models and depictions

Dan Schwartz <>
Date: Sun, 16 May 93 16:44:14 -0400
From: Dan Schwartz <>
Message-id: <>
To:, interlingua@ISI.EDU
Subject: models and depictions
I just came back from a trip where I had a chance to talk with Pat Hayes
a bit about the recent controversy.  There I was suggesting that in a
way, both John and Pat may be right.  Then, after returning, I was
catching up on my email and encountered John's more recent paragraphs
together with Chris Menzel's comments, particularly in reference to

: My point is that model theory solves only one problem:  the relation
: between formal symbols and mathematical constructions.  Although this
: is a very important part of semantics, it does not and cannot by itself
: address the question of how those mathematical constructions are
: related to the real world.  Claiming that the real world things are
: somehow included in those constructions is just begging all the most
: difficult questions.  By assuming that those models contain symbolic
: surrogates instead of actual physical objects, I have openly admitted
: that model theory doesn't solve those problems.  Then I can begin to
: address the separate question of how those surrogates map to the world.
: (Or I can, like you, just ignore that question if it is not of interest
: to me at the moment.)
: > NO!! The denotation functions do not recognise (and are not computed, 
: > and do not access or DO anything else). They are simply a mathematical 
: > way of talking about correspondences between names and things. 
: Exactly!!!  Model theory is a system of pure mathematics.  The only
: thing it can do is relate mathematical symbols to mathematical things.
: To relate those mathematical things ("surrogates" in DB terminology)
: to physical objects presupposes philosophy of science, psychology of
: perception & language learning, or pattern recognition in AI.

Now I tend to agree with Pat and Chris, that the points expressed by the
first and last sentences above are just plain wrong.  To my mind, when
Tarski gave his famous ``Snow is White'' example, he was clearly
allowing that formal symbols refer directly to real world objects, and
the reason he proceeded to study set-theoretic interpretations of his
languages was merely that he and his colleagues were at that time
concerned with formalizations of mathematical theories (arithmetic, set
theory, etc.).

This I allow is partly speculative, since I can't claim to know for sure
what Tarski might have said about this.  However, I do recall that it
snowed once here in Tallahassee, and I remember looking out my window
and saying ``Hey!  It's Snowing!'' and observing that it indeed was very
white, and I honestly don't believe I used any depictions or other
set-theoretic entities in relating the words I had just uttered to the
real-world objects I perceived.

This is not to say, though, that depictions are of no use at all.  On
the contrary, as one moves up to the higher levels of abstraction as
required for modeling cognitive processes, it does seem that something
like depictions can play an important role.  In doing so, however, one
is now merely expanding the formalism to include both the original
formal language AND the depictions serving as interpretations of the
linguistic elements---so that the relation between language and
depictions becomes a formal model of the relation between the perceiver
and the world (material or abstract) being perceived, to wit:

          Formal Logical System <---> Depictions/Interpretations
                    |                             |
                    |                             |
                    |                             |
                   \/                            \/
            Human Perceiver     <--->      Things Perceived




Daniel G. Schwartz                                Office    904-644-5875
Dept. of Computer Science, B-173                  CS Dept   904-644-2296
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