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
settheoretical 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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