ONT Re: Models & Theories -- New Names for Some Old Ways of Thinking
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
I remembered what was bothering me about my earlier use
of the word "comprehension" to label the summit point
in Aristotle's paradigm of analogy. As it happens,
I had already written out an amendment this summer,
but that was before vacation ...
http://suo.ieee.org/ontology/msg02887.html
Here are some pieces of the discussion with Jean-Marc Orliaguet
that led up to my re-introducing Aristotle' picture of analogy:
I still see our lack of congruence in this area
as going back to a misunderstanding about the
nature and the use of explicit formal models.
A person can "do phenomenology" for a very long time before they
have to make a deliberate effort to dredge up some formal model
to organize the complexity of their accumulating observations.
We are always swimming in the ocean of experience, and there
is nothing that we have to do to "particularize" anything,
or to anchor what we do to the surrounding whatevers.
Indeed, my experience has taught me, to the contrary,
just when I think that the problem is how to connect,
to integrate, or to synthesize diverse elements of
experience, that the real problem is only why did
I even think that I knew how to distinguish them
in the first place. Many times, the best way
to achieve the true integration between two
bits of experience is just to quit drawing
the imaginary lines of a false distinction.
But when we do get to the point of needing to formulate,
more reflectively than reflexively, an explicit model,
then we are crossing the threshold of abstraction,
of one kind or the other. As a matter of fact,
I think that the names that Peirce uses for
the two kinds of abstraction, "prescissive"
and "hypostatic", do not really draw out
the way in which they are actually kin,
and I have been tempted to coin the
name "hyperstatic" for the former.
In a sense, both types of abstraction start out the same way, merely
emboldening particular patterns kenned in the steam of consciousness
until they condense or desublimate into fixtures of suspended doubts.
Thus is precipitated a superficial but practically essential tension
between the casual circus and the formal arena, and the show is just
not the same after that. The best picture of the evolving situation
that I have found so far, at least, under the rose of simplicity, is
the one that Aristotle gives in his paradigm of reasoning by analogy:
http://suo.ieee.org/email/msg01350.html
http://suo.ieee.org/email/msg01772.html
http://suo.ieee.org/email/msg04768.html
Here, for the sake of comparison,
is the picture as I drew it and
the story as I told it last time:
http://suo.ieee.org/ontology/msg02361.html
http://suo.ieee.org/ontology/msg02363.html
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:
http://suo.ieee.org/ontology/msg03338.html
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.
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.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