Another URL is:
http://psyche.cs.monash.edu.au/psyche-index-v2.html#som
(maybe the same thing; Psyche is an Australian on-line journal)
This has critiques of Penrose by such as Moravec, Chalmers, John McCarthy,
and other AI philosophers, including McDermott. Penrose has a rebuttal as
well. Quite technical, especially in terms of the discussions of Godel.
> Why not program computer in a similar way? I think program that uses
> guesses could many times finds proof faster than program that thinks
> formally. Conjectures would be zero order uncertain proofs.
I believe there have been various AI programs which worked on heuristic
reasoning (smart guesses). Doug Lenat's Eurisko was a well known example
from the early 1980's.
Hal