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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.47. Mutually Intelligible Codes===
===6.47. Mutually Intelligible Codes===
<pre>
Before this complex of relationships can be formalized in much detail, I must introduce linguistic devices for generating "higher order signs", used to indicate other signs, and "situated signs", indexed by the names of their users, their contexts of use, and other types of information incidental to their usage in general. This leads to the consideration of SOI's that maintain recursive mechanisms for naming everything within their purview. This "nominal generosity" gives them a new order of generative capacity, producing a sufficient number of distinctive signs to name all the objects and then name the names that are needed in a given discussion.
Symbolic systems for quoting inscriptions and ascribing quotations are associated in metamathematics with "godel numberings" of formal objects, enumerative functions that provide systematic but ostensibly arbitrary reference numbers for the signs and expressions in a formal language. Assuming these signs and expressions denote anything at all, their formal enumerations become the "codes" of formal objects, just as programs taken literally are code names for certain mathematical objects known as computable functions. Partial forms of specification not withstanding, these codes are the only complete modes of representation that formal objects can have in the medium of mechanical activity.
In the dialogue of A and B there happens to be an exact coincidence between signs and states. That is, the states of the interpretive systems A and B are not distinguished from the signs in S that are imagined to be mediating, moment by moment, the attentions of the interpretive agents A and B toward their respective objects in O. So the question arises: Is this identity bound to be a general property of all useful sign relations, or is it only a degenerate feature occurring by chance or unconscious design in the immediate example?
To move toward a resolution of this question I reason as follows. In one direction, it seems obvious that a "sign in use" (SIU) by a particular interpreter constitutes a component of that agent's state. In other words, the very notion of an identifiable SIU refers to numerous instances of a particular interpreter's state that share in the abstract property of being such instances, whether or not anyone can give a more concise or illuminating characterization of the concept under which these momentary states are gathered. Conversely, it is at least conceivable that the whole state of a system, constituting its transitory response to the entirety of its environment, history, and goals, can be interpreted as a sign of something to someone. In sum, there remains an outside chance of signs and states being precisely the same things, since nothing precludes the existence of an IF that could make it so.
Still, if the question about the distinction or coincidence between signs and states is restricted to the domains where existential realizations are conceivable, no matter whether in biological or computational media, then the prerequisites of the task become more severe, due to the narrower scope of materials that are admitted to answer them. In focussing on this arena the problem is threefold:
1. The crucial point is not just whether it is possible to imagine an ideal SOI, an external perspective or an independent POV, for which all states are signs, but whether this is so for the prospective SOI of the very agent that passes through these states.
2. To what extent can the transient states and persistent conduct of each agent in a community of interpretation take on a moderately public and objective aspect in relation to the other participants?
3. How far in this respect, in the common regard for this species of outward demeanor, can each agent's behavior act as a sign of genuine objects in the eyes of other interpreters?
The special task of a nuanced hermeneutic approach to computational interpretation is to realize the relativity of all formal codes to their formal coders, and to seek ways of facilitating mutual intelligibility among interpreters whose internal codes can be thoroughly private, synchronistically keyed to external events, and even a bit idiosyncratic.
Ultimately, working through this maze of "meta" questions, as posed on the tentative grounds of the present project, leads to a question about the "logical reference frames" or "metamathematical coordinate systems" that are supposed to distinguish "objective" from "symbolic" entities and are imagined to discriminate a range of gradations along their lines. The question is: Whether any gague of objectivity or scale of virtuality has invariant properties discoverable by all independent interpreters, or whether all is vanity and inane relativism, and everything concerning a subjective point of view is sheer caprice?
Thus, the problem of mutual intelligibility turns on the question of "common significance": How can there be signs that are truly public, when the most natural signs that distinct agents can know, their own internal states, have no guarantee and very little likelihood of being related in systematically fathomable ways? As a partial answer to this, I am willing to contemplate certain forms of pre established harmony, like the common evolution of a biological species or the shared culture of an interpretive community, but my experience has been that harmony, once established, quickly corrupts unless active means are available to maintain it. So there still remains the task of identifying these means. With or without the benefit of a prior consensus, or the assumption of an initial, but possibly fragile equilibrium, an explanation of robust harmony must detail the modes of maintaining communication that enable coordinated action to persist in the meanest of times.
