge evolutionary advantage to be able to compute NP or R functions in polynomial time. (That ability is not _strictly_ implied by Penrose Mechanics, but it's a very likely consequence.) Penrose needs to explain why only humans are taking advantage of the computational power of microtubules, when microtubules have existed for billions of years and across millions of species.

[dilemma]

>2. Gödel's Incompleteness Theorem only applies to systems that are perfectly logically consistent. Not sure how Penrose didn't notice, but humans... aren't.

Why are humans not logically consistent then, if they are as materialists claim, something that can be abstracted with a computer program if we have full information of their workings?

[Chronos]

Um, you seem to be operating on a confusion of ideas. Materialism does not imply that humans are logically consistent. The universe in which we exist is (probably?) a logically consistent system, but that's true for both materialism and non-materialism. The difference between the two is which set of rules the universe runs on, not whether those rule sets are internally consistent.

When I say "systems that are perfectly logically consistent" and "humans... aren't", I'm saying that the ideas humans have in their heads are not logically consistent. It's possible to write down "2+2=5" on a piece of paper, even if 2 plus 2 doesn't actually equal 5, and it's likewise possible for humans to believe "2+2=5" even if 2 plus 2 doesn't equal 5.