[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Commentary Note 11

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I am going to stick with the Index-Induction side of the problem
until I feel like I understand what's going on with this linkage
between the faces of the sign relation and the phases of inquiry.

The New List (1867) account of the relationship between
the kinds of signs and the kinds of arguments says this:

| 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.

In general, the components of an argument
have the following sign relational duties:

<Conclusion, Premisses, Interpretant>  =  <Object, Sign, Interpretant>

| The premisses may afford a likeness,
| index, or symbol of the conclusion.

In the case of the inductive argument,
we have the following role assigments:

<Conclusion, Premisses, Interpretant>  =  <Object, Index, Interpretant>

Premisses (Index):

| 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.

Conclusion (Object):

| All M is P.

Remark:

| 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.

One of the questions that I have at this point is whether Peirce
is speaking loosely or strictly when he refers to the conclusion
and the premisses of the argument in question.  Strictly speaking,
the conclusion has the form M => P and the premisses have the forms
S_j => M and S_j => P.  But taken more loosely, as often happens in
contexts where the antecedent of a conditional statement is already
assumed to hold true, people will sometimes refer to the consequent
of a conditional conclusion as the conclusion and the consequents
of conditional premisses as the premisses.  In the present case,
such a practice would lead to speaking of the predicate M as
one of the premisses and the predicate P as the conclusion.
So let us keep that interpretive option in mind as we go.

Jon Awbrey

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