[Inquiry] Re: Examples Of Inquiry

[Jon Awbrey]

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EOI.  Note 8

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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:
|
|     [Therefore], 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:
|
|     [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.
|
| Peirce, 'Collected Papers' CP 1.559, 'Chronological Edition' CE 2, p. 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:

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| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` |
| ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` |
| ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` |
| ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
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Figure 4.  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 5.  Induction to the Rule M => P

Reference:

| C.S. Peirce, "New List", CP 1.559, CE 2, p. 58.
|
| Charles Sanders Peirce, "On a New List of Categories" (1867),
|'Collected Papers' CP 1.545-567, 'Chronological Edition' CE 2, pp. 49-59.
|
| http://www.peirce.org/writings/p32.html
| http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-frame.htm

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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