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

[Jon Awbrey]

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SMILE.  Commentary Note 7

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Re: SMILE 4.  http://stderr.org/pipermail/inquiry/2005-November/003166.html
In: SMILE.    http://stderr.org/pipermail/inquiry/2005-November/thread.html#3166

Returning to the present locus of viscosity,
let's see if we've acquired any momentum of
angular velocity, or even a virtual variety,
that'll do to get us unstuck from the point:

| Again, given certain data concerning 'x',
| we may ask, what else needs to be known in
| order to compel 'x' to be !v! or to be !f!.
|
| C.S. Peirce, 'Collected Papers', CP 4.250

Given the amendments to the constitution of 'x' that we've
been entertaining over the past few sessions, I think that
we have now succeeded in recasting this variety of inquiry
as a special case of the one that Peirce treated before it:

| 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

It will help to remember the analysis that I gave of this type of problem:

| 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?
|
| Cf: SMILE-COM 3.  http://stderr.org/pipermail/inquiry/2005-December/003314.html
| In: SMILE-COM.    http://stderr.org/pipermail/inquiry/2005-December/thread.html#3313

If we view the initial problem to be solved as one of acertaining,
determining, finding, or, as they say, "computing" the value of a
function 'x' : M -> !B!, then the turnabout that Peirce describes
in this variation is customarily convened as an "inverse problem",
to wit, to find all of the source elements in M that 'x' sends to
any given target element in !B!.  Analogous observations apply to
the scene where 'x' is regarded as being a relation 'x' c M x !B!.

Jon Awbrey

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