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Professor Hyman Bass
Department of Mathematics
Columbia University
New York, NY 10027

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Dear Professor Bass:

	I just read the article by Judith Grabiner in the October
 {\it Bulletin}, and it has suggested to me offering to write
a short article on mathematical aspects of artificial intelligence.

	I disagree with Grabiner's view that the controversies are
primarily about ``the nature of man''.  Instead I think the problems
are mainly those of the development of a suitable mathematical theory
relating the information available in an environment and the
procedures needed for successful behavior in the environment.
An important specialization of this is the relation between
problems --- even mathematical problems --- and the methods available
for solving them.

	On the other hand, I think I agree with her criticisms of
BACON in that the program starts at a point a lot closer to the
solution than what confronted the scientists whose discoveries
Simon, et. al. undertook to make their program repeat.  My opinion
is that AI has a long way to go before such simulations can be
realistic.

	However, the article I would write would not be an answer
to Grabiner, although a few paragraphs might be devoted to expressing
an opinion on those issues.  The main content would concern the
problem of formalizing the mathematical structure of the common sense
world in which a person or robot has to act on the basis of extremely
partial information and without having in advance a mathematical model
that isolates the relevant phenomena.  Such a model, when obtainable,
is a result of thought not a precondition.  The main recent relevant
mathematical results involve the formalization of non-monotonic
reasoning.

	The subject is not deep yet, so the article would be entirely
self-contained except for some use of languages and concepts of
mathematical logic.  It would be easier than almost all the research-
expository articles.

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Sincerely,

John McCarthy    
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P.S. Incidentally, it seems to me that the other two research-expository articles
are below the previous expository standard, and should have explained
more of the concepts being used.
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JMC/ra 
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