[Inquiry] Re: Simple Meanings In Limnal Expressions -- Commentary

[Jon Awbrey]

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SMILE.  Commentary Note 3

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On reflection, I suppose it's not all that surprising
that this algebraic language seems magically tailored
to the considerations of signs becoming more informed --
or is it more informative? -- either way, it's all to
say becoming more ascertained, determined, or settled
in either or both of the dimensions of comprehensive
connotation and extensive denotation, since all of
this algebraic business first arose from the need
to solve problems in everyday practical affairs.
And problem solving is inquiry by another name.

Continuing with the reading of CP 4.250, we find Peirce
pausing to name three more of the very simplest species
of fauna and flora in this first garden of inquiry:

| Or when the last problem cannot be resolved,
| we may ask whether, supposing 'x' to be !v!,
| will 'y' be !v! or !f!?  And similarly,
| supposing 'x' to be !f!.
|
| C.S. Peirce, 'Collected Papers', CP 4.250

This expresses a familiar heuristic in mathematics:
If you can't solve a problem in general, can you
solve it in a special case, that is, contingent
on the assumption of additional constraints on
some of the "unknowns" or "variables"?

By way of example, consider a 2-variate problem of finding x in X, where
x = <x_1, x_2> is a value to be determined in X = X_1 x X_2.  In general,
we have some information about the situation that constrains the allowed
values of x, and this information is tantamount to saying that we have a
particular 2-adic relation L c X_1 x X_2 in mind, specified by the given
state of information.  In such a setting, one of the questions that next
comes to mind might be this:  If we have information that constrains x_1
in some further respect, how does that inform us about the values of x_2,
and vice versa?

Jon Awbrey

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