Re: Penrose (Was: Infinities)

Leevi Marttila (
09 Nov 1997 11:54:35 +0200

Hal Finney <> writes:

> I just skimmed Penrose's book, but my impression is that he claims that
> mathematicians have an instinctive ability to recognize mathematical
> truth. Machines, which are deterministic computer programs and therefore
> can be in principle be described as formal systems, are limited by Godel's
> theorem and are unable to recognize certain truths. Since people are
> (according to Penrose) unlimited in their ability to recognize mathematical
> proof, this would mean that they are not formal systems and therefore no
> machine can do mathematics in the way a person does. (And hence, among
> other things, uploading and AI are impossible.)

Wouldn't adding random input to machine make Penrose's argument about
Godel's theorem irrelevant?