"If the human mind has a transcendent ability to perceive mathematical truth, placing it outside of mathematics, then Penrose has found a mechanism that can resolve the undecidability he found in the foundation of physics.
In other words, Penrose has shown mathematically that the physical world requires a mind’s transcendent power in order to operate, at least within the two physical systems he has analyzed.
So, the world isn’t matter.
It isn’t energy.
It isn’t even information.
The world is fundamentally controlled by a mind.
Talk about mind-blowing!
As you might expect, Penrose’s view is not without critics.
The common objections are:
The mind is not a complete mathematical system. It has some random and inconsistent elements which means it can prove its own Gödel sentence.
The mind is too complex and inscrutable for humans to ever identify its Gödel sentence.
If humans could understand the truth of the mind’s Gödel sentence, this would be a contradiction. Therefore, it is a logical impossibility for humans to understand the truth of the mind’s Gödel sentence.
Penrose thinks that only the second objection has significant weight.
Based on the universality of mathematical insight, it is impossible for the mind to have a Gödel sentence without resulting in a contradiction. Since the mind cannot have a Gödel sentence, then the mind cannot be a mathematical system. Therefore, Penrose believes, the mind is beyond mathematics and thus it can solve the undecidable problems at the foundation of reality."
The mind is too complex and inscrutable for humans to ever identify its Gödel sentence.
If humans could understand the truth of the mind’s Gödel sentence, this would be a contradiction. Therefore, it is a logical impossibility for humans to understand the truth of the mind’s Gödel sentence.
Penrose thinks that only the second objection has significant weight.
Based on the universality of mathematical insight, it is impossible for the mind to have a Gödel sentence without resulting in a contradiction. Since the mind cannot have a Gödel sentence, then the mind cannot be a mathematical system. Therefore, Penrose believes, the mind is beyond mathematics and thus it can solve the undecidable problems at the foundation of reality."
MindMatters