Lexicon of Arguments

 

I 221
Penrose claims that the very existence of a kind of open mathematical intuition is incompatible with the existing structure of physics and in particular with the Turing principle.
If the Turing principle is true, we can conceive the brain (like any other object) as a computer executing a certain program. Such a program embodies a set of Hilbert's rules of proof, which cannot be complete according to Gödel's theorem.
Therefore, the mathematician whose mind is a computer can also never accept this statement as proven.
Penrose then suggests to present the statement to this mathematician. The mathematician understands the proof. It is, after all, self-evidently valid, and therefore the mathematician can presumably see that it is valid. But that would contradict Gödel's theorem. So there must be a mistake here somewhere. And this is, according to Penrose" opinion, the Turing principle.
I 222
DeutschVsPenrose: E.g.

Deutsch cannot consistently prove the truth of this statement.

I cannot, although I see that it is true. And I also understand the proposition. So it is at least possible that a statement that is inconceivable for a person, can of course be true, however for any other person.
Cf. >Turing machine, >Evidence, >Understanding.