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From: ladkin@kestrel.ARPA (Peter Ladkin)
Newsgroups: net.ai
Subject: Re: Searle, AI, NLP, understanding, ducks
Message-ID: <13571@kestrel.ARPA>
Date: Thu, 16-Oct-86 17:51:18 EDT
Article-I.D.: kestrel.13571
Posted: Thu Oct 16 17:51:18 1986
Date-Received: Sat, 18-Oct-86 00:36:56 EDT
References: <1933@well.UUCP>
Distribution: world
Organization: Kestrel Institute, Palo Alto, CA
Lines: 35

In article <1933@well.UUCP>, jjacobs@well.UUCP (Jeffrey Jacobs) writes:
> [..] which do
> you understand better, a proof of a theorem, or the lead
> story in today's paper, describing why the summit, (which
> wasn't a summit), failed?

If the theorem is the Four Color Theorem, Friedman's theorem
on the four-sphere, or any of many others,
then I understand the newspaper story much better.

What do you intend to conclude from your example?

> >Are you aware that one of the biggest problems in formalising
> >mathematics is trying to figure out what it is that
> >mathematicians do to prove new theorems?
> 
> That's not a problem in mathematics, it's a problem in psychology!

Have you heard of the `definition' of mathematics as whatever it
is that mathematicians do?

> The end result of mathematics is "formalism"; well defined, algorithmic
> procedures to transform a set of symbols into a different set of symbols
> (or to describe the transformations, etc).  It is much more rigorous
> and well defined (aka understood) than other realms of human
> endeavor (such as psychology, or even physics).

So mathematics consists of procedures?
Neither theorems nor proofs are procedures. 
Should I conclude from this that theorems and proofs are not
mathematics?
Or should I conclude that you don't really mean this?

Peter Ladkin
ladkin@kestrel.arpa