[Inquiry] Re: Examples! Examples! Examples!

[Jon Awbrey]

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EEE.  Note 37

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Semiotic Reflections (cont.)

I have kept before you a particular picture of the way that
our significant languages relate to our objective realities --
there's a double meaning in that, that word "objective", that
can also refer to an intentional object, a thing not yet, and
yet to be, if our aim be ept -- it's just one of the dimensions
of meaning that is now largely lost in the translation from the
Greek grammed "pragma" to the Latin sieved and winnowed "object".

o-----------------------------o-------------------o-----------------------------o
|         Language 1          |   Object Domain   |         Language 2          |
o-----------------------------o-------------------o-----------------------------o
|                                                                               |
|           o----------o                                     o----------o       |
|          /| "T"      |\                 1                 /| " "      |\      |
|         / | "x => x" |~\~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~/~| "(x(x))" | \     |
|        /  | ...      |  \              / \              /  | ...      |  \    |
|       /   o----------o   \            /   \            /   o----------o   \   |
|      /                    \          /     \          /                    \  |
|     /           o----------o        /       \        /           o----------o |
|    /            | "x"      |       /         \ x    /            | "x"      | |
|   /             | "T => x" |~~~~~~/~~~~~~~~~~~o~~~~/~~~~~~~~~~~~~| "((x))"  | |
|  /              |          |     /           /    /              | ...      | |
| o----------o    o----------o    /           /    o----------o    o----------o |
| | "~x"     |              /    /           /     | "(x)"    |              /  |
| | "x => F" |~~~~~~~~~~~~~/~~~~o~~~~~~~~~~~/~~~~~~| "(x(()))"|             /   |
| | ...      |            /  (x) \         /       | ...      |            /    |
| o----------o           /        \       /        o----------o           /     |
|  \                    /          \     /          \                    /      |
|   \   o----------o   /            \   /            \   o----------o   /       |
|    \  | "F"      |  /              \ /              \  | "()"     |  /        |
|     \ | "x & ~x" |~/~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~\~| "x(x)"   | /         |
|      \| ...      |/                 0                 \| ...      |/          |
|       o----------o                                     o----------o           |
|                                                                               |
o-------------------------------------------------------------------------------o
Figure 7.  Lattice of Objects Inducing a Diversity of Sign Partitions

But for the present I ought to say what I intend by this:

Infinite diversity poses an obstacle to nominal thinking.

Let's look to the future contingent story of a prospectively
many-wiled problem-solving siftware -- to give it a name and
a local habituation, and thus personify the object narrative
of our quest, let's call it "him", where he be "Peirce Eval".

A problem about the relationship between signs and more signs and objects
presents itself to our many-wiled hero.  What is the quickest and easiest
wile that he downlifts from off his pegboared of wiles?  Well, one way to
reduce the problem is to ignore the problematic domain of objects in toto,
whether intentional or clear and present, and one way to get away with it
is suggested by the very k-ptyches that we have staring at all this while.

Here is how it just might work.  Suppose that we had in hand
a complete survey of all the signs that we needed to use for
denoting the objects in our pragmatic domain.  Suppose, also,
that we had them all the signs nicely partitioned and sorted
into the mutually exclusively exhaustive parts that refer to
the several objects in our objective domain.  Well, then, we
would have a form-preserving copy of the object domain quite
well in hand with the quotient object of the sign domain and
the object domain should be a "world well wiled" out of mind.
That might leave some people quite content with the 2-dim or
1-dim or 0-dim world that is weft behind, according to their
taste and just how far they were wont to go, but it does not
manage to master the possibilities, not if the real world is
infinitely diverse, for example, if it just keeps on sending
new objects, classifiable or otherwise, not to mention, till
we make a sign to mention them under, entirely novel objects.

So we find ourselves forced by the nature of reality to the
point of standing on the standpoint that shall henceforward
be called "rational thinking", at least, at the very least.

Jon Awbrey

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