Newsgroups: sci.logic,comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!news.sprintlink.net!howland.reston.ans.net!ix.netcom.com!netcom.com!jqb
From: jqb@netcom.com (Jim Balter)
Subject: Re: Putnam reviews Penrose.
Message-ID: <jqbDBIEFq.C54@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <3ss4sm$cjd@mp.cs.niu.edu> <95Jul9.214427edt.6061@neat.cs.toronto.edu> <jqbDBI4u8.K6I@netcom.com> <3trblc$em9@netnews.upenn.edu>
Date: Mon, 10 Jul 1995 16:43:02 GMT
X-Original-Newsgroups: sci.logic,comp.ai.philosophy
Lines: 93
Sender: jqb@netcom7.netcom.com
Xref: glinda.oz.cs.cmu.edu sci.logic:12119 comp.ai.philosophy:29863

In article <3trblc$em9@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>In article <jqbDBI4u8.K6I@netcom.com>, jqb@netcom (Jim Balter) writes:
>>>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.
>
>The only ideology I am in the grips of is a reliance on observation and
>logic and evidence.
>
>It is evident that robots, by definition, ultimately depend on some
>equivalent of formal proofs to output "belief".

This is utterly false.  I build robots every day that produce no formal proofs
yet have heuristics, state information, etc.  Being ontologically
sophisticated, I consider these a form, perhaps an embryonic form, of
"belief".  Goedel only puts very specific limits on certain beliefs connected
to the precise formal system at hand, and in a context of complete
consistency.  My robots have inconsistent beliefs, even if they are modeled
within a consistent formal system.  Thus Goedel isn't applicable.

Anyone who concludes that no robot can shout "Eureka!" because of some
limitation of the underlying formalism is ignoring observation, logic,
and evidence.

>
>It is also evident that human seem to see things to be true, in a
>Platonic manner.

This "Platonic manner" stuff is a matter of philosophical interpretation
that has no place in a discussion about logic.

It is also evident that humans hold inconsistent beliefs, although I don't
quite seem able to enunciate an example of my own just now.  Perhaps you could
demonstrate the superiority of the human mind by stating two inconsistent
things, both of which you currently believe to be true.  Or perhaps you would
prefer to claim that you hold no inconsistent beliefs.  If so, you could try
providing a proof.  Or perhaps this is something that you can simply see as
true, without needing proof.  Myself, I can see, without needing proof, that
all humans hold partially inconsistent beliefs.  I can also see as true,
without needing proof, that any significantly intelligent robot would also
hold partially inconsistent "beliefs", that this would not prevent it from
reasoning or shouting "Eureka!", and that this would make it immune to all
arguments concerning Godelian limits.

>There is no equivocation involved.

Just argumentum ad ignorantiam.

>
>>>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",
>
>Why should it be carefully defined?  It merely refers to the process
>whose end point is human mathematician declares "X is indeed true",
>regardless of whether he has a proof or not.

And nothing prevents robots from declaring "X is indeed true", regardless if
whether it has a proof or not.  To declare otherwise is truly to disregard
observation and evidence, overriding it with faulty logic.

>
>>		    slipping in anthropomorphic assumptions that beg
>>the question and circularly entail the desired conclusion.
>
>Identify such.

Uh, you defined "see" in terms of human mathematicians.  How about

>Why should it be carefully defined?  It merely refers to the process
>whose end point is robot mathematician declares "X is indeed true",
>regardless of whether it has a proof or not.

If you want to claim that that cannot happen because it contradicts Goedel,
you are just being silly.  Here, I will build a little perl mathematician
robot, and see what it can do:

Con(ZF) is indeed true.

There, you see, my robot saw that Con(ZF) was true, by your definition
of "see".  If that's not what you meant by "see", then give a another
definition.  One that doesn't slip in anthropomorphic assumptions
that beg the question and circularly entail the desired conclusion.
-- 
<J Q B>

