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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: Thu, 8 Feb 2007 11:50:19 -0600
Message-id: <p06230919c1f10c64f20f@[]>
>Chris M. and Pat,
>As I said in a previous note, I seriously doubt that any legal
>system (including the rules and regulations of Texas A & M)
>are perfectly accurate statements of what actually happens.    (01)

No doubt that is true. I fail to see how it is relevant to this 
thread, however. It simply means that there are more kinds of 
interpretation one might use, and perhaps two different senses of 
"correct" for the ontology in question. As I expect you know, writers 
of business rule systems have to face up this particular distinction 
rather directly, since such systems are usually written to describe 
the way the world would be if everyone obeyed the rules.
...    (02)

>PH> 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.
>How do you do that construction?  How do you identify the individuals?    (03)

However you choose. Different ways of individuating will produce 
different interpretations. So?    (04)

>Perhaps by labeling the parts or by specifying their coordinates.
>In that case, the model consists of those labels    (05)

No, it consists of the pieces of reality so labelled or identified. 
(This is really a very obvious and simple point: why do you insist on 
denying it? As you just said, this labelling is how I identify the 
parts of reality, right? Right. So now I have identified them, they, 
and not the labels I used, are what I am talking about.)    (06)

>, which can never
>represent more than a tiny fraction of what actually exists in the
>selected chunk of reality.    (07)

Indeed, the interpretation is a relational structure which will only 
reflect a very  small part of all the structure that is actually 
there. But that does not prevent the entities in the relational 
structure from being actual parts of this (very complicated) reality. 
If I tell someone to go and pat John Sowa on the back, I am using the 
tiny label "John Sowa" to refer to a much more complicated piece of 
reality; but I am in fact referring to you, the real biological piece 
of the actual world, not to the label.    (08)

>PH> You are muddling up conceptual analysis, with questions of
>  > empirical verification for certain kinds of physical theory.
>I am making explicit what some armchair philosophers prefer to
>sweep under the rug.  Philosophers like to compartmentalize
>ontology, epistemology, and philosophy of science in different
>textbooks and courses.   But when you're designing a robot,    (09)

Yes, but we are here NOT designing a robot. We are trying to talk 
about ontology design. Robots, and AI issues about how beliefs are 
grounded through perception and so on are only marginally relevant 
here, if at all. The entire semantic web, for example, isnt likely to 
have any sensors attached to it, but it will be rich with ontologies.    (010)

>you have to face the questions of how that robot relates its
>mental (or computerized) models to its sensory inputs and
>motor outputs.  You can't just declare that certain things
>in a crowd scene magically become part of its internal models.    (011)

When talking about ontologies and their interpretation, that is 
exactly what you can do. Theres nothing magical about it, you just do 
it.    (012)

>PH> 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'.
>I agree that the source of the information is different, but the
>result is equivalent.  When a child builds a model airplane, the
>goal is to model an existing physical object.  But when Boeing built
>a model of the 777 in their computer, they began with a specification
>in math & logic (SQL, etc.) from which they generated pictures and
>templates of how the nonexistent airplane would look.  After they
>constructed physical embodiments of the model, the result fit
>very nicely into my tripartite diagram.    (013)

I don't see this. What they built with this model (sense 2) can be 
viewed as a rather complicated description of a hypothetical 
airplane, very detailed (as we say, right down to the metal.) That is 
on the right of your diagram. Since no such plane has been 
constructed yet, it has no actual physical interpretations. Then they 
built an actual plane which satisfied the description. This is a real 
physical thing, and it is also a model (sense 1) of their 
description, i.e. it is an interpretation which satisfies the 
description. In many cases this was ensured by giving the description 
to a machine tool which used it to create the part satisfying the 
description. So what I see here is a right-hand thing- a description, 
a model-2 - and a physical Tarskian model (sense 1) of it. I don't 
see any graph-like things anywhere standing between them.    (014)

>PH> 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.
>I truly believe that there is a major categorical distinction between
>a mathematical structure and a physical object.    (015)

I know you believe this. But if you were right, then most of 
engineering, much of science and all of applied mathematics would be 
impossible. As it all seems not to be, I conclude that you are likely 
to be mistaken.    (016)

>  The former is abstract,
>has zero mass, and does not have a location in space-time.    (017)

Nonsense. Mathematics is about structure. It says nothing about the 
nature of how that structure is embodied. It may be a Platonic 
abstraction, or it may be the Bay Bridge. Have you ever counted the 
number of people in a room, or the number of coins you have in your 
hand? If numerals cannot refer to entities with mass in spacetime, 
how was this possible?    (018)

>  The latter
>most definitely has mass and location.  Furthermore, there is only a
>homomorphism, not an isomorphism between them, since the physical object
>has much more detail than any model we are capable of specifying.    (019)

Your way of expressing this is self-defeating. If there is a 
homomorphism between them then they must both be mathematical 
structures.    (020)

>PH> Why did you choose to represent the [model] 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.
>I used a graph because it's a clearer illustration than a table, and
>the reason why I omitted the labels is that there wasn't enough space
>to write them in (although I personally prefer labeled graphs).
>A crowd scene or a view of anything physical is not a relational
>structure until you identify the individuals and the relations.    (021)

Of course. Neither is a graph or a table, for the same reasons.    (022)

>The number of individuals depends on your preferred model.  Do you
>consider the individuals in a crowd to be the people in it?  What
>about body parts, such as hands and noses?  And do you want to identify
>body parts by their English labels or by their Russian labels, which
>consider the "ruka" to include the hand and forearm?    (023)

You can do it any way you like.    (024)

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