[Arisbe] Re: Abstraction, Analogy, Example, Icon, Metaphor, Model, Morphism, Paradigm, Prototype, Simulation
Jon Awbrey
arisbe@stderr.org
Fri, 04 May 2001 11:44:01 -0400
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Arisbeans, SemioCompères, SUOphiles, &
immediate incitements due to Jean-Marc:
Maybe it's just the time o' year ...
but bits and pieces of unfinished shoots
just keep on colluding in my mind, and so
I am stuck with re-runs and retrospectives --
maybe it's a hint to branch out from my rows
with these "insistent reductionists" (IR's)
and apply a bit of retroduction to the mass.
Thus, I will try to pull together a variety
of related themes, a few of which have been
touched on of late under the "Expostulation"
and "Brouillon Projet" threads, but all of
which go back in my own mind to the kinship
among many different ideas, of which we may
say that "Abstraction" and "Analogy" should
be counted the most salient, with the ideas
of "Models" and "Morphisms" coming up close
in the order of their pragmatic pragnanz.
Let me return to the quotation from Chomsky,
and try to say what I see in it, as I think
that it highlights a very important subject,
namely, the theme of "Holism" in the nature,
and especially in the use, of formal models.
| In linguistic theory, we face the problem of constructing
| this system of levels in an abstract manner, in such a way
| that a simple grammar will result when this complex of abstract
| structures is given an interpretation in actual linguistic material.
|
| Since higher levels are not literally constructed out of lower ones,
| in this view, we are quite free to construct levels of a high degree
| interdependence, i.e., with heavy conditions of compatibility between
| them, without the fear of circularity that has been so widely stressed
| in recent theoretical work in lingustics. (Chomsky, LSOLT, page 100).
|
| Noam Chomsky, 'The Logical Structure of Linguistic Theory',
| Based on a widely circulated manuscript dated 1955.
| University of Chicago Press, Chicago, IL, 1975.
What this is saying, among other things, is that formal models
are meant to be evaluated as whole systems, in comparison with
the whole corpi of data that they are meant to explain, and as
these corpi of data are reflective of whole systems of objects
that impress us with that obsistent character that we commonly
know and love as "reality". Just saying that renders me weary,
so I will have to put off pursuing it further until I have the
help of a few able cohorts. But it does evoke a certain brand
of picture that continues to burn in my mind, and so I can try,
as a quantum, to pass on the form, if not quite the fire of it.
Way Back Last Autumn, Jon Awbrey Wrote:
| I keep coming back to the following two pictures or configurations:
|
| 1. There is that A-frame construction in Aristotle's discussion
| of reasoning by way of Analogy, Example, or Paradigm, which
| he articulates as a combination of Induction and Deduction.
|
| Atrocious Adversity
| A
| o
| /*\
| / * \
| / * \
| / * \
| / * \
| / * \
| / R u l e \
| / * \
| / * \
| / Bellicose \
| / Battles \
| F a c t B F a c t
| / Between \
| / Bordermates \
| / * * \
| / * * \
| / C a s e C a s e \
| / * * \
| / * * \
| / * * \
| / * * \
| / * * \
| o o
| C D
| Contest: Debacle:
| Athens versus Thebes Thebes versus Phocis
|
| Figure 1. Aristotle's "War Against Neighbors" Example
|
| Legend for Figure 1:
|
| A = Atrocious, Adverse to All, A bad thing.
| B = Belligerent Battle Between Brethren.
| C = Contest of Athens against Thebes.
| D = Debacle of Thebes against Phocis.
|
| Syllogistic Terminology:
|
| A is a major term,
| B is a middle term,
| C is a minor term,
| D is a minor term, similar to C.
|
| Note on Terminology:
|
| I am using the terms "Case", "Fact", "Rule" in the medieval fashion
| that was added to the classical treatment of syllogism at a somewhat
| later time, but predating our present usage by several hundered years.
| In this style of schematization, one has the following forms of reasoning:
|
| 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 Model-Theory-World 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.
Aristotle's A-Frame structure of analogy equips us with an archetype
for understanding the relation between abstraction and analogy, plus
the relationship of models and morphisms. Let us trace it like this:
| Comprehension
| C
| o
| /|\
| / | \
| / | \
| / | \
| / | \
| / | \
| / R u l e \
| / | \
| / | \
| / | \
| / | \
| F a c t A F a c t
| / Abstraction \
| / Hypostasis? \
| / * * \
| / * * \
| / C a s e C a s e \
| / * * \
| / * * \
| / * * \
| / * * \
| / * Arrow * \
| o---------------------->----------------------o
| X <------------------<----->------------------> E
| Unknown Analogy Effective
| Reality Facsimile
I have labeled the top node "Comprehension" because I believe that this
is the classical word for the conjunction of all of the intensions that
a collection of subjects have in common, but my impression is hazy here,
and so I will just have to use it this way provisionally for the moment.
The middle term A is an explanatory, pertinent, or relevant Abstraction,
the property that accounts for all of the rest of the properties in the
Comprehension.
Have to break ...
Be back later ...
Jon Awbrey
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An Assortment Of Beads On This Thread:
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/msg01969.html
http://suo.ieee.org/email/msg01973.html
http://suo.ieee.org/email/msg02005.html
http://suo.ieee.org/email/msg02123.html
http://suo.ieee.org/email/msg04748.html
http://suo.ieee.org/email/msg04749.html
http://suo.ieee.org/email/msg04758.html
http://www.bestweb.net/~sowa/ontology/
http://www.bestweb.net/~sowa/ontology/gloss.htm
http://www.bestweb.net/~sowa/ontology/causal.htm
http://www.bestweb.net/~sowa/ontology/mthworld.gif
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