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===6.38. Considering the Source===
===6.38. Considering the Source===
<pre>
There are several ways to contemplate the supplementation of signs, the sorts of augmentation that are crucial to meaning in the case of indices. Some approaches are analytic, in the sense that they regard signs as derivative compounds and try to break up the unitary concept of an individual sign into a congeries of seemingly more real, more actual, or more determinate sign instances. Other approaches are synthetic, in the sense that they accept a given collection of signs at face value and try to reconstruct more objective realities through the formation of abstract categories on this basis.
1. One analytic method takes it as a maxim for the logic of context that: "Every sign or text is indexed by the context in which it occurs." This means that all signs, including indices, are themselves indexed, though initially only tacitly, by the objective situation, the syntactic context, and the actual interpreter that makes use of them.
To begin formalizing this brand of supplementation, it is necessary to mark salient aspects of the situational, contextual, and inclusively interpretive features of sign usage that were previously held tacit. In effect, signs once regarded as primitive objects need to be newly analyzed as categorical abstractions that cover multitudes of existential sign instances or "signs in use" (SIU's).
To develop these dimensions of the A and B dialogue, I will attempt to articulate these interpretive parameters of signs by means of subscripts or superscripts attached to the signs or their quotations, in this way constituting a brand of "situated signs" or "attributed remarks".
The attribution of signs to their activating interpreters preserves the original object domain but produces an expanded syntactic domain, the set of "attributed signs":
O = { A, B },
S = I = {"A"A, "B"A, "i"A, "u"A, "A"B, "B"B, "i"B, "u"B}.
Table 73 displays the results of indexing every sign of the dialogue between A and B with a superscript indicating its source or "exponent", namely, the interpreter who actively communicates or transmits the sign. Ostensibly, the operation of attribution produces two new sign relations for A and B, but it turns out that both sign relations have the same form and content, so a single Table will do. The new sign relation generated by this operation will be denoted as "At (A, B)" and called the "attributed sign relation" for A and B.
Table 73. Attributed Sign Relation for Interpreters A & B
Object Sign Interpretant
A "A"A "A"A
A "A"A "A"B
A "A"A "i"A
A "A"A "u"B
A "A"B "A"A
A "A"B "A"B
A "A"B "i"A
A "A"B "u"B
A "i"A "A"A
A "i"A "A"B
A "i"A "i"A
A "i"A "u"B
A "u"B "A"A
A "u"B "A"B
A "u"B "i"A
A "u"B "u"B
B "B"A "B"A
B "B"A "B"B
B "B"A "i"B
B "B"A "u"A
B "B"B "B"A
B "B"B "B"B
B "B"B "i"B
B "B"B "u"A
B "i"B "B"A
B "i"B "B"B
B "i"B "i"B
B "i"B "u"A
B "u"A "B"A
B "u"A "B"B
B "u"A "i"B
B "u"A "u"A
Thus informed, the SER for interpreter A yields the semantic equations:
["A"A]A = ["A"B]A = ["i"A]A = ["u"B]A,
or "A"A =A "A"B =A "i"A =A "u"B.
In comparison, the SER for interpreter B yields the semantic equations:
["A"A]B = ["A"B]B = ["i"A]B = ["u"B]B,
or "A"A =B "A"B =B "i"A =B "u"B.
Consequently, both SER's now induce the same semantic partition on S:
{{ "A"A, "A"B, "i"A, "u"B }, { "B"A, "B"B, "i"B, "u"A }}.
By means of a simple attribution step a certain level of congruity has been reached in the community of interpretation constituted by A and B. This newfound agreement on what is abstractly a single SER means that its equivalence classes reconstruct the structure of the object domain within the parts of the SEP. This allows a measure of objectivity or inter subjectivity to be predicated of the sign relation's representation.
An instance of Y using "X" is considered to be an objective event, the kind of happening to which all suitably placed observers can point, and adverting to an occurrence of "X"Y is more specific and less vague than resorting to instances of "X" as if being issued by anonymous sources. The situated sign "X"Y comprises a "wider sign" than "X" in the sense that it takes in a broader field of view on the interpretive situation and provides more information about the context of use. As to the reception of attributed remarks, the interpreter that can recognize signs of the form "X"Y is one that knows what it means to "consider the source".
It is best to read the superscripts on attributed signs as accentuations and integral parts of the quotation marks, taking ("..."A) and ("..."B) as variant inflections of ("..."). Thus, I can refer to the sign "X"Y just as I would refer to the sign "X" in the present informal context (PIC), without any additional marks of quotation.
Taking a cue from this usage, the ordinary quotes that I use to mark salient relationships of signs and expressions with respect to the informal context can now be regarded as quotes that I myself, operating as a casual interpreter, tacitly index. Even without knowing the complete sign relation that I have in mind, the one that I presumably use to conduct this discussuion, the sign relation that "I" represents can nevertheless be partially formalized by means of a certain functional equation, namely, the equation between semantic functions: "..." = "..."I.
By way of vocal expression, the attributed sign "X"Y can be pronounced as '"X" quoth Y ' or '"X" used by Y '. To facilitate visual imagery, each token of the type "X"Y can be pictured as a specific occasion where the sign "X" is being used or issued by the interpreter Y.
There is one remaining form of useful continuity that can be established between these newly formalized inventions and the ordinary conventions of common practice that are customary to apply in the informal context. Conforming to the ascriptions made above, I revive an old usage for framing interjections and enunciate the quotation "X"I as '"X" quotha '. Readers who find this custom too curious for words might consider the twofold origins of inquiry and interpretation, one in the virtue of addressing uncertainty and another in the acknowledgment of surprise.
