SUO: Re: Abstraction, Analogy, Example, Icon, Metaphor, Model, Morphism, Paradigm, Prototype, Simulation

[Jon Awbrey <jawbrey@oakland.edu>]

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Philip Jackson wrote:
>
> Jon Awbrey wrote:
> >
> > Abduction:  Fact + Rule ---> Case,
> > Deduction:  Case + Rule ---> Fact,
> > Induction:  Case + Fact ---> Rule.
> >
> > -------------------------------------------------------------------------
> >
> > The cardinal- or hinge-point to note about Aristotle's example
> > of reasoning by example is that the middle term B serves as an
> > explanation of 'why' the major term A should be considered as
> > applicable to the contemplated instances of conflict, C and D,
> > instance C a future contingent whose advisability of rendering
> > actual was presently, at that time in Athens, being disputed,
> > instance D already a part of the discussants' previous history,
> > from which they might reasonably be expected to have learned.
> >
> > 2.  The other picture is John Sowa's World-Model-Theory Triptych:
> >
> > <http://www.bestweb.net/~sowa/ontology/mthworld.gif>
> >
> > Well, it took me so much time to find the loose ends of this thread
> > that I have plumb forgot what I was going to say, but I remember
> > that I saw some kind of analogy between these two pictures --
> > (Between Analogy Analogy Triptych)? -- and so I am sure that
> > if I take a little break it will all come back to me, soon.
> 
> One way to construct an analogy might be along the lines:
> 
> "The world is all that is the case." as Wittgenstein said at one time.

I am taking a bit of a risk trying to preserve these antic notions
of "Case", "Fact", "Rule", and their relationships to various forms
of inference, both demonstrative and otherwise, especially alongside
of the more finely geared up and more sharply tooled up instrumental
senses that we have become accustomed, in modern times, to be using --
and so I genuinely fear exceeding my margin of tolerance by trying
to bring that "Master of those Games that are Played with Stones",
Ludovico Wittgenstein, into the mix of my concrete foundations.

If you wish to do this, then we will have to make sure that
we carefully examine the assembled tokens and playing pieces,
for instance, these little bitty words, "case", "fact", "rule",
to see if all of the puzzle pieces really do belong in, or even
ever came from, the same box, otherwise I fear that we will soon
become the mercilessly strained victims of a hopelessly scrambled
and inescapably dis-integral picture.

> A model (of a theory) may be considered as a collection of facts.

Well, you are stealing some of my most portentous rumbling here,
but one of my aims in stringing out this thread is to introduce
a "trial" notion of what constitutes a "model".  Up until a few
days ago, I would have said "dual" notion, but as every good
Peircean (and every good Freudian) eventually must, I am
beginning to e-spy the spectre of thirdness raising its
three urly heads.

I used to think that a "model" was "anything about which
a statement or a theory holds", thereby putting it into
close relationship with the notion of a semantic object,
that is, anything that a sign denotes.  Moreover, I was
used to thinking -- or was that just my imagination? --
that this was the sense of it that currently prevailed
in the logical subject that we know as "model theory",
and yet, I am beginning to have my doubts about that.

So let me distinguish this sense of the word "model" from
whatever it is that does presently dominate the thinking
of those who currently practice this "theory of models",
and let me give it a name, that nobody else will desire,
dubbing it the "naive" or the "natural" sense of "model".

Let me re-capitulate the triune heads of this dogma:

1.  The naive meaning or the natural sense of the term "model".

2.  The logical meaning of "model" that we find, or hope to find,
    in the customary conduct and the standard practices of that
    formal subject that is called, by convention, "model theory".

3.  The analogical meaning of "model", wherein it is related to
    a whole host of notions like "analogue", "avatar", "copy",
    "facsimile", "icon", "image", "likeness", "representation",
    "reproduction", "simulacre", "simulation", and so on.

> A theory may be considered as a collection of rules.

Well, I usually consider a theory to be a collection of sentences,
or, perhaps, the abstract propositions, the hypostatic statements,
or the "logical equivalence classes" (LEC's) of signs that may be
thought to correspond with these expressions, formulae, sentences.

> These statements are open to further discussion, of course.

Do ya think?

> Patrick Grim's book "The Incomplete Universe" presents a collection of arguments
> against "The world is all that is the case."  We could (indeed, must) accept
> incompleteness and talk in terms of "everything we know that is the case",
> while granting that the world is larger than what we know.

Do ya think?

> Viewing a model as a collection of facts which satisfies a theory,
> is not the same as viewing a model as something that explains or
> emulates some phenomenon or situation.  This second concept of
> model is closer to the concept of a scientific theory ...
> 
> Well, back to lurking.  These SUO threads are very interesting --
> I wish I had more time to contribute to SUO, and will try
> to do so on occasion in future.
> 
> Best Regards,
> 
> Phil Jackson
> --------------------------------------------------------------------
> "Imagination is more important than knowledge.
> Knowledge is limited.  Imagination encircles the world." - Einstein
> --------------------------------------------------------------------
> Standard Disclaimers. www.philjackson.prohosting.com

I appreciate the visit -- hope to see it continue ...

Cheers,

Jon Awbrey

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