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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Infinite Minds? (was re: Definition of understanding)
Message-ID: <1992Feb29.014127.9300@husc3.harvard.edu>
Date: 29 Feb 92 06:41:25 GMT
Article-I.D.: husc3.1992Feb29.014127.9300
References: <1992Feb27.025740.8034@a.cs.okstate.edu> <1992Feb27.041137.29433@mp.cs.niu.edu> <1992Feb28.192132.14324@neptune.inf.ethz.ch>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Feb28.192132.14324@neptune.inf.ethz.ch> 
santas@inf.ethz.ch (Philip Santas) writes:

>Assume that the total number of characters that represent all the possible
>human sounds are `m'.
>Suppose that the maximum number of characters a human can spell, write, etc
>during his whole lifetime is `n'
>Now the maximum number of conversations in ALL the existing and non-existing
>languages and their combinations is:
>
>                n
>                S m^i
>               i=0 (absolute silence)
>
>This theoretical object CAN speak in any language you can think or imagine
>or whatever. It can do everything that has a verbal form. Of course not all
>of these conversations are acceptable. But there is an upper limit as you see.
>
>If you want to speak about images and not words, you can do relevant things with 
>pixels. There IS still an upper limit.
>
>Plato's world of ideas IS finite for the mankind.

Nonsense.  Why is m, the number of all possible sign-types, a finite
number?  Furthermore, if meaning is a function of the meaning of
constituent sign-tokens, which in turn is context-dependent, there is
yet another potentially infinite factor to be accounted for.

You are assuming the truth of the discrete mathematical model of a human
mind; in other words, you are assuming the finitude of mind to prove the
finitude of its world of ideas.  Where I come from, this is called begging
the question.

Conjecture: the human mind is best modelled by recursion on admissible
ordinals.  Proof: why not? empirical evidence shows that all we can do,
could be simulated by a computer performing computations involving less
than, say, \omega^c_1 steps.

Why is this argument any less persuasive than the AI perversion of Church's
thesis?  (I would appreciate if my interlocutors were to abstain from
reiterating hackneyed would-be rebuttals.  Also, if you think that you
don't know what I'm talking about, you are probably right.)  The bottom
line to any answer is: "I don't know how to make such a computer."  In
effect, this is the same as saying, circa 1870: "I don't know what humans
can do, that couldn't be done by a steam engine."  Yet better engines were
made.  So until you give me a principled answer as to why such a computer
is *logically* impossible (remember that our best physical theories are
subject to empirical falsification), I will continue to regard the claims
of strong AI as yet another millenial folly.

>Philip Santas

`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
: Qu'est-ce qui est bien?  Qu'est-ce qui est laid?         Harvard   :
: Qu'est-ce qui est grand, fort, faible...                 doesn't   :
: Connais pas! Connais pas!                                 think    :
:                                                             so     :
: Mikhail Zeleny                                                     :
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