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Article 2534 of comp.ai.philosophy:
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>From: daryl@oracorp.com
Subject: How to outdo Roger Penrose
Message-ID: <1992Jan7.212922.20851@oracorp.com>
Organization: ORA Corporation
Date: Tue, 7 Jan 1992 21:29:22 GMT

In analogy with Roger Penrose' essay "How to outdo an algorithm" in
his book _The Emperor's New Mind_, I would like to show how you can
outdo Roger Penrose in a task of reasoning about the world.

In this thought experiment, I put both you and Roger Penrose in an
examination room and give you each an answer sheet and a sharpened
pencil. I then ask you both to write on your respective sheets the
answer to the following question: Will Roger Penrose ever write the
word "no" on his answer sheet? Only yes-no answers are allowed, and
you can only give one answer, after which your answer sheet is taken
from you.

Using introspection, intentionality, consiousness, reflection, and
non-algorithmic intuition, you reason that the answer is "no", so you
write that down. On the other hand, if Roger Penrose answered "no",
then he would be lying. Assuming that Roger is going to play fair,
then he will never write "no" on his answer sheet, so your answering
"no" is correct. You have beaten Penrose! You have solved the
Penrose-halting problem, which Penrose himself could not solve.

P.S. Exercise: show why this thought experiment doesn't prove that you
are smarter than Penrose. Extra credit: show why Penrose' argument doesn't
prove that he is smarter than any machine.

Daryl McCullough
ORA Corp.
301A Harris B. Dates Dr.
Ithaca, NY 14850-1313



