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Re: [ontolog-forum] Confusion about 'model'

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 15 Jul 2007 14:44:55 -0400
Message-id: <469A6B27.7070906@xxxxxxxxxxx>
Gary and Barry,    (01)

In any scientific endeavor, there is some aspect of reality that
determines the subject matter of the research.  Studying that
aspect requires some methodology, which until the 17th century
was limited by the human sense organs.  Since then, telescopes,
microscopes, thermometers, X-ray machines, and an ever increasing
variety of instruments have extended what is perceptible far beyond
the limits of the sense organs of any organism on earth.    (02)

GB-C> I would say that we have 3 subjects here.
 > There is the cell in reality.  There are what are called biological
 > models of a cell that have been developed as part of that science
 > and there is now an attempt an ontological "model" of the cell.    (03)

Before microscopes were invented, there was no notion of "cell".
Even after microscopes became available, what people saw through
their microscopes depended very heavily on their preconceived
notions of what they were expected to see.    (04)

The psychologist Edwin Boring studied drawings of cells that were
made by professional biologists both before and after the discovery
of chromosomes.  And he made an interesting observation:  "Chromosomes
kept showing up in the later drawings, not in the former.  In other
words, microscopes do not reveal concepts until the concepts have been
invented."  (Ref:  E. G. Boring, The role of theory in experimental 
psychology, _American J. of Psychology_, 2:66, pp. 169-184, 1953.)    (05)

BS> But when one is building an ontology for, e.g., cell biology,
 > is one trying to build a model of the cell, or rather to create
 > a formally coherent controlled vocabulary for talking about cells
 > and their parts?    (06)

In every science (with or without the aid of special sense enhancers), 
the data, theories, paradigms, models, methodologies, and vocabulary
(whatever anyone might like to call them) are developed together.
They influence one another inextricably.  It may be useful to focus
on one or another in order to clarify various notions.  But there is
no such thing as a formal ontology that can be separated from the
theories, models, methodologies, and logical predicates that are
labeled with words in various languages.    (07)

BS> and Tarski would not say that the sentences (e.g. of cat biology)
 > for which we have a formal model are themselves about that model.    (08)

In the informal discussion of his famous paper of 1933 (English
title, "The concept of truth in formalized languages"), he began
with an informal discussion that used the sentences "Snow is white"
in English and "Schnee is weiss" in German.  Unfortunately, that
example could not be translated to the formalism he actually used.    (09)

For his more informal paper of 1944, see    (010)

    The Semantic Conception of Truth    (011)

In that paper, he used the word 'model' only in the phrase "model
of an axiom system".  Therefore, it would be correct to say that
his axioms, as stated in his notation for logic, were "about" the
model.  People have debated the question whether such models should
be considered part of reality, isomorphic to some part of reality,
or approximations to some part of reality.    (012)

The overwhelming majority of Tarski's published papers were about
mathematical subjects.  For those, it would be correct to say that
his statements, expressed in various notations for math and logic,
were about the models.  In their informal discussions, mathematicians
rarely distinguish structures that are isomorphic, and Tarski did
not clearly state his preferences.    (013)

My preference is to assume a two-step mapping from a theory to a model
and then to the world.  See the following diagram:    (014)

    Theories, Models, and the World    (015)

On the left is an image of the world; on the right are the FOL
statements of some theory; and in the middle is a formal model.
This mapping makes it possible to talk about the two-valued
denotation of a theory in terms of a model and about the degree
of approximation of the model to the world.    (016)

With this approach, it is possible to use classical FOL to reason
with the axioms of a theory and to use continuous methods to
evaluate the probability or degree of verisimilitude of a model.    (017)

John    (018)

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