Re: [ontolog-forum] The class of the planet Venus

[Chris Menzel <chris.menzel@xxxxxxxxx>]

On Thu, Jul 12, 2012 at 11:03 AM, Ed Barkmeyer <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

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