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Article 2474 of comp.ai.philosophy:
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>From: ken@dakota (Kenny Chaffin)
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan2.174436.26054@cherokee.uswest.com>
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References: <1991Dec23.112144.6884@husc3.harvard.edu> <1991Dec30.172852.3305@csc.canterbury.ac.nz>
Date: Thu, 2 Jan 1992 17:44:36 GMT

In article <1991Dec30.172852.3305@csc.canterbury.ac.nz> chisnall@cosc.canterbury.ac.nz writes:
>From article <1991Dec23.112144.6884@husc3.harvard.edu>, by zeleny@zariski.harvard.edu (Mikhail Zeleny):
>> In article <1991Dec23.042312.10049@cambridge.oracorp.com> 
>> ian@cambridge.oracorp.com (Ian Sutherland) writes:
>> 
>> IS:
>>>Intuitionism of the sort you're mentioning rejects the MEANINGFULNESS
>>>of mathematical objects that are beyond the grasp of the human mind,
>>>where "grasp" is interpreted extremely narrowly.  Daryl raises the
>>>possibility that there may be certain things which we can describe
>>>using ordinary mathematics which the human mind cannot, in a certain
>>>well-defined sense, grasp.  That does not mean that he rejects the
>>>MEANINGFULNESS of such objects.  It seems to me that even someone who
>>>agreed with your position would admit that there are SOME mathematical
>>>objects that the human mind cannot, in this same sense, grasp, without
>>>asserting that such objects are therefore meaningless.
>> 
>> Semantic grasp is identical with (the realization of) meaningfulness.  
>> To use the idiom due to David Kaplan, this is both incontrovertible and
>> uncontroversial.  Incidentally, my mind has just grasped 10^10^10.
>
>But "10^10^10" is an exceedingly compact representation for the number
>it denotes.  It is a mere 8 ascii characters, and the function "^" can
>be defined fairly succintly.  Can your mind grasp, say, the base 10
>representation of "10^10^10"? 
>
	But they are not the same thing (are they?). 10^10^10 is simply a
pointer or a place holder for the concept of the actual number, but so is
the number as a whole number. They are just two different ways of expressing
a particular idea. Does the thing pointed to by 10^10^10 really exist? No,
other than as a concept. The concepts exists, but there is no physical object
other than the patterns of neuron firings which represent it differently in
every brain that "grasps" it.

KAC


Kenny A. Chaffin                      {...boulder}!uswat!ken
U S WEST Advanced Technologies         ken@dakota.uswest.com
4001 Discovery Drive  Boulder, CO 80303	     (303) 541-6355
 



