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

[Jon Awbrey]

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SMILE.  Commentary Note 2

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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

Cf: SMILE-COM 1.  http://stderr.org/pipermail/inquiry/2005-November/003168.html
In: SMILE-COM.    http://stderr.org/pipermail/inquiry/2005-November/thread.html#3168

Peirce's story of "mathematics at its simplest" (MAIS) stretches back toward the
instant of its birth, and further back toward the dawn of its primal evolution,
taking those moments in an archetypal rather than a historical sense, and as
far as it can probe it finds it borne upon the surf of signs and inquiry.

Proceeding through some of the simplest conceivable forms of inquiry,
in so far as they can be expressed in quasi-algebraic terms of art,
we previously encountered a primitive species of inquiry's genus:

| Then the first kind of problem of this algebra will be,
| given certain data concerning an unknown object, 'x',
| required to know whether it is !v! or !f!.
|
| C.S. Peirce, 'Collected Papers', CP 4.250

This amounts to a variable "x" whose value 'x' is considered to be unknown
at the moment of discussion in question but which is furthermore conceived
to be constrained to one among the collection that is conventionally known
as !B! = {!f!, !v!}.  The primal sort of inquiry contemplated here is then
expressed or modeled in the matter of ascertaining more constrainedly what
value in !B! is the value of 'x', or else, what is denoted by the sign "x".

Continuing with reading CP 4.250, we encounter gradually more complex beasts:

| Or similar problems may arise concerning several unknowns, 'x', 'y', etc.
|
| C.S. Peirce, 'Collected Papers', CP 4.250

If we express the collective ignorance that's embodied in several unknowns
by means of a list, for example, letting 'x' = <'x_1', ..., 'x_k'>, where
the value of 'x_j' is constrained to rest in the collection X_j, then we
have an inquiry into the value that 'x' takes in the cartesian product
X = X_1 x ... x X_k.  In the special case where each X_j equals !B!,
we have an inquiry into the value that 'x' takes in the power !B!^k.

Jon Awbrey

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