[Inquiry] Re: Examples Of Inquiry

[Jon Awbrey]

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EOI.  Note 15

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In reviewing some of my previous writing on the issues in this area,
I came across the following collection of thoughts that seem of use.

For my part in this investigation, I have been
trying to resolve a couple of related 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 authors
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 discuss
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:

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| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Sign ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` Object o---------O` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` `o Interpretant ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 15.1  Elementary Sign Relation

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| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | Ab` > \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\ /` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | <-o-De` o Y ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/ \` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | In` > / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
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Figure 15.2  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".

o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` Z ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `\` Rule` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` `\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` Fact` | Ad ---> o Y ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` `/` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` / ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` `/` Case` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` / ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 15.3  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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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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