ONT Re: Inquiry Driven Systems
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Note 4
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Reflection
You might say that we are trying to understand the very conception
of a concept, that is to say, the process by which a concept comes
to be conceived, and this is a different matter from understanding
the state of grace that it may have enjoyed in its ethereal heaven
before it came time for it to be borne into this earthly existence.
More prosaically, we would like to understand the process by which
a potential concept, hypothesis, idea, sign, term, or similar item
transits from being a formal possibility in nobody in particular's
mind and passes into a term of utility in somebody in particular's
conduit of thought.
There is nothing terribly novel about this question, and maybe later
I will indicate the sources of my own particular currents of thought,
but for the moment I'll try think it through on my own without notes.
I do remember that Kant started something that seemed rather new,
to wit, asking "what's the use, what's the good of a good idea?",
and suggesting that we can get some clue to why a concept has to
be invented in the first place, whose time might be inaccessible,
by looking at what function tends to keep it going and in demand
in the 2nd and 3rd and 4th and 5th and 6th and 7th and kth place.
Since this seems to me like one of those good ideas that is worth
keeping around just a little while longer, at least, I will apply
it experimentally to what would otherwise be a bedevilled problem,
namely, the logical scruple and the secular gap between the first
enlistment of a rookie concept and the aptly ever after mustering
of it to do its duty in the times and trials and troubles to come.
Continuation
Let's try to focus for a while on what we may see as
the "differential" or the "distributional" aspect of
inquiry. If you follow the idea that inquiry begins
with a state of tension in the affected agent of the
process, then you are likely to recognize the legion
of diverse names for this annoyingly irritating mode
of being -- doubt, problem, surprise, uncertainty --
as forming variable manifestations of a differential
theme, for example, that a difference exists between
what an agent observes or accepts as actual and what
that agent either expects or intends to be the case.
For instance, let us consider once again Dewey's "Sign of Rain" example:
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| |
| Air Warm Air Cool Clear Sky Cloudy Sky |
| A_1 A_2 C_1 C_2 |
| o~~~~~>~~~~~o o~~~~~>~~~~~o |
| \ / |
| \* * * */ |
| \ / |
| \ * * * * / |
| \ / |
| \ * * * * / |
| \ / |
| \ * * * / |
| \ / |
| \ * * * * / |
| \ Balmy Boding / |
| \ B_1 o~~~~~>~~~~~o B_2 / |
| \ * * / |
| \ / |
| \ * * / |
| \ / |
| \ * * / |
| \ / |
| \ * * / |
| \ / |
| \ * * / |
| \ / |
| \*/ |
| o |
| C |
| Current Situation |
| |
| A_1 = Air Warm A_2 = Air Cool |
| B_1 = Balmy Day B_2 = Bodes Rain |
| C_1 = Clear Sky C_2 = Cloudy Sky |
| |
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Figure 1. Dewey's "Sign of Rain" Example
Here, the agent has an initial expectation of fair weather,
due most likely to his initial observations of a clear sky,
but then discrepant sensations of significantly cooler air
cause him to pause, to reflect, and to update his forecast
of the imminent weather conditions to a foreboding of rain.
I would like to retrace once more time the recurring Figure
of Dewey's precipitating inquiry, but this time I intend to
point out some features of it that may well bring us to ask:
"What's wrong with this picture?"
To start with, it's beginning to seem like a familiar problem,
the likes of which I have run into on several other occasions.
For example, it reminds me of similar patterns of incoherence
that occurred in my initial attempts to explicate Aristotle's
theory of analogy. So let us review the record of that prior
trial as a way of exploiting precendents for the current case.
Here is a flash montage of just the principal Figures in my
development of the story, with minimal notes of explanation:
First, we have the initial Figure for Aristotle's "War Against Neighbors"
example, illustrating how he articulates reasoning by analogy as a mixed
form of syllogism that combines the patterns of induction and deduction:
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| |
| 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 vs Thebes Thebes vs Phocis |
| |
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Figure 2. Aristotle's "War Against Neighbors" Example
The cardinal-axis, hinge-point, or linch-pin of Aristotle's example
of reasoning by analogy is the middle term B, which is supposed to
serve as an explanation of why the major term A should be regarded
as applicable to the contemplated instances of conflict, C and D.
Here, C is a future contingent whose advisability of being rendered
actual was presently under discussion at that time in Athens, and D
was already a part of the discussants' previous history, the sort of
example from which they might reasonably be expected to have learned.
This initial picture rests easily, all too easily within a logical latticework,
that is, it situates itself in an implicational ordering with no real sense of
difficulty or effort, but it manifests in doing so a strangely static quality
for what is actually a problematic and a tension-filled situation of inquiry.
There we had the following Figure and the following attempt at an explanation:
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| |
| Comprehension Theory |
| A T |
| o-------------------<-------------------o |
| /|\ Denotation . |
| / | \ . |
| / | \ . |
| / | \ . |
| / R u l e \ . |
| / | \ . |
| / | \ . |
| / | \ . |
| / | \ . |
| F a c t B F a c t . |
| / Abstraction \ . |
| / * * \ . |
| / * * \ . |
| / * * \ . |
| / C a s e C a s e \ . |
| / * * \ . |
| / * * \ . |
| / * * \ . |
| /* Model Arrow *\ . |
| o------------------>>>------------------o |
| X <<<----------<<<------->>>---------->>> E |
| Unknown Analogy Effective |
| Reality Facsimile |
| |
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Figure 3. Abstraction over an Appropriate Arrow of Analogy
I have labeled the top node "Comprehension" because I believe that this
is the classical term for the conjunction of all of the intensions that
a set of subjects have in common. The middle term B is the explanatory,
the pertinent, or the relevant Abstraction, the property that is posed
to account for all of the rest of the properties in the Comprehension.
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 3 is an object in the hierarchical object domain O.
If you take what is said and drawn here quite literally, then it all just
fails to make good sense. For if the comprehension A is the conjunction
of "all" the relevant intensions, then whatever intension evolves as the
accountable abstraction B is already among them, and so we have A => B.
But the picture given appears to suggest that B => A. This could happen,
of course, 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.
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| |
| Initial |
| Comprehension Theory |
| A T |
| o-------------------<-------------------o |
| /|\ Denotation . |
| / | \ . |
| / | \ . |
| / | \ . |
| / R u l e \ . |
| / | \ . |
| / | \ . |
| / | \ . |
| / | \ . |
| F a c t B F a c t . |
| / Evolute \ . |
| / Comprehension \ . |
| / * * \ . |
| / * * \ . |
| / C a s e C a s e \ . |
| / * * \ . |
| / * * \ . |
| / * * \ . |
| /* Model Arrow *\ . |
| o------------------>>>------------------o |
| X <<<----------<<<------->>>---------->>> E |
| Unknown Analogy Effective |
| Reality Facsimile |
| |
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Figure 4. Amended Abstraction Over An Appropriate Arrow Of Analogy
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
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