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From: jqb@netcom.com (Jim Balter)
Subject: Re: Lucas & Penrose's use of Godel
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References: <3tjha2$id2@whitbeck.ncl.ac.uk> <3tjrr2$4ft@cnn.Princeton.EDU> <3tp <3tt84c$lro@aurora.cs.athabascau.ca>
Date: Tue, 11 Jul 1995 16:17:27 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:29935 sci.logic:12184

In article <3tt84c$lro@aurora.cs.athabascau.ca>,
Burt Voorhees <burt@cs.athabascau.ca> wrote:
>>In article <3tp2v6$hei@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthe
>w P Wiener) writes:
>>>The Lucas/Penrose argument is that human intuition will find a way to
>>>see the truth of the statement for which no proof exists.
>>Ok. That seems to be a fairly reasonable statement. However, I still
>>don't see why a machine cannot "see the truth" of a statement for
>>which no proof exists. I can't think of any piece of Godel's theorem
>>which leads to that implication. Doesn't he merely show that there are
>>true statements without proof?
>
>The machine can't "see" the truth of
>statements which are undecidable within
>the formal system which that machine
>is running.

This is not true if "seeing" consists, e.g., of publishing in a reputable
journal.  *Whatever* "seeing" is for human mathematicians, it is *not* the
result of a formally consistent process as described by Goedel.  Thus, Goedel
doesn't tell us whether robots can "see" in this sense (unless you *assume*
that such "seeing" has a non-computational aspect, or you conclude it via
"empirical observation" which, per Hume, is no better than assumption within a
deductive analysis).  This could be *either* because humans are not formal
systems of the right sort, *or* because human thought processes are not
consistent, or both.  The machine can't seeG the truth of statements which are
undecidable within the formal system which that machine is running, where
"seeG" is in the formally consistent sense used by Goedel.  Whatever "seeing"
is for human mathematicians, it is not "seeGing".

>The entire point of the
>argument over this, as far as I am
>concerned, is whether or not the
>machine can be programmed so that
>there is "somebody at home" to do
>the seeing.  

Well, metaphysics certainly isn't *my* point.
-- 
<J Q B>

