Re: (biassed) summary of the argument so far.

sowa <>
Date: Wed, 2 Jun 93 04:41:06 EDT
From: sowa <>
Message-id: <>
To: interlingua@ISI.EDU,
Subject: Re:  (biassed) summary of the argument so far.

Some comments on your "biassed summary".  But your line lengths are going
over the 80-character limit.  I can still read them, but it is harder for
me to embed them.  So I will respond to some of the major points, but with
a minimum of quotes.

I believe that my last note seemed to get at the heart of the problem.
I was making a distinction between model theory and an application of
model theory, or between set theory and an application of set theory.

> ... Pat repeatedly concurs, but does not find this to
> be a 
> criticism of model theory so much as simply an observation about what is its 
> business. John is unable to countenance the combination of such talk with the 
> claim that model theory can describe relations between symbols and the actual 
> world. 

As I pointed out, I was never criticizing model theory.  It is a very
important part of semantics, but Pat seems at some points to be extending
model theory to include its applications to the world.  That, I would
claim, is no longer model theory.  In an earlier note, Pat mentioned
tensor calculus as an example of applied mathematics.  I disagreed,
saying that tensor calculus as a system of mathematics is every bit
as pure as number theory or any other part of math.  In fact, it was
first developed for the purpose of applying it to stresses and strains
in physical bodies (whence the name "tensor").  Later, the same theory
without its application to stresses and strains was applied to
relativity.  The applications are part of the domain of stresses or
the domain of relativity, but tensor calculus itself is "pure" --
it is not about anything in the real world.  But someone could USE
it for anything or everything.

So the main disagreement between Pat and me was about the boundary
between model theory and its applications.  I claim that model theory
as developed by the mathematical logicians isn't about the world.
An application of model theory to the world is a separate subject
and belongs to a different domain.  That application presupposes
other branches of philosophy -- ontology, the study of what kinds
of things exist, and epistemology, the study of how we acquire
knowledge of what exists.

When we are talking about things like tables, chairs, and people,
the issues of ontology and epistemology are relatively familiar
"commonsense" notions that don't seem to require much discussion.
But when we go to very large or very small realms, we must appeal
to philosophy of science and experimental procedure as guides.
And when we are trying to implement our theories in a robot, which
has no built-in commonsense, we have to extremely careful about
making distinctions between the lexical object types that are
representable inside the computer and the nonlexical things that
must be recognized by complex pattern recognition techniques.