ONT Re: Models & Theories -- New Names for Some Old Ways of Thinking
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Sorry, I made a number cut-and-paste errors in that
last submission under this line that totally hashed
all my good intentions to amend what I said before --
persistence of error, I guess. Here is a fix of
the messed up section:
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Here is my amendment and extension of this use of Aristotle's picture:
In my anticipation of a future development whose time is not yet prepared,
I created a potential for a certain confusion in the picture that I drew
last time, attempting to show the connections among abstract hypostases,
reasoning by analogy, the invocation of formal models, and the combined
intensions, or "comprehension", that is common to an object and its icon,
that is, its formal likeness. So let me try to make amends this time around,
and maybe even foreshadow where I believe this discussion is eventually going.
Here, for the sake of comparison,
is the picture as I drew it and
the story as I told it last time:
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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.
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If you take what I say here quite literally -- and I gave you no
reason to do otherwise -- then this just fails to make good sense.
For if the comprehension C is the conjunction of "all" intensions,
then whatever intension evolves as the accountable abstraction A
is already among them, and so we have C => A. But the picture
appears to suggest that A => C. Of course, this could happen,
but it does not represent the most generic state of affairs.
By way of excusing myself, let me explain what caused me to say this.
First, I am jumping ahead in my thoughts to a text of Peirce's where
he overlays a type of abductive reasoning on this picture of analogy.
Second, the order of development that I am trying to diagram here is
not a static hierarchy of implications but a dynamic evolution, thus
involving at least two distinct moments in time.
I think that I can fix up the rest of this discussion by redrawing and
relabeling slightly the adaptation that I made of Aristotle's A-Frame.
| Initial
| Comprehension
| A = IC
| o
| /|\
| / | \
| / | \
| / | \
| / | \
| / | \
| / R u l e \
| / | \
| / | \
| / | \
| / | \
| F a c t B = EC F a c t
| / Evolute \
| / Comprehension \
| / * * \
| / * * \
| / C a s e C a s e \
| / * * \
| / * * \
| / * * \
| / * * \
| / * Arrow * \
| o---------------------->----------------------o
| X <------------------<----->------------------> E
| Unknown Analogy Effective
| Reality Facsimile
Let us now consider the two chief moments in the development of the argument
as they work out in Aristotle's paradigmatic example of analogical reasoning.
The apical node is labeled "Initial Comprehension" (IC) to indicate
the conjunction of the intensions that are implicit in an agent's
initial understanding of what the analogue subjects have in common.
The middle node is labeled "Evolute Comprehension (EC) to indicate
the conjunction of the intensions that are evolved in an agents's
reflective understanding of the situation or the state of affairs.
In Aristotle's original example the argument began with the conjunction
of many qualities that were called to mind in regard to several well-known
battles, whose effects could be summed up by saying that that their results
turned out to be "Adverse" (A) for all sides. After a moment of reflection,
the reasoning agent becomes aware of a new intension, whose significance has
gone previously unnoticed, to wit, the common case that all of these debacles
were instances of "Battles Between Bordermates" (B), and this serves as the
pivot point for an extension of the argument by analogy to an anticipated
application, one that is actively being contemplated but still avoidable,
amounting to a prediction of adversity arising from a future contingent
war against neighbors, anticipated but not yet engaged.
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TGIF,
Jon
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