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Article 2796 of comp.ai.philosophy:
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>From: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan16.123103.2429@arizona.edu>
Date: 16 Jan 92 19:31:02 GMT
References: <1992Jan14.211840.2423@arizona.edu> <1992Jan15.143037.7600@husc3.harvard.edu> 
 <1992Jan15.222457.4889@galois.mit.edu> <1992Jan16.112129.7632@husc3.harvard.edu>
Reply-To: bill@NSMA.AriZonA.EdU (Bill Skaggs)
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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.
>

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.

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

	-- Bill


