SUO: Approches To Inquiry Driven Systems
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I continue to examine the role of inquiry in ontology development,
with a special focus on the role of abduction in forming concepts.
If we want to build computational support for ontology building,
we will not be able to escape the issues of abductive reasoning.
For my part, I have been trying to resolve a couple of problems:
1. What is the proper articulation of the inquiry process in terms
of the various kinds of inference, apodictic and approximate,
that various thinkers have identified as being relevant to it?
2. What is the proper placement of inquiry within a theory of signs?
My approach to this problem area has been to track back to the sources
of some of our initial ideas about signs and inquiry, to see if I could
work out for myself what they were thinking and how they moved from one
stage of their thought to the next, and maybe along the way to see if
I can see anything that they may have missed, or omitted to mention
clearly enough. I am especially interested in the transition that
C.S. Peirce made from syllogistic to relational forms of thinking
about signs and inquiry, as that corresponds to an important task
in what might be called "computational architectronics", that of
building adequate logical systems on a solid propositional layer.
I have spent a fair amount of time staring at the likes
of the following two structures and trying to figure out
how they fit together, figuratively speaking, of course:
| o Sign
| /
| /
| /
| Object o---------@
| \
| \
| \
| o Interpretant
|
| Figure 1. Elementary Sign Relation
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | Ab > \
| | \ / \
| Fact | <-¤-De o Y
| | / \ /
| | In > /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 2. Three Kinds of Inference
After I had stared at the second picture a very long time,
I came to see that the two approximate forms of inference,
Abduction and Induction, have in common the property that
they bring a middle term into the immediate configuration.
Then I remembered that Aristotle is supposed to have said:
The essence of quick wit lies in grasping the middle term.
But where do these middle terms come from, anyway? It is
conventional to say that they come in with the abductions
of the cases that first evidence any need to call on them,
and that this is what puts them in the pot for inductions
and deductions to bid for them on any subsequent occasion.
But maybe it would make sense to recognize an independent
process, solely dedicated to finding or making mediations.
Conceived in this way, this process would be a duction in
the opposite direction from Deduction, dub it "Adduction".
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | \
| | \
| Fact | Ad ---> o Y
| | /
| | /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 3. Adduction of a Middle Term
I'm not too committed to this name for the action,
and it has been used on one or two rare occasions
as yet another name for abduction, but I will use
it until I come up with a name that I like better.
Jon Awbrey
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