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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.29. Projects of Representation===
===6.29. Projects of Representation===
<pre>
There are numerous modalities of description and representation that are involved in linking the extensions and intensions of terms and concepts. To facilitate the building of a suitable analytic and synthetic framework for this task, and to abbreviate future references to the categories of modalities that come into play, I will employ a set of technical notions, along with their aliases and acronyms, to be indicated next.
First of all, I want to call attention to a "mode of description" (MOD) or a "category of representation" (COR) that logically precedes all forms of "extensional representation" (ER) and "intensional representation" (IR). To do this, I introduce the notion of a "project of representation" (POR) and the mode or category of "pretensional representation" (PR) that contains the elements for attempting its actualization.
A "project of representation" (POR), in the interval before its completion or its viability can be assured with any measurable degree of certainty, initiates a mode of description called a "prospective representation" or a "pretended representation" (PR). Taken over time, the POR issues in a series of PR notices, a sequence of explicit expressions that constitute its "prospectus" or "pretension". If the POR turns out to be feasible, and if all goes well with its realization, then the promises tendered by these notes can be redeemed in full. Regarded from a retrospective vantage point, and ever contingent on the eventual success of the POR, what amounts to little more than a species of potentially attractive PR bulletins can be valued ultimately as a set of successive approximations to the intended concept and, further, to the objective reality intended. It is only at this point that a piece of PR achieves the virtues of an "actual representation" (AR), embodying in its purported description a modicum of "actually resolved tension" (ART), and becoming amenable to formalization as a non degenerate example of a sign relation. This tells how a POR develops in time under conditions ideal enough to achieve its aim. Next, I describe the features of PR as a form of existence sub specie aeternitatis.
Under the banner of PR parades an uncontrolled and wide ranging variety of pretended signs and prospective signs, entities with the alleged or apparent significance of signs, of likely stories that are potentially meaningful and useful as descriptions and representations, but the character of whose participation in a sign relation is yet to be judged and warranted. A certain quality of PR marks the brand of significance that a candidate sign possesses before it is known for certain whether it will be genuine or spurious in its role as a sign, the meagre benefit of the doubt that can be granted any reputed sign before its character as an authentic sign has been tested in the performance of its assigned functions.
The prospects and pretensions of PR are associated with a quality of tension that prevails on the scene of representation even before it is definite that objects have signs and signs have objects, an uncertain character that supervenes on the stage before one is sure that a "project of representation" (POR) will succeed in its intentions: far enough for its extension to stretch over many determinate instances, or well enough for its intension to hold forth any distinctive properties. This whole modality of allegation and aspiration, given the self described significance and uncertified self advertisement that signs in all their immature phases and developmental crises cannot help but affect, taken along with the valid ambitions of potential signs to become signs in fact, is a class of pretended and prospective meaning that it seems fitting to label as a category of "pretensional representation" (PR).
The assortment of PR mechanisms that goes into a run of the mill POR is a rather odd lot, drawing into its curious train every style of potential, preliminary, prospective, provisional, purported, putative, and otherwise "pretensional representation". The motley array of artifice and device that is permitted under this gangly heading seems ill suited to becoming recognized as a natural category, and perhaps it is destined to persist for all time pretty much as one presently finds it, too quixotic to regiment fully and too recalcitrant to organize under compact terms. For the purposes of the current project, the point of distinguishing the category of PR as a mode of description is twofold:
1. The category of PR is drawn up to encompass the categories of "extensional representation" (ER) and "intensional representation" (IR) and to allow the creation or recognition of a collection of continuities and correspondences between them.
2. The PR mode of description draws attention to several important facts about the more problematic phases of interpretation and inquiry processes, especially including the inchoate actions of their initial stages and the moments when global paradigm shifts are manifestly in progress. All that interpreters have to go on for much of the mean time that they spend involved in the sign formation processes of inquiry is a type of PR.
The purpose of these PR labels is to draw attention to the indirect character and the allusory nature of the interpretive processes that contribute to the initial stages and non routine phases of inquiry.
The point of pointing out the indirect character and the allusory nature of all PR is to draw attention to the circumstamce that intelligent agents of interpretation and inquiry have to be capable of waiting, trading, and acting on purported and potential representations. To proceed at all from the conditions prevailing at the outset of inquiry, they have to lead off from the slightest inklings that a problematic phenomenon may disclose an objective reality that is a key to its resolution, to take their initial direction from uncertain signs that an object of value might be in the offing, and to open the bidding on a brand of improper symbols whose very qualifications as representations are required by the nature of interpretive inquiry to remain in question for much of the mean time taken up by the pursuit of the alleged objects. It is part of task that PR is all these agents have to go on, ...
Extensional descriptions of n place relations are the kinds that can be presented in relational data tables, or at least initiated and partially illustrated in this form. If an n place relation is constituted as a "finite information construction" (FIC), where the relation as a whole plus each of its elements is specified in "finite and discrete" (FAD) terms, then the prospective tabulation can be carried out to completion, at least in principle, explicitly enumerating the "elementary relations" or the n tuples of relational domain elements that enter into the relation.
