[Inquiry] Re: Examples Of Inquiry -- Discussion

[Jon Awbrey]

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EOI.  Discussion Note 9

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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:
|
|     [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.
|
| 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:

o-------------------------------------------------o
|                                                 |
|           P_1   P_2         P_3   P_4           |
|            o     o           o     o            |
|             \*    \         /    */|            |
|              \ *   \       /   * / |            |
|               \  *  \     /  *  /  |            |
|                \   * \   / *   /   |            |
|                 \    *\ /*    /    |            |
|                  .     Q     .     |            |
|                  |     | *   |     |            |
|                  |     |   * |     |            |
|                  |     |     |     |            |
|                  |     |     | *   |            |
|                  |     |     |   * |            |
|                  .     |     .     M            |
|                   \    |    /    *              |
|                    \   |   /   *                |
|                     \  |  /  * Case             |
|                      \ | / *   S=>M             |
|                       \|/*                      |
|                        o                        |
|                        S                        |
|                                                 |
o-------------------------------------------------o
Figure A.  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 B.  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, pages 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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