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Article 1208 of comp.ai.philosophy:
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>From: jmc@SAIL.Stanford.EDU (John McCarthy)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Is there any such thing as informal logic?
Message-ID: <JMC.91Nov5212441@SAIL.Stanford.EDU>
Date: 6 Nov 91 05:24:41 GMT
References: <1991Oct22.041210.5931@watserv1.waterloo.edu>
	<JMC.91Nov3225619@SAIL.Stanford.EDU>
	<1991Nov4.182613.5073@husc3.harvard.edu>
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In-Reply-To: zeleny@zariski.harvard.edu's message of 4 Nov 91 23:26:12 GMT

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.

The amusing thing about this one is the Q.E.D. at the end.  Does this
purport to be a proof?

Intensional entities are indeed needed for intelligence.  Moreover,
the levels can indeed get higher and higher.  In fact they can go
up into transfinite ordinals.  However, one needs higher and
higher levels of intension in the same sense as one needs larger
and larger natural numbers.  Just as the natural numbers actually
mentioned in any single mathematical argument are bounded, so are
the levels needed in any given intensional argument.  I rather doubt
that you can find any that go beyond 3 levels.
--
"There's not a woman in his book, the plot hinges on unkindness to
animals, and the black characters mostly drown by chapter 29."

John McCarthy, Computer Science Department, Stanford, CA 94305


