ONT Re: Zeroth Order Theories (ZOT's)
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We were in the middle of pursuing a few questions about
sign relational transformations in general, in particular,
the following Example of a sign transfornation that arose
in the process of setting up and solving a classical sort
of constraint satisfaction problem.
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| s_1 = Logue(o) | |
| / | |
| / | |
| @ | |
| · \ | |
| · \ | |
| · i_1 = Model(o) v |
| · s_2 = Model(o) | |
| · / | |
| · / | |
| Object = o · · · · · · @ | |
| · \ | |
| · \ | |
| · i_2 = Tenor(o) v |
| · s_3 = Tenor(o) | |
| · / | |
| · / | |
| @ | |
| \ | |
| \ | |
| i_3 = Sense(o) v |
| |
o-----------------------------------------------------------o
Figure. Computation As Semiotic Transformation
1. Logue(o) = Consat.Log
o-----------------------------------------------------------------------o
| |
| (( pete_plays_guitar ),( pete_plays_sax ),( pete_plays_drums )) |
| (( paul_plays_guitar ),( paul_plays_sax ),( paul_plays_drums )) |
| (( jane_plays_guitar ),( jane_plays_sax ),( jane_plays_drums )) |
| |
| (( pete_plays_guitar ),( paul_plays_guitar ),( jane_plays_guitar )) |
| (( pete_plays_sax ),( paul_plays_sax ),( jane_plays_sax )) |
| (( pete_plays_drums ),( paul_plays_drums ),( jane_plays_drums )) |
| |
| (( pete_fears_13 ),( pete_fears_cats ),( pete_fears_height )) |
| (( paul_fears_13 ),( paul_fears_cats ),( paul_fears_height )) |
| (( jane_fears_13 ),( jane_fears_cats ),( jane_fears_height )) |
| |
| (( pete_fears_13 ),( paul_fears_13 ),( jane_fears_13 )) |
| (( pete_fears_cats ),( paul_fears_cats ),( jane_fears_cats )) |
| (( pete_fears_height ),( paul_fears_height ),( jane_fears_height )) |
| |
| (( |
| |
| ( pete_plays_guitar ) |
| ( pete_fears_height ) |
| |
| ( pete_plays_guitar pete_fears_height ) |
| ( paul_plays_guitar paul_fears_height ) |
| ( jane_plays_guitar jane_fears_height ) |
| |
| ( paul_fears_cats ) |
| ( paul_plays_sax ) |
| |
| ( pete_plays_sax pete_fears_cats ) |
| ( paul_plays_sax paul_fears_cats ) |
| ( jane_plays_sax jane_fears_cats ) |
| |
| ( pete_plays_drums pete_fears_13 ) |
| ( paul_plays_drums paul_fears_13 ) |
| ( jane_plays_drums jane_fears_13 ) |
| |
| ( pete_plays_drums pete_fears_height ) |
| ( paul_plays_drums paul_fears_height ) |
| ( jane_plays_drums jane_fears_height ) |
| |
| )) |
| |
o-----------------------------------------------------------------------o
2. Model(o) = Consat.Mod ><> http://suo.ieee.org/ontology/msg03718.html
3. Tenor(o) = Consat.Ten (Just The Gist Of It)
o-------------------------------------------------o
| (pete_plays_guitar ) | <01> -
| (pete_plays_sax ) | <02> -
| pete_plays_drums | <03> +
| (paul_plays_drums ) | <04> -
| (jane_plays_drums ) | <05> -
| paul_plays_guitar | <06> +
| (paul_plays_sax ) | <07> -
| (jane_plays_guitar ) | <08> -
| jane_plays_sax | <09> +
| (pete_fears_13 ) | <10> -
| pete_fears_cats | <11> +
| (pete_fears_height ) | <12> -
| (paul_fears_cats ) | <13> -
| (jane_fears_cats ) | <14> -
| paul_fears_13 | <15> +
| (paul_fears_height ) | <16> -
| (jane_fears_13 ) | <17> -
| jane_fears_height * | <18> +
o-------------------------------------------------o
4. Sense(o) = Consat.Sen
o-------------------------------------------------o
| pete_plays_drums | <03>
| paul_plays_guitar | <06>
| jane_plays_sax | <09>
| pete_fears_cats | <11>
| paul_fears_13 | <15>
| jane_fears_height | <18>
o-------------------------------------------------o
We can worry later about the proper use of quotation marks
in discussing such a case, where the file name "Yada.Yak"
denotes a piece of text that expresses a proposition that
describes an objective situation or an intentional object,
but whatever the case it is clear that we are knee & neck
deep in a sign relational situation of a modest complexity.
I think that the right sort of analogy might help us
to sort it out, or at least to tell what's important
from the things that are less so. The paradigm that
comes to mind for me is the type of context in maths
where we talk about the "locus" or the "solution set"
of an equation, and here we think of the equation as
denoting its solution set or describing a locus, say,
a point or a curve or a surface or so on up the scale.
In this figure of speech, we might say for instance:
| o is
| what "x^3 - 3x^2 + 3x - 1 = 0" denotes is
| what "(x-1)^3 = 0" denotes is
| what "1" denotes
| is 1.
Making explicit the assumptive interpretations
that the context probably enfolds in this case,
we assume this description of the solution set:
{x in the Reals : x^3 - 3x^2 + 3x -1 = 0} = {1}.
In sign relational terms, we have the 3-tuples:
| <o, "x^3 - 3x^2 + 3x - 1 = 0", "(x-1)^3 = 0">
|
| <o, "(x-1)^3 = 0", "1">
|
| <o, "1", "1">
As it turns out we discover that the
object o was really just 1 all along.
But why do we put ourselves through the rigors of these
transformations at all? If 1 is what we mean, why not
just say "1" in the first place and be done with it?
A person who asks a question like that has forgetten
how we keep getting ourselves into these quandaries,
and who it is that assigns the problems, for it is
Nature herself who is the taskmistress here and the
problems are set in the manner that she determines,
not in the style to which we would like to become
accustomed. The best that we can demand of our
various and sundry calculi is that they afford
us with the nets and the snares more readily
to catch the shape of the problematic game
as it flies up before us on its own wings,
and only then to tame into the amenable
demeanors that we find to our liking.
In sum, the first place is not ours to take.
We are but poor second players in this game.
That understood, I can now lay out our present Example
along the lines of this familiar mathematical exercise.
| o is
| what Consat.Log denotes is
| what Consat.Mod denotes is
| what Consat.Ten denotes is
| what ConSat.Sen denotes.
To be continued ...
Jon Awbrey
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