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Re: [ontolog-forum] models : logical & analogical

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 16 Jul 2007 01:38:57 -0400
Message-id: <469B0471.30506@xxxxxxxxxxx>
Jon,    (01)

I agree:    (02)

> This is all true, well enough, but it always helps me to realize
> that some people I know (logicians, model theorists) use "model"
> to mean anything that satisfies a theory, whether it be a formal
> construct that we make out of sticks and strings or another sort
> of thing in the world, while other people I know (engineers and
> applied mathemticians) use "model" to mean an analogue model or
> the target of a morphismin, in semiotic terms, an icon of the
> object being modeled.  These senses of the word are not the
> same but they are perfectly compatible.    (03)

In Ch. 1 of my 1984 book, I included a brief discussion of a similar 
comment by Carl Adam Petri (of Petri-net fame).  Excerpt below.    (04)

> Taking all that into account, it still makes sense to say that
> a theory is "true of" the syntactic constructs that the model
> theorist constructs and also "true of" other sorts of things
> in the world.  The theory picks out only those properties
> that the object and its icon share, which sharing is
> just what makes the icon an icon of its object.    (05)

I agree.    (06)

____________________________________________________________________    (07)

Excerpt from Ch. 1 of _Conceptual Structures_, by J. F. Sowa:    (08)

The word _model_ has multiple meanings in engineering, logic, and common 
speech.  Petri (1977) noted three different meanings in the phrases 
_model of an airplane_, _model of an axiom system_, and _model farm_:    (09)

    * Simulation. A model airplane is a simplified system that simulates 
some significant characteristics of some other system in the real world 
or a possible world.    (010)

    * Realization. A model for a set of axioms is a data structure for 
which those axioms are true. Consistent axioms may have many different 
models, but inconsistent axioms have no model.    (011)

    * Prototype. A model farm is an ideal or standard for evaluating 
other less perfect farms or for designing new ones.    (012)

Petri maintained that a common basis should be found for these three 
different ways of modeling. Conceptual graphs, indeed, form models in 
all three senses of the term: the graphs simulate significant structures 
and events in a possible world; a set of axioms, called laws of the 
world, must at all times be true of the graphs; and certain graphs, 
called schemata and prototypes, serve as patterns or frames that are 
joined to form the models.    (013)

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