The formal character of these questions, in the potential complexities that can be forced on contemplation in the pursuit of their answers, is independent of the species of interpreters that are chosen for the termini of comparison, whether person to person, person to computer, or computer to computer. As always, the truth of this kind of thesis is formal, all too formal. What it brings is a new refrain of an old motif: Are there meaningful, if necessarily formal series of analogies that can be strung from the patterns of whizzing electrons and humming protons, whose controlled modes of collective excitation form and inform the conducts of computers, all the way to the rather different patterns of wizened electrons and humbled protons, whose deliberate energies of communal striving substantiate the forms of life known to be intelligible?
A full consideration of the geometries available for the spaces in which these levels of reflective abstraction are commonly imagined to reside leads to the conclusion that familiar distinctions of "top down" versus "bottom up" are being taken for granted in an arena that has not even been established to be orientable. Thus, it needs to be recognized that the distinction between objects and signs is relative to a definite SOI. The pragmatic theory of signs is designed, in part, precisely to deal with the circumstance that thoroughly objective states of systems can be signs of each other, undermining any pretended distinction between objects and signs that one might propose to draw on essential grounds.
From now on, I will reuse the ancient term "gnomon" in a technical sense to refer to the godel numbers or code names of formal objects. In other words, a gnomon is a godel numbering or enumeration function that maps a domain of objects into a domain of signs, Gno : O > S. When the syntactic domain S is contained within the object domain O, then the part of the gnomon that maps S into S, providing names for signs and expressions, is usually regarded as a "quoting function".
In the pluralistic contexts that go with pragmatic theories of signs, it is no longer entirely appropriate to refer to "the" gnomon of any object. At any moment of discussion, I can only have so and so's gnomon or code word for each thing under the sun. Thus, apparent references to a uniquely determined gnomon only make sense if taken as enthymemic invocations of the ordinary context and of all that is comprehended to be implied in it, promising to convert tacit common sense into definite articulations of what is understood. Actually achieving this requires each elliptic reference to the gnomon to be explicitly grounded in the context of informal discussion, interpreted with respect to the conventional basis of understanding assumed in it, and relayed to the indexing function taken for granted by all parties to it.
In computational terms, this brand of pluralism means that neither the gnomon nor the quoting function that forms a part of it can be viewed as well defined unless it is indexed, explicity or implicitly, by the name of a particular interpreter. I will use the notations "Gnoi(x)" = "<x, i>" to indicate the gnomon of the object x with respect to the interpreter i. The value Gnoi(x) = <x, i> C S is the "nominal sign in use" or the "name in use" (NIU) of the object x with respect to the interpreter i, and thus it constitutes a component of i's state.
In the special case where x is a sign or expression in the syntactic domain, then Gnoi(x) = <x, i> is tantamount to the quotation of x by and for the use of the ith interpreter, in short, the nominal sign to i that makes x an object for i. For signs and expressions, it is usually only the quoting function that makes them objects. But nothing is an object in any sense for an interpreter unless it is an object of a sign relation for that interpreter. Therefore, ...
If it is now asked what measure of invariant understanding can be enjoyed by diverse parties of interpretive agents, then the discussion has come upon an issue with a familiar echo in mathematical analysis. The organization of many local coordinate frames into systems capable of supporting communicative references to relatively "objective" objects is usually handled by means of the concept of a "manifold". Therefore, the analogous task that is suggested for this project is to arrive at a workable definition of "sign relational manifolds".
The discrete nature of the A and B dialogue renders moot the larger share of issues of interest in continuous and differentiable manifolds. However, it is still possible to get things moving in this direction by looking at simple structural analogies that connect the pragmatic theory of sign relations with the basic notions of analysis on manifolds.
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===6.48. Discourse Analysis : Ways and Means===
===6.48. Discourse Analysis : Ways and Means===