The construal of objects as classes of attributed signs leads to a measure of inter subjective agreement between the interpreters A and B. Something like this must be the goal of any system of communication, and analogous forms of congruity and gregarity are likely to be found in any system for establishing mutually intelligible responses and maintaining socially coordinated practices.
Nevertheless, the particular types of "analytic" solutions that were proposed for resolving the conflict of interpretations between A and B are conceptually unsatisfactory in several ways. The constructions instituted retain the quality of hypotheses, especially due to the level of speculation about fundamental objects that is required to support them. There remains something fictional and imaginary about the nature of the object instances that are posited to form the ontological infrastructure, the supposedly more determinate strata of being that are presumed to anchor the initial objects of discussion.
Founding objects on a particular selection of object instances is always initially an arbitrary choice, a meet response to a judgment call and a responsibility that cannot be avoided, but still a bit of guesswork that needs to be tested for its reality in practice (RIP).
This means that the postulated objects of objects cannot have their reality probed and proved in detail but evaluated only in terms of their conceivable practical effects.
2. One synthetic method ...
Suppose now that each of the agents A and B reflects on the situational context of their discussion and observes on every occasion of utterance exactly who is saying what. By this critically reflective operation of "considering the source" each interpreter is empowered to create, in effect, an "extended token" or "situated sign" out of each utterance by indexing it with the proper name of its utterer. Though it arises by reflection, the augmented sign is not a higher order of abstraction so much as a restoration or reconstitution of what was lost by abstracting the sign from the signer in the first instance.
In order to continue the development of this example, I need to employ a more precise system of marking quotations in order to keep track of who says what, and in what kinds of context. To help with this, I use pairs of raised angle brackets (<...>) on a par with ordinary quotation marks ("...") to call attention to pieces of text as signs or expressions. The angle quotes are especially useful for embedded quotations and for text regarded as used or mentioned by interpreters other than myself, for instance, by the fictional characters A and B. Whenever possible, I save ordinary quotes for the outermost level, the one that interfaces with the context of informal discussion.
A notation like "<<A>, B, C>" is intended to indicate the construction of an extended (attributed, indexed, or situated) sign, in this case, by enclosing an initial sign "A" in a contextual envelope "<< >, , >" and inscribing it with relevant items of situational data, as represented by the signs "B" and "C". When a salient component of the situational data represents an observation of the agent B communicating the sign "A", then the compressed form "<<A>B, C>" can be used to mark this fact. If there is no addiutional contextual information beyond the marking of its source, then the form "<<A>B>" suffices to say that B said "A".
With this last modification, "angle quotes" become like "ascribed quotes" or "attributed remarks", indexed with the name of the interpretive agent that issued the message in question. In sum, the notation "<<A>B>" is intended to situate the sign "A" in the context of its contemplated use, and to index the sign "A" with the name of the interpreter that is considered to be using it on a given occasion.
The notation "<<A>B>", read "<A> quoth B" or "<A> used by B", is an expression that indicates the use of the sign "A" by the interpreter B. The expression inside the outer quotes is refered to as an "indexed quotation", since it is indexed by the name of the interpreter to which it is referred. Since angle quotes with a blank index are equivalent to ordinary quotes, "<A>B" = <<A>B>?
Enclosing a piece of text with raised angle brackets and following it with the name of an interpreter is intended to call to mind ...
Object domain:
O = { A, B }
Indexed syntactic domain or extended sign system:
S = { "[<A>]A", "[<B>]A", "[<i>]A", "[<u>]A",
"[<A>]B", "[<B>]B", "[<i>]B", "[<u>]B" }
The situated sign or indexed expression "[<A>]B" presents the sign or expression "A" as used by the interpreter B. In other words, the sign is indexed by the name of an interpreter to indicate a use of that sign by that interpreter. Thus, "[<A>]B" augments "A" into a new and more complete sign by including additional information about the context of its transmission, in particular, by the consideration of its source.
Table 74. Adequated Sign Relation for Interpreters A & B
Object Sign Interpretant
A "[<A>]A" "[<A>]A"
A "[<A>]A" "[<A>]B"
A "[<A>]A" "[<i>]A"
A "[<A>]A" "[<u>]B"
A "[<A>]B" "[<A>]A"
A "[<A>]B" "[<A>]B"
A "[<A>]B" "[<i>]A"
A "[<A>]B" "[<u>]B"
A "[<i>]A" "[<A>]A"
A "[<i>]A" "[<A>]B"
A "[<i>]A" "[<i>]A"
A "[<i>]A" "[<u>]B"
A "[<u>]B" "[<A>]A"
A "[<u>]B" "[<A>]B"
A "[<u>]B" "[<i>]A"
A "[<u>]B" "[<u>]B"
B "[<B>]A" "[<B>]A"
B "[<B>]A" "[<B>]B"
B "[<B>]A" "[<i>]B"
B "[<B>]A" "[<u>]A"
B "[<B>]B" "[<B>]A"
B "[<B>]B" "[<B>]B"
B "[<B>]B" "[<i>]B"
B "[<B>]B" "[<u>]A"
B "[<i>]B" "[<B>]A"
B "[<i>]B" "[<B>]B"
B "[<i>]B" "[<i>]B"
B "[<i>]B" "[<u>]A"
B "[<u>]A" "[<B>]A"
B "[<u>]A" "[<B>]B"
B "[<u>]A" "[<i>]B"
B "[<u>]A" "[<u>]A"
</pre>
===6.39. Prospective Indices : Pointers to Future Work===
===6.39. Prospective Indices : Pointers to Future Work===
