Newsgroups: comp.ai.philosophy,sci.logic
Path: cantaloupe.srv.cs.cmu.edu!europa.chnt.gtegsc.com!news.mathworks.com!gatech!news.sprintlink.net!noc.netcom.net!netcom.com!jqb
From: jqb@netcom.com (Jim Balter)
Subject: Re: Putnam reviews Penrose.
Message-ID: <jqbDBorqB.IJM@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <3ss4sm$cjd@mp.cs.niu.edu> <3tttjh$j5p@netnews.upenn.edu> <3u101c$efu@sun001.spd.dsccc.com> <DBnsFp.5r6@festival.ed.ac.uk>
Date: Fri, 14 Jul 1995 03:15:47 GMT
Lines: 75
Sender: jqb@netcom7.netcom.com
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:30119 sci.logic:12346

In article <DBnsFp.5r6@festival.ed.ac.uk>,
J W Dalton <jeff@festival.ed.ac.uk> wrote:
>afargnol@spd.dsccc.com (Al Fargnoli) writes:
>
>>Ah, but Weiner's logic is intellectually dishonest.  
>
>Sure, keep the insults going.

How selective of you.  So when Wiener calls all and sundry retards and morons,
it goes without comment, but when Fargnoli call his logic intellectually
dishonest, it's an insult.  I suppose if I were to call you "inconsistent",
you would say that I was insulting you.  How silly.  But then, it's what I
have come to expect of you.

>>Weiner seems to be arguing that humans don't have Goedel sentences
>>because none have been determined/found. 
>
>That's not it.  The argument is that it's an empirical observation
>that human mathematicians can see that certain unprovable statements
>are in fact true.  This is positive evidence,

Positive evidence of *what*, pray tell?

>not the negative
>evidence that no Goedel limits on humans have been found.

Positive evidence that human mathematicians can see that certain unprovable
statements are in fact true is not evidence that humans have no Goedelian
limits, unless you claim that Goedel showed that nothing with Goedelian limits
can see that those same unprovable statements are in fact true.  But Goedel
applies to proof procedures, not to seeing, and if you insist that the only
way a robot could see a mathematical truth is through a consistent proof
procedure, then you've won the argument by defining "see" in an unnecessarily
limited way for robots, a different definition than for humans.  But I'll win
it right back by admitting that robots cannot see* unprovable mathematical
truths given this limited definition of see*, but they can see+ unprovable
mathematical proofs, where see+ is a method by which robots generate claims
about mathematics that are not guaranteed to be consistent.  Note that we
already accept such claims from human mathematicians whose claims are not
guaranteed to be consistent.

The funny thing about Penrose is that he wants to show that robots cannot have
aesthetics, etc., etc., by first showing that they cannot have mathematical
insight.  But, since his "proof" that they cannot have mathematical insight is
based on a requirement that their procedures be consistent, the proof simply
does not extend to any other area where the pretense (it is one, you know) of
requiring consistency can be maintained.  No amount of twisting of Goedel will
get you to the conclusion that robots cannot see that something is beautiful.
For that you need prior metaphysical assumptions.

>   In article <95Jul10.044337edt.6061@neat.cs.toronto.edu>, cbo@cs (Calvin Bruce Ostrum) writes:
>   >To repeat the original point, the problem with these attempts to
>   >show man surpasses machine is that they equivocate on the nature of
>   >proof.  They insist that a machine use the "impoverished" formal
>   >notion of proof,
>
>   [...]
>
>   >		  whereas man is entitled to use a richer "informal"
>   >kind of proof. 
>
>   It is not that we are "entitled".  It is an empirical observation that
>   we seem to really on this richer informal kind of proof.  I would call
>   it inductive logic on a platonic realm.

As you equivocate on the nature of proof.  It's an "entitlement" if you refuse
to accept that the same activities carried out by robots constitute "proof" or
if you define the activities in such a way that only humans can carry them
out, or if you just say, as Wiener does, "everybody knows what we mean by
`see'", an approach I know you have great sympathy with.  And no wonder, since
such an approach is inherently intellectually dishonest.

-- 
<J Q B>

