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:
> >
> > 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."

This is just my personal reading for some of the connotations that I found
in Aristotle's  "vera causa", but this is a topic that I skimmed over once
and lightly quite a ways back, and so I am in dire need of a return trip
to check out some of my hasty, all too hasty impressions.  In German, it
would be "Einfall", I think, the way that things "fall in" or "fall out",
as the case may be.

> 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)".

I love a striking phrase as much as anybody can -- to a fault, some would say --
but after the initial impression has been struck, one has to settle down and
sort out the stars from one's eyes.

What I get from all of this talk is the human circumstance
that we have our "initial descriptions" (ID's) of things --
states of affairs, of becoming, of being, of constraints --
and we think that our descriptions, well, describe something.
Then we find that some descryptions serve to explain others.
And then the fun begins.

> 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."

That is just my reading of the etymology, and the way that the word
is used in certain archaic contexts, as in the Classics and the Law.

> 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.

Oh boy, causality, now my karma has really hit the fan!
I have my own peculiar way of thinking about causality,
but I would really like to find a way of stalling here.
John Sowa has some good webpages on this subject, and
I think that there was considerable ontology-related
discussion of various formalizations for causes and
processes, a little before my time in this forum.
>From the "Quantum And Relativity Mechanics" (QARM)
that I had as a child I remain impressed with the
"fact" that this is one of those ostensibly simple,
"facile" in the obliviscent way of all common sense,
but really really not so obvious when you get down to
really really trying to think about it sort of problems,
for a sample, the way that one gets tangled in the exchange
relations of a complementarity between your average spacetime
picture and your casual causal picture of the world.  And I have
just spent the last dozen years or so thinking about how to --
let me consult an old paper just to see how I put it when --
"address the problem of dealing with change and diversity
in logic-based intelligent systems".  You may recognize
this as a somewhat old problem, going back to the days
of Heraclitus and Parmenides, at least.

> 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.

As a Crypto-Pythagorean Numinalist, I take some offence at your defence,
for it is my "form of intuition" (FOI) that generals are merely numbers,
and thus that all the worlds' great truths are but a play on surds, and
we but the actors, numb and getting number, that are getotalled up & out
in the score of this grand play.  Seriesly, Folks.

> 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" ...

Well, a person cannot serve two gurus,
not of thisilk, and not of thisort, &
I have my premisses to Peirce to keep, ...

> 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.

Do not forget "transverse" ...

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

Let me try to remember what you wrote:

| 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.

Maybe.  I will have to let you tell me.

I have this picture of walking along a path,
one foot up and one foot down, any given time,
in the human, all too human constitutional way.

Up in the air, off the ground, but not too far,
all of that suggests abductive reasoning to me,
the casual, chaotic, flexing, fluxing, formative,
inchoate, informal, un-formal-ized, -izable even,
all of that is what the real world is like to me.

The rest is more like a formal arena (Latin "dry sand"),
the solid ground that some people think they wish they
could stand on all of the time, where everything seems
to be "cut and dried" and clearly possible to decide,
in the recursèd sort of way to which we have re:sort
when all on site is ordered in a confluent hierarch.
Alas, an old sand-reckoner like me knows how shifty
this appearance can be, for we had sandstorms where
I grew up that would blast the flesh from your bones
if you dared to play in the open air a bit too long.

> > > 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".

Now, does that sound naive to you!?
 
> 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 ...

Thanks for these sources.  On a potnetially related note,
Christopher Spottiswoode sent me a link last week about
the work in "algebraic semiotics" that Joseph Goguen is
currently doing.  Here is the notice:

