Path: utzoo!attcan!uunet!husc6!linus!mbunix!bwk
From: bwk@mitre-bedford.ARPA (Barry W. Kort)
Newsgroups: comp.ai
Subject: Re: Limits of AI
Summary: Progress in AI may be an unbounded sequence.
Keywords: Infinity, Maximum, Unbounded Sequence, Peano Lessons
Message-ID: <41682@linus.UUCP>
Date: 9 Nov 88 18:57:27 GMT
References: <1651@ndsuvax.UUCP> <1666@cadre.dsl.PITTSBURGH.EDU> <3802@cs.utexas.edu> <2413@cs.Buffalo.EDU> <3833@cs.utexas.edu> <2149@bucsb <3876@cs.utexas.edu>
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Reply-To: bwk@mbunix (Kort)
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In article <3876@cs.utexas.edu> berleant@cs.utexas.edu (Dan Berleant) 
argues in support of his thesis

 > "if we can build a machine smarter than
 > we are, we can obtain a machine of infinite -- or at least
 > maximum possible -- intelligence."

Dan, the ability to augment a system does not automatically
imply that it can be infinitely augmented or that it can
be augmented to finite maximum.

Suppose that the degree of intelligence of a system could be mapped
onto the counting numbers: 0, 1, 2, 3, etc.

Suppose that you knew how to take a system of intelligence n,
and use it to build a machine of intelligence n+1.

Then you could build a machine of any finite intelligence (there
is no theoretical maximum), but you would never arrive at a machine
of infinite intelligence.  

Thinking about infinity is a little tricky.  Georg Cantor created
quite a furor when he came up with a meaningful way to think and
talk about transfinite numbers.  I think you would enjoy a course
in Abstract Algebra, where such ideas are carefully developed.

--Barry Kort