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Re: [ontolog-forum] Visual Complexity

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 7 Feb 2007 14:02:30 -0600
Message-id: <p0623090dc1efdaec596d@[]>
>There are two independent questions here:
>  1. The historical or hermeneutic question of what exactly
>     Tarski, Quine, or Montague intended.
>  2. The question of whether it is useful to make a distinction
>     between models and what they are intended to model.    (01)

Aside, but the two uses of "model" here illustrate how dangerous this 
word can be if used casually. Its meaning in "model theory" aka 
Tarskian semantics is almost exactly the opposite or dual of its 
sense as in "to make a model of something". A Tarskian 
model/interpretation is a called a model of the SENTENCES it 
interprets, not a 'model' or reality in the sense of being a 
simplified artifact representing something more complicated, as in 
'model aircraft'. The latter sense, if it applied at all here, would 
be a relationship between the model/interpretation and the actual 
world. So if your first usage here is supposed to refer to a Tarskian 
model, then the second usage should have a clear and unambiguous 
answer: it models the sentences. But this not what you mean, of 
course: you mean the second use to be understood in the second sense 
of 'model'. Perhaps this is the source of the misunderstanding: 
Tarskian models/interpretations do not (better, need not) 'model' the 
world in this sense, of being a simplified alternative version of the 
world. They can be actually PART of the world, constructed from real 
things and real stuff. It is less like building a model airplane than 
standing next to a real airplane and saying "I'm only going to 
consider the metal parts of the airframe for now, ignore the 
electrical and hydraulics."    (02)

>I'm sorry that I raised question #1 in my previous note,
>because the important issue, in my opinion, is #2.    (03)

Agreed. Let us agree to not get sidetracked into historical debates.    (04)

>The diagram I use to illustrate the distinction is the attached
>mthworl2.gif.  On the left is a representation of the world in
>a picture that suggests its complexity.  On the right are some
>formulas of some theory.  In the middle is a Tarski-style model
>represented as a graph.    (05)

And I maintain that this diagram is SERIOUSLY misleading, suggesting 
as it does that there is some kind of categorical distinction or 
difference between the Tarski model/interpretation and the Real 
World. Why did you choose to represent the former as an unlabeled 
graph? This is tendentious. I could just as well use a photograph of 
a crowd scene, or a view through a telescope, as an illustration of a 
relational structure.    (06)

>The point I emphasize is that model theory evaluates the formulas
>of a theory in terms of a model to determine a value T or F for
>each formula.    (07)

Yes, indeed it does.  So?    (08)

>  But the question of degree of approximation is
>best considered in terms of how accurately the model corresponds
>to that aspect of reality it is intended to characterize.    (09)

Why are you talking of degrees of approximation? Why is this topic 
even relevant to semantics at all? (It is not.) When it becomes 
relevant, the appropriate ontological engineering response to it is 
to try to construct a good ontology of approximations. (BTW, I don't 
mean to suggest this is easy to do.)    (010)

>When I show that diagram to various people who know logic and model
>theory, I get two sharply polarized reactions.  Some immediately say
>"Of course, that's obvious."  But others get angry and say that I
>am misrepresenting logic, or model theory, or analytic philosophy.    (011)

You agreed not to get involved in citation games, but I bet I can 
beat you at this one if we need to settle who is misrepresenting 
model theory.    (012)

>The point I make is that the right side of the diagram involves
>logic, which by itself is independent of any application until we
>try to apply it.    (013)

Of course the logic itself is independent of any subject-matter. That 
is the point of using it. But that is merely saying that the 
*relationship between* the right and the middle parts of your diagram 
is independent of the particular structure found in the middle. True. 
It does NOT follow from this that there is any distinction, other 
than sheer complexity, between the middle and the left. The 
interesting relational structures for ontology are exactly PARTS of 
the real world.    (014)

>  The left side involves an application, which
>gets into an enormous number of issues that are outside the realm
>of pure logic and address philosophy of science, engineering,
>experimental error, and practical problems of all kinds.    (015)

It may, in some very special and particular cases, but it need not 
and usually does not. Take your own work: your book on ontology, 
widely cited, makes many conceptual distinctions between ontological 
categories, such as between concrete things and abstracta. What kind 
of observation or measurement is relevant to this? Or take the 
well-known ontological distinction between continuants and 
occurrents: what kind of experimental test can detect that 
distinction? You are muddling up conceptual analysis, with questions 
of empirical verification for certain kinds of physical theory.    (016)

>I believe it's important to make that distinction, and this diagram
>(or something else along those lines) helps to clarify the issues.    (017)

I believe it seriously distorts them, and serves only to muddle what 
is in fact a clear (and widely accepted and used) foundation for 
thinking about semantics.    (018)

Pat    (019)

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