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

["Philip Jackson" <phil.jackson@computer.org>]

Jon Awbrey wrote:
> Philip Jackson wrote:
> > Jon Awbrey wrote:
> > >
> > > Abduction:  Fact + Rule ---> Case,
> > > Deduction:  Case + Rule ---> Fact,
> > > Induction:  Case + Fact ---> Rule.
> > >[...]
> > > 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.

Very true. Wittgenstein's use of "case" was closer to "fact" than to your
description given on 9/4/00 for "case" in the case-fact-rule triptych, i.e.
"a hidden or a hypothetical cause, that is, a type of event that is not
immediately observable to all concerned."

Wittgenstein followed "the world is all that is the case" with "the world is
the totality of facts, not of things", "what is the case - a fact - is the
existence of states of affairs", and "a state of affairs (a state of things)
is a combination of objects (things)".

These statements are closer to your 9/4/00 description of "fact": "In its
original usage a statement of Fact has to do with a deed done or a record
made, that is, a type of event that is openly observable and not riddled
with speculation as to its very occurrence."

Later on in Tractatus Logico-Philosophicus, Wittgenstein discusses
"causality" by writing "the law of causality is not a law but the form of a
law", and "mechanics is an attempt to construct according to a single plan
all the true propositions that we need for the description of the world",
etc.

My defense for using "the world is all that is the case" is only that it
seemed an interesting way of constructing an analogy between the
case-fact-rule triptych and Sowa's diagram, with potential to be more than
just a play on words. However, that would require re-interpreting
Wittgenstein's statement. A more profitable approach could be to forsake
trying to construct the analogy and focus instead on leveraging
Wittgenstein's many insights into the nature of language, logic, semantics,
etc. in the construction of SUO, which itself is a great "language game"...

Perhaps all that we can draw that is of direct relevance to SUO is to
recognize that the concepts of "world", "universe", "multiverse", "reality",
etc. would belong in a complete SUO, and that these concepts are subtle and
will be difficult to formalize.

I'm interested in whether the analogy I proposed is close to what you had in
mind, or were you thinking of something else?

> > 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".

If I understand correctly, you are pondering what would be a "semiotic model
theory".

Searching via Google, at first glance I find only one web page that
discusses semiotics in conjunction with logical model theory, which is an
interesting discussion of semiotics and models in nature at
http://www.geneticengineering.org/dna5/default.htm.

Haskell Curry gave a discussion of semiotics relative to formal languages
for mathematics in "A Theory of Formal Deducibility", pp. 11-23. This is
about the semiotics of formal languages rather than a formal model for
semiotics...

Returning to Wittgenstein, while TLP apparently does not directly refer to
"semiotics", he has much to say about relationships between signs, symbols,
pictures, propositions, and reality, which may provide the essence of a
formal model for semiotics....

>
> 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.

Well, "rules" as logical sentences seems in close enough agreement for an
analogy to hold, at least at this point. The logical sentences shown for
"theory" in Sowa's diagram could be seen as "rules".

Cheers,

Phil Jackson
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