[FOM] Recursion Theory and Goedel's theorems
silver_1 at mindspring.com
Mon Aug 6 09:16:54 EDT 2007
I don't wish to argue about Penrose. One reason is
that discussing Penrose's views on consciousness seems inappropriate
for FOM (besides, there are many other groups dedicated to discussing
Penrose). Another reason is that Penrose is a moving target. He's
issued then changed several different claims--while adding others.
I'll present just a few aspects of Penrose's views, then, with
apologies, I'll retreat from the discussion.
The always-engaging, logician George Boolos wrote in "On
'Seeing; the Truth of the Gödel Sentence":
“Penrose has said nothing that shows that we can recognize the truth
of the Gödel sentence for ZF or for any other reasonable
approximation to [the] whole of …mathematics that we ourselves use.
What we can see the truth of is this conditional proposition: The
Gödel sentence for ZF is ZF-unprovable (and therefore true) if ZF is
consistent. We cannot see that the Gödel sentence is true precisely
because we cannot see that ZF is consistent. We may hope or believe
that it is, but we do not know it, and therefore cannot see it.” (p.
390, _Logic_, etc.)
One of Penrose's claims is that: “the very way in which it is
shown that statement G is formally unprovable also establishes the
truth of G”. [Please note the phrase: "the very way".]
He has also allied himself with Stuart Hameroff, and they together
now subscribe to the view that consciousness is caused by
"microtubules" in the brain. I heard Hameroff speak on this topic,
and one of the physicists in the audience said with a hearty laugh
that the physics behind it was all nonsense. A flustered Hameroff
then replied that he wasn't a physicist and wished Penrose were present.
Incidentally, the following has no merit at all except as an <ad
hominem>, but it's been bandied about that Penrose found two
difficult kinds of problems, one pertaining to quantum mechanics and
the other pertaining to consciousness. So, he thought the two must
I prefer not to pursue this discussion any further for the reasons
presented above. If this doesn't seem fair, I apologize. (Again:
there are many other computer groups in which Penrose's views are
actively discussed and debated.)
More information about the FOM