ONT Re: Inquiry Driven Systems
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Note 2
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Bain's maxim, in the way that I elect to recall it,
added up to words that were roughly to this effect:
| Belief is that on which one is prepared to act.
Part of what this means to me I can express like so:
| When you accept a symbol, when you employ a concept,
| when you believe a proposition or hold it to be true,
| then your conduct forms an interpretant of those signs.
In effect, the pragmatic meaning of any sign to me
is the way that it determines my conduct in future.
The word "determine" has a particular meaning here,
and I can supply the reader with the beginnings of
a Persean gloss on the theme by citing these links:
Determination
01. http://suo.ieee.org/ontology/msg02377.html
02. http://suo.ieee.org/ontology/msg02378.html
03. http://suo.ieee.org/ontology/msg02379.html
04. http://suo.ieee.org/ontology/msg02380.html
05. http://suo.ieee.org/ontology/msg02384.html
06. http://suo.ieee.org/ontology/msg02387.html
07. http://suo.ieee.org/ontology/msg02388.html
08. http://suo.ieee.org/ontology/msg02389.html
09. http://suo.ieee.org/ontology/msg02390.html
10. http://suo.ieee.org/ontology/msg02391.html
11. http://suo.ieee.org/ontology/msg02395.html
12. http://suo.ieee.org/ontology/msg02407.html
13. http://suo.ieee.org/ontology/msg02550.html
14. http://suo.ieee.org/ontology/msg02552.html
15. http://suo.ieee.org/ontology/msg02556.html
16. http://suo.ieee.org/ontology/msg02594.html
17. http://suo.ieee.org/ontology/msg02651.html
18. http://suo.ieee.org/ontology/msg02673.html
19. http://suo.ieee.org/ontology/msg02706.html
20. http://suo.ieee.org/ontology/msg03177.html
21. http://suo.ieee.org/ontology/msg03185.html
22. http://suo.ieee.org/ontology/msg03188.html
Let us now return to the Figure of Adduction:
o-------------------------------------------------o
| |
| P |
| o |
| |\ |
| | \ |
| | \ |
| | \ |
| | \ Rule |
| | \ |
| | \ |
| | \ |
| | \ |
| Fact | Ad ---> o M |
| | / |
| | / |
| | / |
| | / |
| | / Case |
| | / |
| | / |
| | / |
| |/ |
| o |
| S |
| |
o-------------------------------------------------o
Figure 1. 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's the "New List" text about the relations between
the types of signs and the types of inference, that is,
the morphological and temporal constituents of inquiry:
| In an argument, the premisses form a representation of
| the conclusion, because they indicate the interpretant
| of the argument, or representation representing it to
| represent its object. The premisses may afford a
| likeness, index, or symbol of the conclusion.
|
| [Deduction of a Fact]
|
| In deductive argument, the conclusion is represented
| by the premisses as by a general sign under which it
| is contained.
|
| [Abduction of a Case]
|
| In hypotheses, something 'like' the conclusion is proved,
| that is, the premisses form a likeness of the conclusion.
| Take, for example, the following argument:--
|
| 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.
|
| [Induction of a Rule]
|
| That it is different with induction another example will show.
|
| 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.
|
| Hence 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.
|
| CSP, 'Collected Papers' CP 1.559, 'Chronological Edition' CE 2, page 58.
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 of Abduction:
o-------------------------------------------------o
| |
| P_1 P_2 P_3 P_4 |
| o o o o |
| \* \ / */| |
| \ * \ / * / | |
| \ * \ / * / | |
| \ * \ / * / | |
| \ *\ /* / | |
| . Q . | |
| | | * | | |
| | | * | | |
| | | | | |
| | | | * | |
| | | | * | |
| . | . M |
| \ | / * |
| \ | / * |
| \ | / * Case |
| \ | / * S=>M |
| \|/* |
| o |
| S |
| |
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Figure 2. Abduction of the Case S => M
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 of Induction:
o-------------------------------------------------o
| |
| P |
| o |
| /|\* Rule |
| / | \ * M=>P |
| / | \ * |
| / | \ * |
| / | \ * |
| . | . M |
| | | | * | |
| | | | * | |
| | | | | |
| | | * | | |
| | | * | | |
| . L . | |
| / */ \* \ | |
| / * / \ * \ | |
| / * / \ * \ | |
| / * / \ * \ | |
| /* / \ *\| |
| o o o o |
| S_1 S_2 S_3 S_4 |
| |
o-------------------------------------------------o
Figure 3. Induction to the Rule M => P
Reference
| CSP, "New List", CP 1.559, CE 2, page 58.
|
| 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
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