>>Since I read the First Things article last night allow me to comment on
this. (Again, this is from the November First Things: "Atheism in the
Gaps" by Barr; disclaimer, my comments are not based on reading the
book.) According to Barr, Roger Penrose's discussion is based on Godel's
theorem which shows that a proposition can be stated using the axioms and
theorems of a mathematical system that cannot be proven in that system,
but which to a human observer "outside" the system can clearly be seen to
be true.
If you believe his argument, he has in effect proven that it is impossible
for a computer to duplicate the activities of the human mind, since a
computer is essentially a mathematical system that cannot stand outside
itself looking in the way that humans do with their capacity for irony,
etc. (The way it was put in the book _Godel, Escher and Bach_, human's can
comprehend sentences such as "The sentence 'this sentence is true' is
false" which deal with self-referential contradictions. I mention this
only because the author o that book, a computer scientist, was attempting
to use Godel to say that computers _can_ duplicate the feats of the human
mind.)<<
I find it strange that Penrose was presenting such an argument in 1994. I
suppose the argument has as much validity in 1994 as when it was first
posited: I specifically recall attending a lecture some 40 years ago
entitled "What Machines Can't Do", which was directed to high school
students and given at the University of Minnesota. It was a good but
challenging talk for such an audience, including this agnostic (at the
time), who really did not know what to make of the message.
Presumably, Penrose's book describes some recently developed ideas.
Gordie