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Article 5844 of comp.ai.philosophy:
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>From: forbis@carson.u.washington.edu (Gary Forbis)
Subject: Re: Universe is a big place ,,,
Message-ID: <1992May22.145109.26123@u.washington.edu>
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Organization: University of Washington, Seattle
References: <1992May21.220532.17325@mp.cs.niu.edu> <1992May22.014751.17847@u.washington.edu> <1992May22.041258.14109@mp.cs.niu.edu>
Date: Fri, 22 May 1992 14:51:09 GMT

In article <1992May22.041258.14109@mp.cs.niu.edu> rickert@mp.cs.niu.edu (Neil Rickert) writes:
>In article <1992May22.014751.17847@u.washington.edu> forbis@carson.u.washington.edu (Gary Forbis) writes:
>>(Neil Rickert) writes:
>>>(Gary Forbis) writes:
>>>>(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.
>>>
>>>>I think Goedel's incompeteness theorem has everything to do with the formal
>>>>aspects of human cognition.  How can you consistently believe otherwise?
>>>
>>> Which formal aspects of cognition do you have in mind?
>>
>>Reason.

> 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? 

>>We have gone out of our way to formalize our reasoning and that which is
>>not formal is labeled "irrational".  I think humanity is most proud of its
>>castles in the sky and trys to sweep the rest under the rugs.  Without our
>>formal reasoning we do not know if our beliefs are consistent with each other
>>or form a complete system.

>  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.

>>We know how to do integer arithmetic and a complete theory of cognition must 
>>include a theory of how we can do integer arithmetic.  Goedel's
>>incompleteness theorem applies to our theories of cognition and this tells 
>>us something about our cognitive abilities. 

>  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?  Do you propose an unformalizable understanding and
in what way is it understanding?  No matter how hard we try we will not be
able to generate a complete and consistent theory of human cognitive abilities.

--gary forbis@u.washington.edu


