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>From: zeleny@coolidge.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Infinite Minds? (was re: Definition of unders
Message-ID: <1992Mar4.142249.9478@husc3.harvard.edu>
Date: 4 Mar 92 19:22:46 GMT
Article-I.D.: husc3.1992Mar4.142249.9478
References: <1992Mar1.192308.5252@neptune.inf.ethz.ch> <1992Mar1.170031.9365@husc3.harvard.edu> <1992Mar2.110028.13029@neptune.inf.ethz.ch>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Mar2.110028.13029@neptune.inf.ethz.ch> 
santas@inf.ethz.ch (Philip Santas) writes:

>In article <1992Mar1.170031.9365@husc3.harvard.edu>
>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes 

>>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:
>But there is still an upper limit on the number of all the possible
>conversations (including those that have any meaning, and those
>thast have absolutely NO meaning) you can lead in your life. 
>That means that there is s finite
>number of concepts you can learn, imagine, express, etc.

Even so, it still doesn't follow that we have to choose them from a finite
set of concepts, as your assertion that "Plato's world of ideas IS finite
for the mankind" would seem to indicate.

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.
>>               ^^^^^^^^^^^^^^^^^^^

MZ:
>>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:
>An *unverifiable* model extremely useful in engineering and in every day life.
>Movies, Cartoons, TV, CD, Cards etc, are all based in this model,
>and they work perfectl (even my dog can watch TV although it does not smell).

Big deal.  The flat earth hypothesis resulted in some nifty maps, too.

PS:
>A model or a theory fails if there is evidence AGAINST it.
>Can YOU share them with us?

I don't have to.  Since you are the one making a categorical claim, the
burden of proof falls on you.  Show me that human mind has "digital
functioning", and don't forget to define your terms beforehand.

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

MZ:
>>This says nothing about the number of character-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).
>>                  ^^^^^^^^

MZ;
>>"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:
>You do remember words, sounds, images, and their sequences.
>Since you do not seem to remember smells and tastes, and you
>don't smell or touch when you dream, then we can put them out of
>our modell (if you don't have any objection).

For a summary of objections, see Proust.

PS:
>If you present the rest with pixels (and as I have explained I do not see any 
>reason why not to) their cominations in a huan life is finite.

First of all, it's not `present', but `REpresent', something that couldn't
be accomplished without the mediation of a concept; secondly, as I already
noted earlier, I am not suggesting that the number of human representations
is finite; still, this has absolutely no bearing on the cardinality of
"Plato's world of ideas".

PS:
>I am wondering what you mean by understanding if you don't have a representative
>pictue or text in your mind, or a Sartrian mechanism for the regeneration
>of the experience.

I don't see any "representative pictures or text in [my] mind"; neither did
Berkeley. As for Sartrian mechanism for the regeneration of the experience,
I'm afraid you have me at a disadvantage once again, as I've no idea what
it might be.  Does it have anything to do with Wilhelm Reich and his orgone
box? 

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.

MZ:
>>I don't define understanding in this way.

PS:
>Can you give a clear definition of understanding?

No.  However I don't see it as reducible to phenomenal experience.

MZ:
>>Moreover, modelling is not identity.

PS:
>A model is the basis for the construction of a machine.
>It is irrelevant if this machine is identical to you or me (since it is irrelevant
>if you ar eidentical to me). The external behaviour of this machine is what matters.

I don't believe that.  

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).

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

PS:
>There is relevance. Many of the concepts you can construct are simply
>non existent since this construction derives from wrong usage of the language.
>On the other hand many of your 'new' relations are nothing else but
>a repetition of already mentioned reletions, so you can reject them.
>I do not know if you can go like this till infinity.

So all that remains is for you to show that you can reject all but finitely
many of them.  Looks like we're back where we started.

MZ:
>>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.

PS:
>You tell me that I do not take Plato seriously? This is a joke,
>since I have learned to admire Plato from my early childhood
>(I had also the luck to read it in the original).

Should I be impressed by this?

PS:
>If you construct a finite number of definitions or axioms, then 
>it is possible that you can derive an infinite number of theorems.
>Notice now that these theorems are already included in these definitions
>although not discovered yet (if I remember correct, Heidegger mentions it).

Note that "construct" is certainly inappropriate in this context.  Try
"discover". 

PS:
>Now if you accept that Plato means that ideas are ALL these theorems
>(the shadows in the cave) then you may have right.

More than that, some Ideas are the truths that will never be discovered or
enunciated.

PS:
>But if the ideas are the basic concepts from which all the rest
>derive (it seems pretty obvious to me, since Plato speaks about
>cave, shadows, and some moments of light) then I do not see how 
>you have the possibility to make an infinite number of such theories.

Again, all I claim is that our conceptual world is not limited by our
finite capabilities.

PS:
>Before you make any criticism of my interpretation of Plato,
>you better read his theories under a differnt perspective.
>Plato used metaphors in an extremely high niveau, and therefore
>any dogmatic interpretation of his concepts from your side is nothing else
>but a fruitless Unsinn.

I'd choose dogma over inconsistency.  Happily, I don't have to choose either. 

>Philip Santas
>
>--------------------------------------------------------------------------------
>email: santas@inf.ethz.ch				 Philip Santas
>Mail: Dept. Informatik				Department of Computer Science
>      ETH-Zentrum			  Swiss Federal Institute of Technology
>      CH-8092 Zurich				       Zurich, Switzerland
>      Switzerland
>Phone: +41-1-2547391
>      


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