Re: Getting back to the notes of May 10th (Chris Menzel)
From: (Chris Menzel)
Message-id: <>
Subject: Re: Getting back to the notes of May 10th
To: (sowa)
Date: Sat, 15 May 1993 13:19:22 -0500 (CDT)
Cc:, interlingua@ISI.EDU,
In-reply-to: <> from "sowa" at May 15, 93 10:30:17 am
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Hi John.

You wrote:

: [Pat wrote:]
: > But in any case, your alternative is even worse. In order to decide 
: > whether one of your set-theoretic models is a reasonable simlacrum of 
: > the world of cats and mats, I have to have a COMPLETE theory of cat/mat 
: > imagery, since everyone of these is an entire world-simulation. Thats 
: > Principia MatCatica. You may claim that this isnt necessary in order 
: > to do the model theory, but how do I know that one of your models isnt 
: > quite inappropriate as a way of interpreting cat-mat talk?
: It is questions like these that lead me to believe that situation
: semantics with its preference for limited regions of space-time is
: on the right track.  Our use of language and logic doesn't depend
: on things that neither we nor anyone else has ever observed.  And
: I believe that a system of semantics that is based only on observable
: regions of space time is preferable to one that claims to speak about
: the entire world as a completed whole.  

I'm not sure how this addresses the original objection, which I took
to be that your approach to understanding reference to cats and mats
would require a complete theory of cat/mat imagery.  If that's true,
then the objection would still seem to stand even with a semantics
that is based on observable regions of space/time.  And anyway,
second, there is nothing about traditional model theory that prevents
us from building semantical models of limited regions of space/time.
If I'm building an information "model" of a typical run of some
manufacturing system using some sort of (typically graphical)
specialized first-order langugage, an "intended" semantical model of
the language will be constructed out of the objects that exist in the
system during that time period (see below!).  Nothing forces me to
speak about the whole world.

: 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.

There seems to be an equivocation on `relate' here.  Taking a relation
in the usual model theoretic way as a set of ordered pairs, surely it
is false that "the only thing [model theory] can do is relate
mathematical symbols to mathematical things."  If I've got the symbol
`John' in my language, then if the interpretation function (taking it
to be a kind of relation) for my language includes the pair <`John',
John Sowa>, then I have related a symbol to a nonmathematical thing
(assuming Pythagorus was wrong :-), viz., you.  When you use the word
`relate' above, by contrast, your concern is with how that particular
semantic relation is *established* so that when I or any other user of
the language utters the word `John', we refer to *you* (or anything
else for that matter).  An explanation of that is of course not
provided by model theory and no doubt involves the disciplines you
mention.  Both these issues will have to be part of a complete theory
of meaning and reference, but one issue is semantic, the other
psychological.  Pat and Len have been arguing for them to be clearly
distinguished, and you want to distinguish them (or very similar
issues) as well; but it seems to muddy the waters when you insist that
model theoretic semantics can't relate (in the model theoretic sense)
words to real world things.  Surely it can, albeit with the
explanatory gaps noted.



Christopher Menzel		    Internet ->
Philosophy, Texas A&M University    Phone ---->   (409) 845-8764
College Station, TX  77843-4237	    Fax ------>   (409) 845-0458