ONT Re: Extension x Comprehension = Information
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Note 93
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With the clarity afforded by a therapeutic slumber, my third thought,
the relatively ultimate, more perfect interpretant of the intervening
struggle toward that final, hopefully neither dying nor raging light,
begins to look ever more like the fitting icon of my first impression.
I was trying to understand the things that Peirce said and wrote about
the conventional, disjunctive, indexical, inductive complex of notions
in the period 1865-1867. And I was focused for the moment on this bit:
| 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. ...
|
| [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:
|
| Therefore, 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, CP 1.559, CE 2, 58.
I've gotten as far as sketching this picture of the possible readings:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| |
| P <------------@------------ "P" |
| ^^^ ^^^ |
| | \ | \ |
| . | .\ . | .\ |
| | \ | \ |
| . | . \ . | . \ |
| | M <------@--------------|--- "M" |
| . | .= . . | .^ # |
| | = | / |
| . | = . . | / . |
| | = . | / # |
| . |= . . |/ . |
| S <------------@------------ "S" |
| . .. .. . . . * .. .# . # |
| . . . . * . . . # |
| . . . . . . * . . . . # . |
| .. . . ... * .. . . #.# |
| o o o o o o o o |
| m h k w "m" "h" "k" "w" |
| S_1 S_2 S_3 S_4 "S_1" "S_2" "S_3" "S_4" |
| |
o-----------------------------------------------------------o
| Disjunctive Subject "S" and Inductive Rule "M => P" |
o-----------------------------------------------------------o
In order of increasing "objectivity", here are three alternatives:
1. The interpretation where "S" is an index of "M"
by virtue of "S" being a property of each "S_j",
literally an implicit sign of each of them, and
by dint of each "S_j" being an instance of "M".
The "S" to "S_4" to "M" link is drawn [# # # #].
2. The interpretation where "S" is an index of M
by virtue of "S" being a property of each S_j,
literally a generic sign of each of them, and
by virtue of each S_j being an instance of M.
The "S" to S_4 to M link is 2-tone [* * . .].
3. The interpretation where S is an index of M
by virtue of S being a property of each S_j,
literally a supersample of each of them, and
by virtue of each S_j being an instance of M.
The S to S_4 to M link is shown as [. . . .].
Perhaps it is the nature of the sign situation that all three
interpretations will persevere and keep some measure of merit.
I'm leaning toward the third one as presenting a higher grade
of objectivity. But what does that mean? In practical terms,
it means that it is well past time for my first cup of coffee.
Jon Awbrey
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