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Article 4177 of comp.ai.philosophy:
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>From: santas@inf.ethz.ch (Philip Santas)
Subject: Re: Infinite Minds? (was re: Definition of understanding)
Message-ID: <1992Mar1.192308.5252@neptune.inf.ethz.ch>
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Organization: Dept. Informatik, Swiss Federal Institute of Technology (ETH)
References: <1992Feb27.041137.29433@mp.cs.niu.edu> <1992Feb28.192132.14324@neptune.inf.ethz.ch> <1992Feb29.014127.9300@husc3.harvard.edu>
Date: Sun, 1 Mar 1992 19:23:08 GMT
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In article <1992Feb29.014127.9300@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>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.

1) The range of frequences the human ear can receive is limited, and discrete
   (example: music tones). Proof: limited number of neurns and connections
   among them; digital functioning.
2) The number of characters a human can type is discrete and limited.
3) The number of different characters you can type on a big piece of paper
   is limited and discrete (remember the pixel combinations).
4) You cannot go endlessly searching for meanings since your life is finite.
5) Contexts are discrete.

>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.

I said 'finite for the mankind', not in theory:
Seeing, listening, speaking, dreaming etc. CAN be modelled with the help of
descrete mathematics. If you define understanding as A combination of all these,
then it is an engineer's task to construct such machine with reasonably limited 
resources.

Your model looks like the transformation of ONE function into a sum of infinite
terms. One can also imagine that any particle can be the collection of an
infinite number of other particles. If these have a meaning or not this is another 
story and it has been already analysed by Russell (the golden-mountain example). 

It is true that a relation between two objects forms a new concept, and a 
relation between two relations is another one, and you can create an endless 
loop by constructing new relations and concepts. This loop IS by itself
a concept that generates new ones. But I do not see how you can 
instanciate all these in your limited discrete life.

Philip Santas

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email: santas@inf.ethz.ch				 Philip Santas
Mail: Dept. Informatik				Department of Computer Science
      ETH-Zentrum			  Swiss Federal Institute of Technology
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