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Re: [ontolog-forum] Models (was The class of the planet Venus)

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sat, 14 Jul 2012 16:50:40 -0400
Message-id: <5001DBA0.6030304@xxxxxxxxxxx>
Pat,    (01)

I agree with the following two definitions:    (02)

PH #1
> The logical, technical, usage of "model" refers to a semantic interpretation
> of a sentence which makes the sentence true: a satisfying interpretation.
> A "model" in this sense *is* a satisfying interpretation of a sentence.    (03)

PH #2
> Saying X is a model of Y implies that Y is some part of reality, and
> (as Petri, quoted by John, says) that X bears some structural similarity
> to some aspect of Y.    (04)

But Petri made the observation that you could relate both of these
definitions by adding a third part Z to the definition of 'model'.    (05)

Note that an engineering model typically has a specification in
some language (natural, artificial, or diagrammatic).  If you call
that spec Z, you get a triadic relation:    (06)

    An engineering model relates three entities: a specification Z
    for implementing some object or system Y with the aid of a model X.
    The model X is an interpretation of the specification Z in a form
    (mathematical or physical) for which all structural relationships
    specified by Z are true.  The object or system Y is the intended
    implementation for which the structural relationships specified
    by Z and interpreted by X are also true.    (07)

Then you can define a logical model in the same terms by keeping
Z and X, but making the aspect of the world Y optional:    (08)

    A logical model relates two entities:  a specification Z and
    a model X, with an optional third entity Y, which is some
    aspect Y of world of which X is a model.  The specification Z
    is stated in some version of logic, and the model X is some
    set-theoretical object (e.g., a set D and a set of relations
    defined over D) that makes every sentence in spec Z true.
    If the optional aspect Y of the world is included, the same
    structural relationships specified by Z are true of Y.    (09)

When you define the terms 'engineering model' and 'logical model'
with the three components X, Y, and Z, you get a generalization
that includes both kinds of models as special cases.    (010)

If you wish, you can also identify certain individuals in Y
with the elements of the set D.  With this option, the domain D
of the model X happens to be a set of physical objects instead
of a set of abstract objects.  Conceptually, X and Y are distinct;
but physically the elements of the domain D are parts of Y.    (011)

John    (012)

PS:  I'll pass over the fact that X, Y, and Z happen to form
a Peircean triad.  In Peirce's terms, the spec Z is the mediating
Thirdness that relates X and Y.    (013)

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