From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!think.com!hsdndev!husc-news.harvard.edu!zariski!zeleny Mon Mar  9 18:34:22 EST 1992
Article 4179 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:4179 sci.philosophy.tech:2220
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!think.com!hsdndev!husc-news.harvard.edu!zariski!zeleny
>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Infinite Minds? (was re: Definition of unders
Message-ID: <1992Mar1.170031.9365@husc3.harvard.edu>
Date: 1 Mar 92 22:00:29 GMT
References: <1992Feb28.192132.14324@neptune.inf.ethz.ch> <1992Feb29.014127.9300@husc3.harvard.edu> <1992Mar1.192308.5252@neptune.inf.ethz.ch>
Organization: Dept. of Math, Harvard Univ.
Lines: 120
Nntp-Posting-Host: zariski.harvard.edu

In article <1992Mar1.192308.5252@neptune.inf.ethz.ch> 
santas@inf.ethz.ch (Philip Santas) writes:

>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:

PS:
>>>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.

MZ:
>>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.

PS:
>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.
		^^^^^^^^^^^^^^^^^^^
This is just ridiculous.  "Digital functioning" is an *unverifiable* model.
If you have evidence to the contrary, please share it with the rest of the
world. 

PS:
>2) The number of characters a human can type is discrete and limited.

This says nothing about the number of chatacter-types he can choose from.

PS:
>3) The number of different characters you can type on a big piece of paper
>   is limited and discrete (remember the pixel combinations).
		   ^^^^^^^^

"Discrete" is meaningless in this context.  I don't communicate in pixels
only.  The fact that you get my messages so encoded doesn't imply that
their meaning gan be quantified independently of the unquantifiable context.

PS:
>4) You cannot go endlessly searching for meanings since your life is finite.

Again, this says nothing of the number of meanings you can find.

PS:
>5) Contexts are discrete.

Unsubstantiated, unverifiable assertion.

MZ:
>>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.

PS:
>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.

I don't define understanding in this way.  

Moreover, modelling is not identity.

PS:
>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). 

I don't see the relevance of Russell's treatment of Meinongian possibilia
to the issues we are discussing here.

PS:
>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.

You aren't taking Plato seriously; what you are describing is a Popperian
"constructed concepts".  *Assuming* the truth of the discrete model, your
argument might go through for the Popperian picture; however it won't go
through for the case in which the concepts preexist their embodiments.

>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                                                     :
: 872 Massachusetts Ave., Apt. 707                                   :
: Cambridge, Massachusetts 02139           (617) 661-8151            :
: email zeleny@zariski.harvard.edu or zeleny@HUMA1.BITNET            :
:                                                                    :
'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`


