Newsgroups: sci.logic,comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!news.mathworks.com!news.kei.com!bloom-beacon.mit.edu!news.moneng.mei.com!uwm.edu!cs.utexas.edu!news.sprintlink.net!noc.netcom.net!netcom.com!jqb
From: jqb@netcom.com (Jim Balter)
Subject: Re: Putnam reviews Penrose.
Message-ID: <jqbDBI4u8.K6I@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <3ss4sm$cjd@mp.cs.niu.edu> <3t0tn4$p32@netnews.upenn.edu> <jqbDBD193.Iv5@netcom.com> <95Jul9.214427edt.6061@neat.cs.toronto.edu>
Date: Mon, 10 Jul 1995 13:15:44 GMT
Lines: 43
Sender: jqb@netcom7.netcom.com
Xref: glinda.oz.cs.cmu.edu sci.logic:12094 comp.ai.philosophy:29835

In article <95Jul9.214427edt.6061@neat.cs.toronto.edu>,
Calvin Bruce Ostrum <cbo@cs.toronto.edu> wrote:
>In article <jqbDBD193.Iv5@netcom.com>
>   Jim Balter <jqb@netcom.com> wrote:
>
>|  So much gibberish, so little time.
>
>So skip the gibberish and get down to what counts.

I prefer hacking at it with a machete, although Wiener's got such a big supply.
I feel a bit like Leiningen and the Ants.

>| Goedel-limited robots could "arrive" at such statements, they could "see"
>| that they are true, they could "believe" that they are true, they could
>| "know" that they are true, they just couldn't *prove* that they are true.
>| Just like human mathematicians.
>
>Very good.  This is the first time I have seen anyone put so simply
>and clearly the basic fallacy in all of the "Goedel proves man exceeds
>machine" stuff.  Goedel's theorem is a *theorem*.  No reasoning system
>whatsoever can escape it, and it's that simple.  No reasoning system
>whatsoever can exhibit a proof of a Goedel sentence for a formal system
>F in that system.  There *is* no such proof, after all.  
>
>The whole fallacy as is normally presented relies on an equivocation
>between "provide a formal proof of" and "see to be true" (along with
>those other locutions).

Of course.  This is blatantly obvious to anyone not in the grips of an
ideology.

>One may want to argue that machines can't "see" anything to be true
>unless they have provided a formal proof, but this has to be argued and
>it seems to have little to do with Goedel's theorem.

The argument is still an equivocation based upon carefully avoiding defining
"seeing", slipping in anthropomorphic assumptions that beg the question and
circularly entail the desired conclusion.


-- 
<J Q B>

