SUO: Re: Inquiry Driven Ontology Development
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| Z
| o
| |\
| | \
| | \
| | \
| | \ Rule
| | \
| | \
| | \
| | \
| Fact | Ad ---> o Y
| | /
| | /
| | /
| | /
| | / Case
| | /
| | /
| | /
| |/
| o
| X
|
| Figure 0. Adduction of a Middle Term
One of the nice things about the concept of "adduction"
is that it allows us to strike a compromise with those
who may not even recognize abduction as such but think
that it is induction that leads new concepts into play.
While we are thinking of the kinds of features that
abduction and induction have in common, and also of
the kinds of circumstances that invite the adduction
of a concept to a factual situation, whether we find
the needed concept already available in our ontology
or whether we are led to make up a new concept to fit
the bill, we ought to remind ourselves of the picture
that Peirce gave us of these two operations that was
especially vivid in drawing out the dualities or the
symmetries of their logical structure and function.
Here is brief review:
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Abduction to a Case
| M is, for instance, P_1, P_2, P_3, and P_4;
|
| S is P_1, P_2, P_3, and P_4:
|
| Ergo, S is M.
|
| Here the first premiss amounts to this, that
| "P_1, P_2, P_3, and P_4" is a likeness of M,
| and thus the premisses are or represent
| a likeness of the conclusion.
Let the expression
"P_1 & P_2 & P_3 & P_4"
denote the proposition
Q = Conjunction (P_1, P_2, P_3, P_4).
Then we may draw the following figure:
| P_1 P_2 P_3 P_4
| o o o o
| \* \ / */|
| \ * \ / * / |
| \ * \ / * / |
| \ * \ / * / |
| \ *\ /* / |
| o Q o |
| | | * | |
| | | * | |
| | | | |
| | | | * |
| | | | * |
| o | o M
| \ | / *
| \ | / *
| \ | / * Case
| \ | / * S=>M
| \|/*
| o
| S
|
| Figure 1. Abduction to the Case S => M
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Induction to a Rule
| S_1, S_2, S_3, and S_4 are taken as samples of the collection M;
|
| S_1, S_2, S_3, and S_4 are P:
|
| Ergo, All M is P.
|
| Here the first premiss amounts to saying that
| "S_1, S_2, S_3, and S_4" is an index of M.
| Hence the premisses are an index
| of the conclusion.
Let the expression
"S_1 v S_2 v S_3 v S_4"
denote the proposition
L = Disjunction (S_1, S_2, S_3, S_4).
Then we may draw the following figure:
|
| P
| o
| /|\* Rule
| / | \ * M=>P
| / | \ *
| / | \ *
| / | \ *
| o | o M
| | | | * |
| | | | * |
| | | | |
| | | * | |
| | | * | |
| o L o |
| / */ \* \ |
| / * / \ * \ |
| / * / \ * \ |
| / * / \ * \ |
| /* / \ *\|
| o o o o
| S_1 S_2 S_3 S_4
|
| Figure 2. Induction to the Rule M => P
Reference
| CSP, "New List", CP 1.559.
|
| Charles Sanders Peirce, "On a New List of Categories" (1867).
| Cf. 'Collected Papers', CP 1.545-567.
| Cf. 'Chronological Edition', CE 2, pages 49-59.
|
| http://www.peirce.org/writings/p32.html
| http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-frame.htm
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