From: Bill Hibbard (firstname.lastname@example.org)
Date: Fri Oct 08 2004 - 10:36:21 MDT
I little more reponse to your last post.
> . . .
> Now, let me come to my refutation of the argument of Penrose:
> . . .
> So, the reason why his argument fails is that he does not
> actually ask the reader the question
> "Will TM_k stop on input k?"
> "Take an extremely complicated true statement S the answering
> of which exceeds your mental capabilities. Is S true or not?"
I think this is equivalent to my answer to Penrose, because
the step of transforming the question "Will TM_k stop on input k?"
into the "extremely complicated true statement S" requires arithmetic
on arbitrary integers, which "exceeds your mental capabilities".
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