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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.11. Higher Order Sign Relations : Application===
===6.11. Higher Order Sign Relations : Application===
<pre>
Given the language in which a notation like "De (q, R)" makes sense, or in prospect of being given such a language, it is instructive to ask: "What must be assumed about the context of interpretation in which this language is supposed to make sense?" According to the theory of signs that is being examined here, the relevant formal aspects of that context are embodied in a particular sign relation, call it "Q". With respect to the hypothetical sign relation Q, commonly personified as the prospective reader or the ideal interpreter of the intended language, the denotation of the expression "De (q, R)" is given by:
De ("De (q, R)", Q).
If Q follows rules that are typical of many species of interpreters, then the value of this expression will depend on the values of the following three expressions:
De ("De", Q),
De ("q" , Q),
De ("R" , Q).
What are the roles of the signs "De", "q", "R" and what are they supposed to mean to Q? Evidently, "De" is a constant name that refers to a particular function, "q" is a variable name that makes a PIR to a collection of signs, and "R" is a variable name that makes a PIR to a collection of sign relations.
This is not the place to take up the possibility of an ideal, universal, or even a very comprehensive interpreter for the language indicated here, so I specialize the account to consider an interpreter QAB = Q(A, B) that is competent to cover the initial level of reflections that arise from the dialogue of A and B.
For the interpreter QAB, the sign variable q need only range over the syntactic domain S = {"A", "B", "i", "u"} and the relation variable R need only range over the object domain O = {A, B}, so long as the latter objects remain subject to analysis as sign relations. These requirements can be accomplished as follows:
1. The variable name "q" is a HA sign that makes a PIR to the elements of S.
2. The variable name "R" is a HU sign that makes a PIR to the elements of O, regarded as sign relations.
3. The constant name "A" is a HI sign that makes a PIR to the elements of A.
4. The constant name "B" is a HI sign that makes a PIR to the elements of B.
This results in a HO sign relation for QAB that is shown in Table 46.
Table 46. Higher Order Sign Relation for Q(A, B)
Object Sign Interpretant
A <R> <R>
B <R> <R>
<A> <q> <q>
<B> <q> <q>
<i> <q> <q>
<u> <q> <q>
<A, <A>, <A>> <A> <A>
<A, <A>, <i>> <A> <A>
<A, <i>, <A>> <A> <A>
<A, <i>, <i>> <A> <A>
<B, <B>, <B>> <A> <A>
<B, <B>, <u>> <A> <A>
<B, <u>, <B>> <A> <A>
<B, <u>, <u>> <A> <A>
<A, <A>, <A>> <B> <B>
<A, <A>, <u>> <B> <B>
<A, <u>, <A>> <B> <B>
<A, <u>, <u>> <B> <B>
<B, <B>, <B>> <B> <B>
<B, <B>, <i>> <B> <B>
<B, <i>, <B>> <B> <B>
<B, <i>, <i>> <B> <B>
<<<A>, A>, A> <De> <De>
<<<B>, A>, B> <De> <De>
<<<i>, A>, A> <De> <De>
<<<u>, A>, B> <De> <De>
<<<A>, B>, A> <De> <De>
<<<B>, B>, B> <De> <De>
<<<i>, B>, B> <De> <De>
<<<u>, B>, A> <De> <De>
Following the manner of construction in this extremely reduced example, it is possible to see how answers to the above questions, concerning the meaning of "De (q, R)", might be worked out. In the present instance:
De ("q", QAB) = S,
De ("R", QAB) = O.
</pre>
===6.12. Issue 1. The Status of Signs===
===6.12. Issue 1. The Status of Signs===