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Article 5846 of comp.ai.philosophy:
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>From: rickert@mp.cs.niu.edu (Neil Rickert)
Newsgroups: comp.ai.philosophy
Subject: Re: Universe is a big place ,,,
Message-ID: <1992May22.163150.13424@mp.cs.niu.edu>
Date: 22 May 92 16:31:50 GMT
References: <1992May22.014751.17847@u.washington.edu> <1992May22.041258.14109@mp.cs.niu.edu> <1992May22.145109.26123@u.washington.edu>
Organization: Northern Illinois University
Lines: 68

In article <1992May22.145109.26123@u.washington.edu> forbis@carson.u.washington.edu (Gary Forbis) writes:
>In article <1992May22.041258.14109@mp.cs.niu.edu> rickert@mp.cs.niu.edu (Neil Rickert) writes:
>>>>>> However, Goedel's incompleteness theorem has NOTHING to say about human
>>>>>>cognitive ability.  It is merely a red herring which some people like to
>>>>>>drag up from time to time.

>> How can you be sure that reason is part of cognition, rather than a
>>cultural construction built with our cognitive abilities, but not itself
>>part of them?
>
>I will grant that our theories about reasoning are cultural constructs.
>I wonder which came first, our ability to reason or our theories about
>those abilities? 

  I'm sure you don't wonder at all.  You obviously need to be able to reason
in order to be able to develop theories about reasoning.

>>  Perhaps humanity is "most proud" of this because it is humanity's
>>invention, rather than part of our native cognitive equipment.
>
>I'll agree as long as we are talking about our theories about our abilities
>rather than our abilities.  Our native cognitive equipment had the capacity
>to reason prior to our invention of theories about reasoning.

 I think you greatly overemphasize the importance of our ability to reason.
Reasoning is a linguistic construction.  Any creature with adequate language
abilities would, in principle, be capable of reasoning.  The question for
cognitive science is how does language itself work.

  Remember that there are some pretty good computer programs out there for
automating reasoning, theorem proving, etc.  If you can do it on a computer
you can in principle do it whenever there is a sufficient language so as to
supply an adequate symbol system.

  What the computerized theorem proving systems are not good at is in
deciding which theorems to try to prove.  The automated reasoning systems
have trouble knowing what to reason about.  That is the hard part.  And that
is surely tied up with semantics, pattern recognition, etc, all of which
are very informal and for which Goedel presumably has little relevance.

>>  I would be quite satisfied to fully understand the cognition of members
>>of a very primitive tribe which had not yet developed arithmetic.  How
>>would Goedel apply to their cognition?  Yet their cognition is, apart from
>>cultural influences, the same as ours.
>
>Even a person who has not learned to do arithmetic has the cognitive capacity
>to do arithemtic.  Do you propose to understand cognition without understanding
>the limits of cognition?

  Even a dumb computer has the ability to do arithmetic.

  Humans are limited by many things.  The boiling point of water limits how
far you can heat water and still have it liquid.  The velocity of light limits
the rate of communication.  Goedel's theorem limits what can be done with the
formal manipulation of abstract symbols.  Why choose one particular limitation
and call that a limit of cognition?

  From the point of view of investigating cognition, the limitations on the
formal manipulation of abstract symbols just does not seem relevant.  The
real questions center around the origin of our symbol system (language),
and the ability of that language system to extend beyond purely abstract
symbols and represent semantic information.

-- 
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  Neil W. Rickert, Computer Science               <rickert@cs.niu.edu>
  Northern Illinois Univ.
  DeKalb, IL 60115                                   +1-815-753-6940


