ONT Re: Models & Theories -- New Names for Some Old Ways of Thinking
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JA = Jon Awbrey
JC = John Collier
RH = Rom Harre
JC, quoting RH:
| The minds of other people are not available to public scrutiny.
| Hence neither their conscious experiences nor their cognitive
| processes, conscious or unconscious, can be the subject matter
| of psychological science. The word 'model' is used widely by
| psychologists, (...) different from its use in the natural
| sciences. In the natural sciences a model is a representation
| or analogue of its subject. The physical sciences have made
| such startling progress because (...) of the resemblance.
| The relevant structure and processes in the real world
| causing that behaviour is a sensible question to ask.
|
| Rom Harre, "The Rediscovery Of The Human Mind",
| 50th Anniversary Conference Proceedings,
| Korean Psych. Asso. (2001)
The mind of JC is not available to public scrutiny, of course,
but I find the words of RH to be accommodating to my previous
remarks that we need to interpret the word "model" in a dual
sense, analogical and logical. This is, of course, a rather
old idea, going back to Aristotle's A-frame blueprint for
reasoning by analogy, example, or "paradigm":
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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, To Avoid.
| B = Belligerent Battle Between Brethren.
| C = Contest of Athens against Thebes.
| D = Debacle of Thebes against Phocis.
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
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 Theory
| C T
| o----------------------<----------------------o
| /|\ Denotation .
| / | \ .
| / | \ .
| / | \ .
| / | \ .
| / | \ .
| / R u l e \ .
| / | \ .
| / | \ .
| / | \ .
| / | \ .
| F a c t A F a c t .
| / Abstraction \ .
| / * * \ .
| / * * \ .
| / * * \ .
| / C a s e C a s e \ .
| / * * \ .
| / * * \ .
| / * * \ .
| / * * \ .
| / * Arrow * \ .
| o---------------------->----------------------o
| X <------------------<----->------------------> E
| Unknown Analogy Effective
| Reality Facsimile
|
| Figure 2. Abstraction Over An Appropriate Arrow Of Analogy
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.
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I am still not sure about the use of the word "comprehension" here,
but let me use it provisionally for the complex of properties that
are held in common by a set of instances, objects, or situations,
and that are intended to be captured by a fitting theory of them.
Then we can say that all of these objects, whether in the object
domain or in the analogue model domain, are logical models that
satisfy the theory. In sign-theoretic terms, the theory T is
a sign in a suitable sign domain S, while everything else in
Figure 2 is an object in the hierarchical object domain O.
Jon Awbrey
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