> ----------------------------------NOTICE----------------------------------
>
>                          University of California
>                       Institute for Software Research
>                          http://www.isr.uci.edu/
> 
>                    Distinguished Speaker Series 2000-2001
> 
>             ****************************************************
>              Joseph Goguen, University of California, San Diego
>                Algebraic Semiotics and User Interface Design
> 
>                             Friday, October 20
>                            10:30 am - 12:00 noon
>                Information and Computer Science, Room 432/438
>                       University of California, Irvine
>             ****************************************************
> 
> No cost to attend.
> Email RSVP requested by Monday October 16, to: 
> Rick Martin, remartin@uci.edu 
> 
> Abstract:  Current HCI results tend to be specialized and precise
> (e.g., Fitt's law), or else general but of uncertain reliability
> and generality (e.g., protocol analysis, questionaires, case studies,
> and usability studies).  What seems to be missing are scientific
> theories that can guide design, e.g., for new media, new metaphors
> (beyond the desktop), new kinds of hardware, or non-standard users
> (e.g., with disabilities).
> 
> Semiotics, as the general theory of signs, would seem
> a natural place to seek a general HCI framework.  However
> (1) semiotics has not developed in a precise mathematical style,
> and hence does not lend itself well to engineering applications;
> (2) it has mostly considered single signs or systems of signs
> (e.g., a novel, or a film), but not representations of signs from
> one system by signs from another, as is needed for studying interfaces;
> (3) it has not addressed dynamic signs, such as arise in user interaction;
> (4) it has not paid much attention to social issues such as arise
> in cooperative work.
> 
> A new project to address such problems has so far developed
> precise algebraic definitions for sign systems and their
> representations, and a calculus of representation providing
> laws for operations that combine representations as well as
> precise ways to compare the quality of representations.
> Case studies have considered browsable proof displays,
> scientific visualization, natural language metaphor,
> blending, and humor, while social foundations are
> grounded in ideas from ethnomethodology.
> 
> About the Speaker:  Joseph Goguen is Professor in the
> Department of Computer Science and Engineering at the
> University of California, San Diego, where he is also
> Director of the Meaning and Computation Lab, and was
> previously Director of the Program in Advanced Manufacturing. 
> From 1988 to 1996, he was the Professor of Computing Science
> at Oxford University, Director of its Centre for Requirements
> and Foundations, and a Fellow of St. Anne's College.
> From 1979 to 1988, he was a Senior Staff Scientist at SRI
> International, and a Senior Member of the Center for the
> Study of Language and Information at Stanford University.
> In 1999, he was a Fellow of the Japan Society for the
> Promotion of Science.
> 
> Professor Goguen has a bachelor degree from Harvard,
> and a PhD from Berkeley. He has previously taught at
> Berkeley, Chicago, and UCLA, where he was a full Professor.
> He held a Research Fellowship in the  Mathematical Sciences
> at the IBM Watson Research Center, held three Senior Visiting
> Fellowships at the University of Edinburgh, and gave distinguished
> lectures at Syracuse, Glasgow, and Austin.  He has recently given
> keynote addresses at conferences on formal methods, metaphor theory,
> software re-use, requirements engineering, and semiotics.  Professor
> Goguen is author or co-author of over 220 publications, co-author of
> two books on algebraic semantics, and editor or co-editor of three
> other books, two of which are titled *Art and the Brain*.
> 
> His research interests include software engineering
> (especially specification, modularization, architecture,
> requirements and evolution);  user interface design;
> theorem proving;  discourse analysis;  sociology of
> technology and science;  object oriented, relational
> and functional programming and their combinations;
> semiotics;  and fuzzy logic.  Professor Goguen is
> particularly known for his role in founding algebraic
> specification, including abstract data types, initial
> model semantics, and the OBJ language, the module system
> of which has influenced designs of the Ada, ML, and C++
> langauges.  Much more information can be found on
> Professor Goguen's website:
>
> <http://www.cs.ucsd.edu/users/goguen/>
> 
> Next meeting:
>
>    Date:     Friday, November 3
>    Speaker:  Jeffrey Kramer, Imperial College, London
>    Topic:    Modelling for Mere Mortals:
>              Mixing Architecture with Analysis & Animation
>
>    Web:      <http://www.isr.uci.edu/distinguished-speakers.html>
> 
> The UC Institute for Software Research wishes to thank
> its corporate sponsors for their support:
> 
>    The Aerospace Corp.
>    Continuus Software Corp.
>    FileNET
>    Printronix
>    Raytheon Company
>    Rincon Research Corp.
> 
> For more information, contact:
> 
>    Debra A. Brodbeck
>    Technical Relations Director
>    brodbeck@uci.edu
>
> ----------------------------------ECITON----------------------------------

> 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 ...

Well, I still have to recommend Peirce's work on all of these scores.

> > 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".

I am trying to be careful.  There are many sorts of specialized argots
in the air -- or the sandstorm -- hereabouts, and I still have no idea
yet which of the many might be your favorite, if any.

I am trying to create, develop, exposit -- whatever -- what I see as
some compelling intellectual continuities that undergirded the more
obviously radical transformations in a particular historical moment
in the evolution of the formal sciences, like logic and mathematics,
as they took place during the course of the Nineteenth Century, and
as they set the stage for our post*modern worldviews upon this scene.
(Yes, that's a kleene star in yer eyes:  post* = post^0 + post^1 + ...)

> Cheers,
> 
> Phil Jackson
> --------------------------------------------------------------------
> "Imagination is more important than knowledge.
>  Knowledge is limited. Imagination encircles the world." - Einstein
> --------------------------------------------------------------------
> Standard Disclaimers. www.philjackson.prohosting.com

Funny, that's the same quote that they have as their motto
at one of the "Weird Science" websites that I surf through:

<http://www.stardrive.org/>

Many Such Journeys Are Possible ...

Jon Awbrey

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