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Article 2434 of comp.ai.philosophy:
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Newsgroups: sci.philosophy.tech,sci.logic,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1991Dec30.172852.3305@csc.canterbury.ac.nz>
>From: chisnall@cosc.canterbury.ac.nz (The Technicolour Throw-up)
Date: 30 Dec 91 17:28:51 +1300
Reply-To: chisnall@cosc.canterbury.ac.nz
References: <1991Dec23.112144.6884@husc3.harvard.edu>
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>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"? 

--
Just my two rubber ningis worth.
Name: Michael Chisnall		email: chisnall@cosc.canterbury.ac.nz


