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Article 1211 of comp.ai.philosophy:
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>From: yodaiken@chelm.cs.umass.edu (victor yodaiken)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Is there any such thing as informal logic?
Message-ID: <38814@dime.cs.umass.edu>
Date: 6 Nov 91 12:52:16 GMT
References: <JMC.91Nov3225619@SAIL.Stanford.EDU> <1991Nov4.182613.5073@husc3.harvard.edu> <1991Nov6.055917.14285@CSD-NewsHost.Stanford.EDU>
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In article <1991Nov6.055917.14285@CSD-NewsHost.Stanford.EDU> costello@CS.Stanford.EDU (Tom Costello) writes:
>I think this rather shows the opposite.  It reminds me of the standard model
>of mathematics.  It is easily shown that there is no finite axiomisation of the 
>standard model.  Thus very simply there is no way of describing the standard
>model.  Of course, if you were a dualist with transfinite amounts of memory
>you could have a description of the standard model.  However there is no way
>that you can describe it to me.  Put simply the standard model of mathematics
>does not exist as a meaningful term in communication.

No *first order theory* can precisely define the standard model of
arithmetic or set theory. But we have algebra in which the theory of the
ring Z is quite precise, we have second order logics, we have primitive
recursive  and other methods of describing the integers and arithmetic. 
The standard model of mathematics may not exist as a "meaningful term
in communication", as I certainly have no idea what "meaningful term
in communication" entails, but we generally have little difficulty in
describing it or reasoning about it. Look at a book on number theory, if
you are in doubt. 


