From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!usenet.coe.montana.edu!milton!petry Thu Jan 16 17:19:52 EST 1992
Article 2661 of comp.ai.philosophy:
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>From: petry@milton.u.washington.edu (David Petry)
Subject: Re: How to outdo Roger Penrose
Message-ID: <1992Jan13.022633.11107@milton.u.washington.edu>
Organization: University of Washington, Seattle
References: <1992Jan7.212922.20851@oracorp.com>
Date: Mon, 13 Jan 1992 02:26:33 GMT

In article <1992Jan7.212922.20851@oracorp.com> daryl@oracorp.com writes:
>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. 

Actually, in this little game, Penrose is the only one who knows beforehand
whether or not he will write "no" on the answer sheet.  But, within the rules 
of the game, he has no way of communicating that information regardless of 
whether the answer is yes or no.  That being the case, it would be silly to 
assert that Penrose is "lying" if he puts down an answer.

The point is that your conclusion that the correct answer is "no", assuming
that Penrose plays fair, is at best a vacuous pseudo-truth.  And, of course,
it would be absurd to think this little game gives us any insight into the
workings of Penrose's mind.

Now I can guess what you're going to say next.  You're going to say that my
reasoning could also be applied to Godel's Theorem.  You'll claim that
Godel's proof is just a meta-mathematical game.  You'll say that the true
but unprovable assertions it produces are merely vacuous pseudo-truths based
on the unprovable assumption that the axiom system under consideration "plays
fair".  You'll point out that within the rules of Godel's metamathematical
game, an axiom system has no way of communicating a proof of it's own
consistency, but that trivial factoid in no way gives us any insight into
the workings of the axiom system.

Well, you can say those things if you want.  But, remember, only crackpots
and ignoramuses question the authority of the great Kurt Godel.

>Extra credit: show why Penrose' argument doesn't
>prove that he is smarter than any machine.

That's tough.


David Petry

********** NEWS  FLASH **************

SEATTLE - Kurt Godel was spotted today eating lunch with Elvis at the local
Arby's.  He ordered a roast beef sandwich and a Dr. Pepper.



