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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5 (view source)
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=====5.1.2.5. The Ark of Types : The Order of Things to Come=====
=====5.1.2.5. The Ark of Types : The Order of Things to Come=====
<pre>
Now westlin winds and slaught'ring guns
Bring Autumn's pleasant weather;
The moorcock springs on whirring wings
Amang the blooming heather:
Now waving grain, wide o'er the plain,
Delights the weary farmer;
And the moon shines bright, as I rove by night,
To muse upon my charmer.
Robert Burns, Now Westlin Winds, [CPW, 44]
The present situation, as far as it goes, is a suitable subject for being investigated along the lines of the pragmatic theory of sign relations. The state of the resulting examination, as it stands at the current stage of analysis, is summarized in Table 27, indicating little more than this hypothetical circumstance: That a couple of terms of a formal language, a prospective calculus of "applications" or "appositions" of the form f.g, are intended to be identified in all of their current objective references. Thus, the terms "y0" and "y.y", formed in accord with the still inchoate and yet developing grammar of the intended "appositional calculus" (AC), are set to denote the very same object or objects, all the while that the precise nature of what these signs actually denote is still up for grabs, and in spite of the circumstance that the bare consistency of its logical possibility remains unknown, for all the plausibility of the posability.
Recalling that a "bit" of a sign relation is any subset of its extension, that is, an arbitrary selection of its ordered triples, Table 27 presents a bit of a sign relation that is needed to interpret "The Initial Equation", also known as "TIE".
Table 27. Bit of a Sign Relation for TIE
Object Sign Interpretant
Y "Y" "Y"
y "y" "y"
y0 "y0" "y0"
y0 "y0" "y.y"
y0 "y.y" "y0"
y0 "y.y" "y.y"
The paitrick lo'es the fruitfu fells,
The plover lo'es the mountains;
The woodcock haunts the lonely dells,
The soaring hern the fountains:
Thro lofty groves the cushat roves,
The path o man to shun it;
The hazel bush o'erhangs the thrush,
The spreading thorn the linnet.
Robert Burns, Now Westlin Winds, [CPW, 44]
In order to refer to an object x, it is necessary to use a sign "x", or something equally good, an equiferent sign, to do so. In a similar vein, in order to refer to a sign "x", it is necessary to use a HO sign <"x">, or something equally good, an equiferent HO sign, to do so.
In referring to the signs "x" and "y0 = y.y", I am of course using a definite style of HO signs to do so, while the corresponding LO signs, the ones that are being denoted by these mechanisms, are homologous to the portions of text that appear within the bounds of these quotations. The chief exception to this rule, attaching a note of practical caution to its exercise that precludes its overly automatic use, is due to the problem already noted, that not every LO sign extracted from quotation is safe to use, semantically speaking, in every discursive context, grammatical environment, syntactic frame, or textual niche.
As long as I am referring to the signs "x" and "y0 = y.y", I can keep on using the HO signs that refer to them, all without having to employ the next layer of encapsulation in arch quotes. I am obligated to use the new order of arches only when I want to awake to, become aware of, and directly mention the order of signs that I find myself employing, in the present case, when I get a notion to critically reflect on and thus to make explicit reference to the HO signs <"x"> and <"y0 = y.y">. It is almost as if, in using an order of signs, that one takes off the wraps that one uses in order to mention them. This is generally true, but subject to exceptions at the boundary conditions, where there are no more lamina to strip away.
Table 28
The bit of a sign relation that is shown in Table 28 is an example of this type of arbit.
Table 28. Arbit of a Sign Relation for TIE
Object Sign Interpretant
y0 "y0" = "y.y"
Thus ev'ry kind their pleasure find,
The savage and the tender;
Some social join, and leagues combine,
Some solitary wander:
Avaunt, away, the cruel sway!
Tyrannic man's dominion!
The sportsman's joy, the murd'ring cry,
The flutt'ring, gory pinion!
Robert Burns, Now Westlin Winds, [CPW, 44]
Table 29 shows a variety of notations that are available for the first two orders of signs above "x".
Table 29. Simple Signs & Their Higher Order Signs
Object Sign Interpretant
x "x" = <x>
"x" <"x"> = <<x>>
"x" <"x"> = "<x>"
But, Peggy dear, the ev'ning's clear,
Thick flies the skimming swallow;
The sky is blue, the fields in view,
All fading green and yellow:
Come let us stray our gladsome way,
And view the charms of Nature;
The rustling corn, the fruited thorn,
And ilka happy creature.
Robert Burns, Now Westlin Winds, [CPW, 44]
Table 30
Table 30. Complex Signs & Their Higher Order Signs
Object Sign Interpretant
TIS "y0 = y.y" = <y0 = y.y>
TIS "y0 = y.y" = <"y0" =E "y.y">
"y0 = y.y" <"y0 = y.y"> = <<y0 = y.y>>
"y0 = y.y" "TIE" = <TIE>
We'll gently walk, and sweetly talk,
While the silent moon shines clearly;
I'll clasp thy waist, and, fondly prest,
Swear how I lo'e thee dearly:
Not vernal show'rs to budding flow'rs,
Not Autumn to the farmer,
So dear can be as thou to me,
My fair, my lovely charmer!
Robert Burns, Now Westlin Winds, [CPW, 44]
Table 31
Table 31. More Complex Signs & Their Higher Order Signs
Object Sign Interpretant
TIS "TIS" = "The Intended State"
TIS TIE = The Initial Equation
TIS TIE = "y0 = y.y"
"TIS" <"TIS"> = <<TIS>>
TIE "TIE" = "The Initial Equation"
TIE "TIE" = <"y0 = y.y">
TIE "TIE" = <TIE>
"TIE" <"TIE"> = <<TIE>>
</pre>
=====5.1.2.6. The Epitext=====
=====5.1.2.6. The Epitext=====