Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!mnetor!seismo!columbia!rutgers!nike!oliveb!glacier!well!jjacobs
From: jjacobs@well.UUCP (Jeffrey Jacobs)
Newsgroups: net.ai
Subject: Searle, AI, NLP, understanding, ducks
Message-ID: <1933@well.UUCP>
Date: Tue, 14-Oct-86 22:39:29 EDT
Article-I.D.: well.1933
Posted: Tue Oct 14 22:39:29 1986
Date-Received: Wed, 15-Oct-86 20:22:03 EDT
Reply-To: jjacobs@well.UUCP (Jeffrey Jacobs)
Distribution: world
Organization: Whole Earth Lectronic Link, Sausalito CA
Lines: 58


In <13428@kestrel.ARPA>, Peter Ladkin writes:

>In article <1919@well.UUCP>, jjacobs@well.UUCP (Jeffrey Jacobs) writes:
>> Mathematics is very well understood, and
>> consists almost entirely of "formal procedures". 

>I infer from your comment that you're not a mathematician.
>As a practicing mathematician (amongst other things), I'd
>like to ask precisely what you mean by *well understood*?

I'd like to answer precisely, but one of the problems with
English, as opposed to mathematics, is the difficulty of answering
precisely.  Let me instead give you an example; 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?

I don't intend to imply that the field of mathematics is
in any way *completely* understood or running out of new things
to do.

>And I would like to strongly disagree with your comment that
>doing mathematics consists almost entirely of formal procedures.

What you are disagreeing with is a misinterpretation on your part.
I didn't use the term "doing mathematics", and didn't intend to.  I
was speaking on the nature of what it is that mathematics consists of.

"doing mathematics"has many aspects; it may be a "canned"
procedure, or it may be an incredibly tough, creative, intuitive
effort.

>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!

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).

>Peter Ladkin
>ladkin@kestrel.arpa

"He only thought he understood what I wrote :-)"

 Jeffrey M. Jacobs
 CONSART Systems Inc.
 Technical and Managerial Consultants
 P.O. Box 3016, Manhattan Beach, CA 90266
 (213)376-3802
 CIS:75076,2603
 BIX:jeffjacobs
 USENET: well!jjacobs