ONT VOFIOTI ADO
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A Thinking Reeder Writes:
>
> Jon,
>
> You said:
>
> > With the pictures of the venn diagram and the truth table
> > before us, we have come to the verge of sensing how the
> > word "model" is used in logic, namely, to distinguish
> > whatever thing it may be that satisfies a description.
>
> Be gentle, remember I'm learning. But I don’t understand
> this definition of "model" unless it’s the concept of
> "a designation" or "a representation". Is it that we
> can talk about a list of the "features" or what I'm
> calling in my work "attributes" modeling the thing
> in the universe (if one assumes that these features
> capture all meaning of the universe, or at least all
> that is at this time under consideration). So in this
> case, the two concepts "same" and "different" combined
> with the values of the possible features are all that
> is needed to "model" the things of the universe.
>
> Did I get it?
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Deer Reeder,
Again I am sorry for taking so long to get back to you,
but I have been afraid of losing (intellectual) momentum
on the "Dif Log & Dyn Sys" project, due partly to all of
the discouraging invitations to peddle my papers elsewhere
that I got from "Some People" in the [X] Phyle, but I did
keep your questions in mind as I strove to come up with
clearer explanations of the material that I CC'd to you.
I have left the [X] Phyle fora while, but you can always
find the stuff I send out in the Arisbe, the SemioCom, or
the SUO Archives. Here are root nodes for "VOFIOTI ADO":
The Following Are Equipollent:
http://suo.ieee.org/email/msg03441.html
http://www.virtual-earth.de/CG/cg-list/msg03750.html
http://stderr.org/pipermail/arisbe/2001-February/000278.html
http://semiocom.listbot.com/cgi-bin/subscriber?Act=view_message&list_id=semiocom&msg_num=772
As I personally understand the word "model", it originally
just meant "anything that a sentence or a theory is true of",
that is, a "pragma" (= object or objective) in a/the "real world",
whatever the heck that is. In this way, a model enjoys two different
senses in which it is a model, one sense that is "logical" and one sense
that is "analogical". Here is the picture that I have of this situation:
| Sentence
| or
| Property Theory
| o----------------o
| / \ / \
| / \ / \
| / \ / \
| o o o o
| Object Object Sign Sign
| 1 2 1 2
An object is a "logical model" of a sentence or a theory
if it "satisfies" that sentence or theory, in other words,
if the sentence or the theory in question "holds true of it" --
or if one is thinking of the object as a whole universe, then
one may say if the sentence or the theory "holds true in it".
To my way of thinking, this means that there is a property
that the sentence or the theory picks out, say, the way
that the "Theory of Groups", as derived from the axioms
for a group, picks out the property of "being a group".
One object is an "analogical model" of some other object
if they share some property, and so, in this sense, they
are analogs, icons, models, or simulations of each other.
Now it ought to be clear from this picture, which goes back as far
as Aristotle, by the way, that these two senses of the word "model"
always go together.
Other than that, there are just a few typical sorts of distortions
that come into play to confuse the situation when people formalize
a subject like model theory or semantics, and then forget how they
went about doing this, thereafter confusing the "real models" with
their somewhat artificial "mock ups", that really live more in the
purely syntactic world of signs. I call this the "coriolis farce".
Here are some links to places in the SUO Archive
where I have discussed this once or twice before:
Abstraction, Analogy, Example, Icon, Metaphor,
Model, Morphism, Paradigm, Prototype, Simulation
http://suo.ieee.org/email/msg00657.html
http://suo.ieee.org/email/msg00671.html
http://suo.ieee.org/email/msg00676.html
http://suo.ieee.org/email/msg01251.html
http://suo.ieee.org/email/msg01293.html
http://suo.ieee.org/email/msg01350.html
http://suo.ieee.org/email/msg01772.html
http://suo.ieee.org/email/msg01812.html
http://suo.ieee.org/email/msg01824.html
http://suo.ieee.org/email/msg01830.html
Coriolis Farce
http://suo.ieee.org/email/msg01717.html
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