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Article 2819 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: <1992Jan16.233232.7674@husc3.harvard.edu>
Date: 17 Jan 92 04:32:29 GMT
References: <1992Jan15.222457.4889@galois.mit.edu> <1992Jan16.112129.7632@husc3.harvard.edu> <1992Jan16.123103.2429@arizona.edu>
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In article <1992Jan16.123103.2429@arizona.edu> 
bill@NSMA.AriZonA.EdU (Bill Skaggs) writes:

Mikhail Zeleny:
>>To sum up, my position is that, were I a Turing machine, there would exist
>>some formal mathematical theory whose meaning I couldn't understand.
>>Personally, I find this implausible; feel free to judge to the contrary.

Bill Skaggs:
>>  What a remarkable claim!  Are you saying that if I create an axiom
>>system consisting of 10^100 axioms, each 10^1000 symbols long, you
>>would be able to understand it?  I envy you.  I myself have never
>>been able to understand quantum gravity, which is surely trivial
>>in comparison.
>>
>>  Or what exactly are you saying?

MZ:
>>You create it, and I'll understand it, provided that there is anything to
>>understand.  One proviso: the axioms must all be written by hand, in your
>>handwriting.  

John C. Baez:
>>Curioser and curioser: there is no formal mathematical theory whose
>>meaning he can't understand, and yet his optical character recognition
>>is so bad he cannot read typewritten material!

MZ:
>>If I have to make an effort to understand it, he has to make an effort to
>>write it down.  See Emile Durkheim, "De la division du travail social":
>>it's all for the sake of social cohesion.

BS:
>Well, okay, but come on!  Suppose I were to take a simple theorem
>of algebra, such as the statement "\pi is transcendental", and
>translate it into the language of Principia -- it would go on
>for pages and pages, but I could do it.  Suppose I were then to
>invert every quantifier, replacing "there exists" with "for every"
>and vice versa.  The resulting statement would be well formed, and
>you would have not a chance in hell of understanding what it means.

You misunderstand me, Bill: I said that I'll understand it, provided that
there is anything to understand.  In other words, I trust that you will
make it meaningful, rather than merely well-formed.  In effect, I believe
that semantics comes before syntax: "take care of the sense, and the sounds
will take care of themselves".  Also keep in mind that we were talking
about mathematical theories, rather than mere theorems.

BS:
>Have you actually worked with mathematical logic?  I can hardly
>believe that you're disputing this.

Although I prefer simple type theory, I can accomodate you in a language
similar to that of the Principia, suitably equipped with comprehensive
syntactical rules and statements of intended interpretation; you may use
Church's formulation of the ramified type theory in his 1985 JSL article.

Perhaps you still haven't figured out my point.  The epistemological claims
of strong AI entail that we can produce a mathematical theory of such
complexity, that we would be unable to reflect on its interpretation.  I
contend that this is absurd, since in order to formulate such a theory, we
would already need to understand its meaning.  Prove me wrong.

>	-- Bill


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: Mikhail Zeleny                                                     :
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