Now suppose that there could be a computer program that could perform all the mental feats of which a man is capable. (In fact, such a program must be possible if each of us is in fact a computer.) Given sufficient time to study the structure of that program, a human mathematician (or group of mathematicians) could construct a "Godel proposition" for it, namely a proposition that could not be proven by the program but that was nevertheless true, and-here is the crux of the matter-which could be seen to be true by the human mathematician using a form of reasoning not allowed for in the program. But this is a contradiction, since this hypothetical program was supposed to be able to do anything that the human mind can do.
The contradiction was introduced just before in the thought experiment's gimmee test condition:
. . . but that was nevertheless true, and-here is the crux of the matter-which could be seen to be true by the human mathematician using a form of reasoning not allowed for in the program.
Sneak it in and "Ta-dah" on it in the next sentence! If the program is a perfect human emulator, you can't disallow it any form of logic humans can do. There may be a Godel proposition for the program, but it's a Godel proposition for the human too so there's no distinction.
Maybe it's the article-writer's fault. I tried to read Penrose's The Emperor's New Mind and gave it up about 2/3 through. He's like a professor that gets lazy about making sure the class is still with him and starts to just drone on while the students, lost, doodle in their notebooks.
I don't buy that the mind is not a machine operating under the laws of physics. Maybe I just need to see the proof written up a little better.
Is it fair to say, Vade, that quantum mechanics "proves" that "particality", the Universe at its most funadmental level (and thus all of the Universe), is an unanswered question since the best that can be done is a probability distribution? Does Free Will answer this question, fill this "gap"? Can there be Free Will without consciousness?
Fun Stuff.