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Article 1209 of comp.ai.philosophy:
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>From: costello@CS.Stanford.EDU (Tom Costello)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Is there any such thing as informal logic?
Message-ID: <1991Nov6.055917.14285@CSD-NewsHost.Stanford.EDU>
Date: 6 Nov 91 05:59:17 GMT
References: <1991Oct22.041210.5931@watserv1.waterloo.edu> <JMC.91Nov3225619@SAIL.Stanford.EDU> <1991Nov4.182613.5073@husc3.harvard.edu>
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In article <1991Nov4.182613.5073@husc3.harvard.edu>, zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
|> In article <JMC.91Nov3225619@SAIL.Stanford.EDU> 
|> jmc@SAIL.Stanford.EDU (John McCarthy) writes:
|> 
|> JMC:
|> >Since the remaining points of the argument are either terminological
|> >or concern the prospects of the logicist approach to AI, there is
|> >no point in continuing unless Zeleny or Yodaiken would like to offer
|> >some arguments against the prospects of AI in general or the logicist
|> >approach in particular.
|> 
|> You mean you haven't been convinced by the Nasruddin story?  I guess this
|> means that I must try harder... please let me know if I get too abstruse.
|> 
|> Consider Davidson's argument in ``Theories of Meaning and Learnable
|> Languages'', in the context of his program of extensional semantics.  Now,
|> various devices like Frege's paradox of the name relation, or Putnam's
|> model-theoretic argument, demonstrate the inadequacy of the extensional
|> approach to the task of characterizing the linguistic relation of denoting;
|> hence I conclude that an adequate semantical theory must be intensional.
|> Furthermore, on the assumption of intensional semantical entities, an
|> infinite hierarchy thereof has to be admitted (all relevant details can be
|> found in Church's papers on the Logic of Sense and Denotation); moreover,
|> for each level of intensions, our cognitive grasp of the lower-level
|> semantical entities can be seen as dependent on that of higher, more finely
|> differentiated intensional level.  Thus it can be seen that the semantics
|> of natural languages fails to satisfy Davidson's finite learnability
|> criteria, the ones required by any equivalent of a finite-state automaton
|> with finite memory, Q.E.D.
|> 
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.

To claim that natural language is not learnable in finite time, is to state
that it is not describable in finite time.  However, each of us does 
learn natural language after we are given a finite amount of infirmation about
it.  Thus unless we somehow acquire language through some extra-physical
process, language is decribable in finite time.  

You claim that Frege's paradox shows that deotation must be intensional.
Rather it shows that Frege's reasoning was flawed, perhaps as a student
of valid forms of argument, you might ask in what way it could be 
flawed.  Remeber, when approaching semantics you cannot assume a shared
common intension understood by all parties for any entity.  Thus on 
a communicational level you must start from syntax.  

Tom


