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Article 2867 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan18.113219.7766@husc3.harvard.edu>
Date: 18 Jan 92 16:32:17 GMT
References: <1992Jan7.191853.17310@gpu.utcs.utoronto.ca> <1992Jan7.162542.7202@husc3.harvard.edu> <1992Jan13.182633.8209@sun!kla>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Jan13.182633.8209@sun!kla> 
kla!zardoz@sun.com (Phillip Wayne) writes:

>In article <1992Jan7.162542.7202@husc3.harvard.edu> 
>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

MZ:
>>Understanding is a faculty of grasping with the mind the concept or
>>proposition that constitutes the cognitive content of a singular term or a
>>declarative sentence, in virtue of expressing which the term or sentence
>>can be said to be meaningful, and may denote a certain object or a
>>truth-value.  This definition, like all other attemps at real definition,
>>is theory-laden, and should be handled with great care.

PW:
>Once again the problem with "understanding" has come up. Let me see if I can
>try a more formal method.
>
>Let C be a set of concepts. If C is an empty set, then it is "understood". If C 
>is not the empty set, then C is understood only if all of it's components are
>understood.

Why is a concept of an empty set easy to understand?  On the adoption of
the classic "intension varies inversely with extension" law, the concept of
an empty set is a very large one indeed.

PW:
>The problem with this definition is that it assumes there is a set of base 
>concepts (such as number?) which are "automatically" understood. Perhaps 
>only {} is understood, and can we (like in Conway's surreal numbers) build
>our concept of understanding on Nothing?

Or Everything, viz. the concept of all self-identical entities.
Unfortulately, there are some well-known difficulties awaiting us on the
level of extension...

>-- 
>+----------------------------------------------+
>| When you do it to me, it's discrimination    | These are my opinions.
>|    When I do it to you, it's AA              |   Oy vey, are they my opinions
>+----------------------------------------------+      Zardoz


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