Re: Models and Depictions

sowa <sowa@turing.pacss.binghamton.edu>
Date: Wed, 12 May 93 07:35:06 EDT
From: sowa <sowa@turing.pacss.binghamton.edu>
Message-id: <9305121135.AA00941@turing.pacss.binghamton.edu>
To: cg@cs.umn.edu, interlingua@ISI.EDU, schubert@cs.rochester.edu,
        sowa@turing.pacss.binghamton.edu
Subject: Re:  Models and Depictions
Cc: sowa@turing.pacss.binghamton.edu

Len,

If our disagreements have no effect on KIF, CGs, or their use in
ANSI, ISO, and KSE, then they can be ignored outside the realm of
papers on philosophical foundations.  And so far, it seems that
we may be able to agree on the implications for KIF without
resolving the metaphysical issues.  However, many philosophical
issues do have computational implications, and we should at least
pursue this one to the point where we can be sure whether it does
or doesn't.

Some comments on some of your comments (with deletions in the
interest of brevity):

> You say (correctly I'm sure) Tarski restricted himself to formalized
> languages. This does not entail that the domain of discourse must
> consist of formal symbolic or mathematical objects....

True.  But a mathematical system is of a very different nature
>From the real world.  Model theory, as Tarski and the mathematical
logicians developed it, is part of pure mathematics.  If you want to
apply it to the world, as I certainly do, then you are obliged to
address the methodological question of how the symbols in your
formalism relate to the world.  Carnap was the first to write a
book-length treatment to address that issue.  Wittgenstein was so
deeply worried about it that he spent the last 25 years of his life
discussing the problems.  And Barwise & Perry have been addressing
that problem as one of the centerpieces of situation semantics.

Pat Hayes said that he doesn't accept any of the approaches that
Carnap, Wittgenstein, and Barwise have suggested.  He is certainly
entitled to his preferences.  I suggested another alternative:  the
practice of AI people doing robotics and pattern recognition as a
more technological counterpart of Carnap's "Logische Aufbau".

My basic point is that model theory is pure mathematics.  If you want
to put "real world objects" into your models, then you are obliged to
address the gap between real and applied mathematics.  You can do
that in any of three different ways:  (a) armchair metaphysics; 
(b) a detailed analysis of scientific method; (c) a computational
approach as in robotics and pattern recognition.

> When I say specialized representations are "in principle" dispensable,
> I am saying that they are dispensable at some computational cost.
> Long ago, the KR systems whose designs I worked on used no special
> representations of times, colors, sets, etc; they worked all the same.
> The "newer" ones (1982-93) use specialists, and work better.

This is the basis for agreement.  I want that level of depictions
for both computational and philosophical reasons.  If you are willing
to grant my depictions for computational reasons without accepting my
metaphysics, then I'm satisfied.  I can do business with people who
have different religious beliefs.

> John, you surely don't want to say that the formalized apple- and 
> planet-recognition procedures I rhetorically asked about (and by 
> extension, procedures for all other objects Newton regarded as subject 
> to his laws) can be found in the works of Ptolemy, Galileo, and Bacon?! 

I don't expect experimental procedures to be as formal as pure
mathematics.  But the people who established the use of mathematics
in physics (Archimedes, Ptolemy, Bacon, Galileo, Newton...) were
very careful to analyze exactly how the mathematical variables were
related to their observations and measurements.  They didn't just
"postulate" them away with magic functions that returned the
planet Jupiter or the acceleration of a falling body.

> You say that model theory is "a method of computing denotations". It's
> not, and that's the crux of our disagreement. 

OK, I'm sorry.  I keep thinking about applications to computers and AI.
For pure mathematics, I grant that you can have countably infinite
models (which I am happy to accept) and even uncountable models
(about which I am agnostic, but willing to let people discuss if they like).
I admit that denotations in such models are not computable.  But
when we are talking about applications to the real world, all of
our sets are finite and computable.

John