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From: anderson@secd.cs.umd.edu (Gary Anderson)
Newsgroups: comp.ai,talk.philosophy.misc
Subject: Re: Artificial Intelligence and Intelligence
Message-ID: <14577@mimsy.UUCP>
Date: 16 Nov 88 16:46:47 GMT
References: <490@soleil.UUCP>
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Reply-To: anderson@secd.cs.umd.edu (Gary Anderson)
Organization: UMIACS, Univ. of Maryland, College Park, MD 20742
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In article <490@soleil.UUCP> peru@soleil.UUCP (Dave Peru) writes:
>In article <484@soleil.UUCP> I write:
>

>All uncomputability problems come from dealing with infinity.
>
>Like naive set theory, naive Artificial Intelligence does not deal with
>paradoxes and the concept of "infinity".
>
>Human beings understand the concept of "infinity", most of mathematics would
>be meaningless if you took out the concept of "infinity".  Mathematicians
>would be quite upset if you told them that they were really fooling themselves
>all this time.  Physicists use "infinity" for predicting reality.


There are very many different concepts of infinity even within mathematics.
I do not know the relevant comp sci literature, but I would be surprised if you could not in some way model or otherwise provide
 some of these  concepts to a program designed to prove theorems in certain
contexts.

It seems to me that the power of the concept of infinity lies in how its is used
to solve or to characterize the solution of certain questions in mathematics
, and that so far as mathematics is concerned it does not have 
an existential basis
independent of how it is or ought to be used.


Anecdote:

Professor Garrett Birkhoff, a prominent mathematician not unfamiliar with the
use of infinity in mathematics, often remarks in his undergraduate ODE class
that when mathematicians begin to speak about infinity, they don't know 
what they are talking about.



From this observation, I suggest another difference between man and machine.

Perhaps man is just better at coping with the "reality" of not "knowing".