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From: jqb@netcom.com (Jim Balter)
Subject: Re: Putnam reviews Penrose.
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Date: Fri, 14 Jul 1995 11:10:36 GMT
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In article <BILL.95Jul13211301@ca2.nsma.arizona.edu>,
Bill Skaggs <bill@nsma.arizona.edu> wrote:
>Edward Faith:
>   Supposing this is settled, do you have proof that a computer would
>   not be able to rely this richer informal kind of proof?
>
>Matthew P Wiener:
>   Yes.  Goedel's theorem.
>
>Edward Faith:
>   Goedel's theorem places a limit on formal proofs.
>   It says nothing about informal proofs.
>
>Matthew P Wiener:
>   Other than a machine not having them, you're right, it says nothing.
>
>Edward Faith:
>   I guess I didn't read the proof carefully.  Could you point out the
>   part where it talks about informal proofs?

Repeated pleas are not likely elicit any such details from Wiener.  He will
claim that he already gave them, and that if you don't understand this then
you are a moron or a retard (we all believe these things of others at times,
and they may even be true, but civilized persons recognize that it is
pointless and arrogant to actually make such assertions).

>Excuse me for answering a question aimed at somebody else, but what
>Wiener is trying to say here (I think) is that, for purposes of this
>discussion, a machine is an entity that does everything according to a
>set of formal rules.  Such an entity cannot, by definition, give an
>informal proof.  If you don't agree with this, you should explain what
>you mean by "informal".

As Wiener as pointed out, we are talking of a certain sort of machine,
not just any old machine.

Since a computing machine could emulate a human's behavior (if not its
internal process) when a human gives an informal proof, such machines do not
have such an incapacity as you claim, unless you use the phrase "informal
proof" in such a way that the activity is informal when done by humans but
formal when done by computing machines.  Of course, this begs the question,
since it carries the assumption that humans are not describable as formal
systems.  Really, we've been through all this over and over, why go over it
again?


-- 
<J Q B>

