ONT Re: Zeroth Order Theories (ZOT's)
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It will be good to keep this picture before us a while longer:
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
The labels that decorate the syntactic plane and indicate
the semiotic transitions in the interpretive panel of the
framework point us to text files whose contents rest here:
http://suo.ieee.org/ontology/msg03722.html
The reason that I am troubling myself -- and no doubt you --
with the details of this Example is because it highlights
a number of the thistles that we will have to grasp if we
ever want to escape from the traps of YARNBOL and YARWARS
in which so many of our fairweather fiends are seeking to
ensnare us, and not just us -- the whole web of the world.
YARNBOL = Yet Another Roman Numeral Based Ontology Language.
YARWARS = Yet Another Representation Without A Reasoning System.
In order to avoid this, or to reverse the trend once it gets started,
we just have to remember what a dynamic living process a computation
really is, precisely because it is meant to serve as an iconic image
of dynamic, deliberate, purposeful transformations that we are bound
to go through and to carry out in a hopeful pursuit of the solutions
to the many real live problems that life and society place before us.
So I take it rather seriously.
Okay, back to the grindstone.
The question is: "Why are these trips necessary?"
How come we don't just have one proper expression
for each situation under the sun, or all possible
suns, I guess, for some, and just use that on any
appearance, instance, occasion of that situation?
Why is it ever necessary to begin with an obscure description
of a situation? -- for that is exactly what the propositional
expression caled "Logue(o)", for Example, the Consat.Log file,
really is.
Maybe I need to explain that first.
The first three items of syntax -- Logue(o), Model(o), Tenor(o) --
are all just so many different propositional expressions that
denote one and the same logical-valued function p : X -> %B%,
and one whose abstract image we may well enough describe as
a boolean function of the abstract type q : %B%^k -> %B%,
where k happens to be 18 in the present Consat Example.
If we were to write out the truth table for q : %B%^18 -> %B%
it would take 2^18 = 262144 rows. Using the bold letter #x#
for a coordinate tuple, writing #x# = <x_1, ..., x_18>, each
row of the table would have the form <x_1, ..., x_18, q(#x#)>.
And the function q is such that all rows evalue to %0% save 1.
Each of the four different formats expresses this fact about q
in its own way. The first three are logically equivalent, and
the last one is the maximally determinate positive implication
of what the others all say.
From this point of view, the logical computation that we went through,
in the sequence Logue, Model, Tenor, Sense, was a process of changing
from an obscure sign of the objective proposition to a more organized
arrangement of its satisfying or unsatisfying interpretations, to the
most succinct possible expression of the same meaning, to an adequate
positive projection of it that is useful enough in the proper context.
This is the sort of mill -- it's called "computation" -- that we have
to be able to put our representations through on a recurrent, regular,
routine basis, that is, if we expect them to have any utility at all.
And it is only when we have started to do that in genuinely effective
and efficient ways, that we can even begin to think about facilitating
any bit of qualitative conceptual analysis through computational means.
And as far as the qualitative side of logical computation
and conceptual analysis goes, we have barely even started.
Jon Awbrey
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