Ah yes, this is the problem of what "model" means in what context.
I think I was misled by John's terminology "model of the world". (01)
I fully agree that the semantic model for a logic language is a set of
things in the "world of interest".
And if what John meant by a "model of the world" is a collection of
things and states taken to be a domain of discourse, then I withdraw my
complaint. (I tend to use the word "world" with that meaning, precisely
because ... ) (02)
The community I work in understands "model" to mean an engineering
model, and "model of the world" to mean a representation of the state of
the actual or intended world in terms of some specific
conceptualization. That is why I said that a model of a building is not
a building. An engineered artefact is the result of a
conceptualization. A data or knowledge base that is a "model of the
world" is an organized repository of information about some "world" (or
in logic terminology, some "model"). In a semantic model for a civil
engineering ontology, the actual building is an element of the model,
and a "building model" might also be. (03)
So, I apologize to all for creating confusion by misuse of terms, and
specifically to John, for miscasting his intent. (04)
-Ed (05)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800 (06)
Chris Menzel wrote:
> On Thu, Jul 12, 2012 at 11:03 AM, Ed Barkmeyer <edbark@xxxxxxxx
> <mailto:edbark@xxxxxxxx>> wrote:
>
> John F Sowa wrote:
> > 4. The distinction between intensions and extensions can be used
> > for individuals as well as for sets, relations, functions, and
> > classes. The basic point is that the extension is something
> > in the world (or a model of the world), and the intension is
> > a definition that is used to characterize and identify the
> > thing or things in the world (or some model of the world).
> ...
> I do wish John had avoided the insertion of the parenthetical
> expressions in the above, because they weaken, perhaps to the point of
> confusing, his thesis.
>
> The reason I object to John's parenthetical references to "models
> of the
> world" is that most "models" in this sense are intrinsically
> intensional. The artefacts in models are /constructed from/ the
> intensions, and two such artefacts may indeed be different even
> when the
> thing they are models of is the same. A model of a building is not a
> building. Two different models of the same building are different
> things, each conforming to a particular characterization of the
> building, whether the building itself exists or not, and in fact,
> whether or not the building in being actually possesses those
> characteristics. (This is a critical idea in Herbert Simon's famous
> work "The Sciences of the Artificial", and in some of Ted Goranson's
> work.) So it is in fact very difficult to argue that two
> conceptualizations of model elements are 'coextensive'. The model
> element is a manifestation of the conceptualization, not the extension
> of it. I would go so far as to say that a model element is a Frege
> Zeichen -- a sign/symbol for the intension (Sinn).
>
>
> I'm afraid that, for the first time I can recall, I have to disagree
> with Ed here. For there is absolutely no reason why the elements of a
> semantical model of a logical language (including most any KR
> language) cannot be exactly the entities we "intend". Indeed, such
> "intended" models are typically exactly what we wish to be talking
> about when we use the language in question: The natural, intended
> model of the language of arithmetic contains the natural numbers; the
> natural model of an ontology for a manufacturing system might well
> contain exactly the actual machines on the assembly line. Furthermore,
> I must say that I am not sure what Ed means when he says that models
> are "intrinsically intensional" or that they are "constructed from
> intensions". In the theory of models for logical languages, this is
> just not the case; the notion of an intrinsically intensional entity
> is simply not a part of the theory. Moreover, I am not sure we've got
> enough of a grip on the notion of an intensional entity beyond the
> idea that that distinct intensions can have the same extensions. This
> is represented in possible world semantics by defining extensions as
> functions from worlds to extensional entities of one sort or another.
> It is represented in the semantics of Common Logic simply by
> distinguishing between semantic objects and their extensions, but
> there is not much more to be said about the nature of intensions than
> that — formally, at any rate.
>
> So, while I think the distinction between intension and extension is
> certainly legitimate, I am skeptical of their introduction into the
> modeling domain in any sense beyond the well-understood (and
> ultimately extensional, from a purely formal perspective)
> representations found in possible world semantics or Common Logic.
>
> -chris
> (07)
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