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Article 2677 of comp.ai.philosophy:
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>From: cash@convex.com (Peter Cash)
Subject: Re: How to outdo Roger Penrose
Message-ID: <1992Jan13.222623.373@convex.com>
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Organization: The Instrumentality
References: <1992Jan7.212922.20851@oracorp.com> <1992Jan13.022633.11107@milton.u.washington.edu>
Date: Mon, 13 Jan 1992 22:26:23 GMT
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In article <1992Jan13.022633.11107@milton.u.washington.edu> petry@milton.u.washington.edu (David Petry) writes:
>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.
...
>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.

I don't understand what Penrose's ability to "communicate" his intentions
has to do with the problem, or why this has any effect on his answer or on
that answer's truth value. 

>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.

I can't say that I followed the subtleties of Daryl's argument--but I did
think that this much is clear: Penrose can't put down an answer. Given the
rules of the analogy, it seems that no matter whether Penrose writes "yes"
or "no" on his answer slip, the answer has got to be wrong. If he writes
"yes", then he will have failed to use "no", and the answer is wrong; if he
writes "no", then he will have used "no", and the answer is wrong. Thus,
Penrose can't write (I suppose that he is "halted"). Furthermore, the other
player knows what Penrose must do: he can write "No" on his own paper.

I think that this is an original and interesting twist on the old "Liar
paradox". As I said, I can't really follow Daryl's argument, so I don't see
the full application of this analogy to Turing machines, or Penrose, or
whatever. (After corresponding with Daryl about this, I'm convinced that
I'm not the right person to press him for a clearer explanation, since I
lack a lot of the technical background of the discussion about Turing
Machines, and halting problems and so on.)




--
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             |      Die Welt ist alles, was Zerfall ist.     |
Peter Cash   |       (apologies to Ludwig Wittgenstein)      |cash@convex.com
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