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Article 5328 of comp.ai.philosophy:
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>From: santas@inf.ethz.ch (Philip Santas)
Newsgroups: comp.ai.philosophy
Subject: symbols per-se (was: Re: Peano and the commerce of ideas and repr)
Message-ID: <1992Apr29.154023.7989@neptune.inf.ethz.ch>
Date: 29 Apr 92 15:40:23 GMT
Article-I.D.: neptune.1992Apr29.154023.7989
References: <5995.111921218@kcbbs.gen.nz>
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In article <5995.111921218@kcbbs.gen.nz> Hakki_Kocabas@kcbbs.gen.nz (Hakki Kocabas) writes:
>In article <kv3lf9INNe8g@exodus.Eng.Sun.COM> silber@orfeo.Eng.Sun.COM (Eric Silber) writes: 
>>
>> Assert for the purpose of disputation that "real mathematical objects"
>> exist independent of the physical world.
>>
>> Hence  Integer-3 for which "3" is a physical representation, exists
>> independent of the physical world.
>>  Does Integer-3 know that it is an integer?
>>  Does Integer-3 know what its successor is?
>
>RMO = Real Mathematical Objects
>PW  = Physical World
>
>In your use, can you say that a reality corresponds to
>'RMO exist independent of the PW' if it is true and we can assert it ?
>If yes, so you have a use for 'RMO exist independent of the PW'
>
>Do you use 'RMO exist independent of the PW' as an explanation of
>the use of the words ?
>
>Can you construct an application of this-symbol/these-symbols ?
>Is this a definition about a symbol ?

Suppose that a symbol exists only per-se, ie it has no meaning,
it is not refereing to anything except to itself. Can one make anything with it
as one does with numbers?

>If you use it as a mathematical proposition, can you prove it in
>mathematics according to certain rules ?

In the same rational, can one show that such symbols have any properties?

>If 'RMO exist independent of the PW' is a rule, do you know how is it used ?

In this case symbols do not mean anything else except their identity.

Symbols have been used extensively in algebra.
The problem is: can one strip them from the objects they
represent and treat them as independent entities?

Philip Santas

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