Extensional descriptions are so close to what one casually and commonly regards as "immediate experience" that the knowledge of a relation one gains by means of their indications is often not thought to lie in the medium of description at all. The acquaintance with the character of an objective relation that extensional descriptions so successfully manage to record and convey is a type of impression that one often fails to reflect on as arriving through signs at all, and thus it can leave an impression of knowing its object that is susceptible to being confounded with a direct experience of the relation itself.
This does not have to be a bad thing in practice. Indeed, it is a factor contributing to the success of extensional descriptions that an agent can usually afford to remain oblivious to the more indirect aspects of their interpretation, to proceed with impunity to take them at face value, and unless there is some obvious trouble to work on the assumption that they are in fact nothing more than what they seem to denote. Thus, one often finds extensional presentations treated as though they arose from radically empirical sources of data, instituting fundamentally pure modes of "knowledge by acquaintance" and reputed to lie in meaningful contradistinction to every other type of representation, the rest falling into categories that grade them as mere "knowledge by description". However, when it comes to the ends of deliberate design and analysis, the usual assumptions can no longer be relied on to justify their own usage, and they need to make themselves available for examination whenever the limits of their usefulness are called into question.
One of the purposes of introducing an explicit theory of sign relations into the present study of inquiry is to examine the status of this idea, namely, that it makes sense to posit an absolute distinction between knowledge by acquaintance and knowledge by description. Pragmatic thinking begins with a certain amount of skepticism toward this notion, on account of the many illusions that appear to trace their origins to it, but overall it seeks to arrive at a language in which to examine the question thoroughly, and to devise a means for individual interpreters to make a clear choice for themselves, with respect to the possibly of their purposes being divergent in the mean time, one way or the other.
Whatever the outcome of these individual decisions, independent in principle no matter how they turn out in practice, and without forcing the preliminary acknowledgement of any unavoidable gulf or unbridgable abyss that might be imagined to separate the modalities of acquaintance and description, one nevertheless wants to preserve the practical uses of the comparative, interpretive, relative, and otherwise sufficiently qualified and circumspect orderings of data and descriptions along these lines that can be organized by individual interpreters and communities of interpretation. It is for these reasons that I have taken the trouble to conduct this discussion in a way that diverts some attention toward its own casual context, and I hope that this strategy is able to reflect, or at least scatter, enough light back on the enfolding context of informal sign relations that it can dispell any inkling of an automatic distinction of this form, or at least to cast doubts on the remaining traces of its illusion.
For the rest of this section I restrict the discussion to sign relations of the type R c OxSxI and elementary sign relations of the form <o, s, i>.
A "discussion of concrete examples" (DOCE), intended to serve as a preparatory treatment for approaching a significantly more complex area, is necessarily limited in its focus to isolated cases, in effect, to those that remain simple enough to be instructive in a preliminary approach to the topic. This means that the observable properties of the initial examples, with respect to the class they are aimed to exemplify, will sort themselves into two kinds: (1) their essential, generic, or genuine properties, and (2) their accidental, factitious, or spurious properties.
But the present discussion of sign relations cannot illustrate the properties of even these elementary examples in an adequate way without considering extended multitudes of other relations, both those that share the same properties and those that do not. Consequently, by way of getting the comparative study of sign relations started on a casual basis, an end that is served in addition by placing sign relations within the broader setting of n place relations, I will exploit a few devices of taxonomic nomenclature, intending them to be applied for the moment in a purely informal way.
An "order", "genus", or "species" of relations is a class or set of relations that obey a particular collection of axioms, or that satisfy a certain combination of operational constraints and axiomatic properties. These respective terms, given in order of increasing specificity, are not intended to be applied too systematically, but only roughly to indicate how many axioms are listed in the specification of a class of relations and thus how narrowly the indicated class is pinned down relative to other classes within the context of a particular discussion.
For example, this terminology allows me to indicate a "general order" G of sign relations R, each of whose connotative components RSI is an equivalence relation, and then it allows me to extend this investigation by pursuing the prospective existence of a "generalized order" G' of sign relations R, each of which has many properties analogous to the sign relations in G, with the exception or extension that G' is more broadly formulated in certain designated respects.
The purpose of these informal taxonomic distinctions is not to specify absolute levels of generality, something that could not be achieved in a global manner without splitting hierarchies of hereditary properties and the whole host of their successive heirs down to the ultimate pedigrees, but merely to organize properties relative to each other in comparative terms, in which case three levels of generality are usually enough to orient oneself locally in any ontology, no matter how wide or deep. Thus, the main interest that the terms "order", "genus", and "species" will subserve in this connection is to indicate the taxonomic directions of generalization and specialization that a particular investigation is trying to achieve among classes of relations: "generalizing" a class by abstracting features or removing constraints from its original definition, and "specializing" a class by concretizing features or adding constraints to its initial characterization.
In order to talk and think about any sign relation at all, not to mention addressing the topic of a "generic order" (GO) of sign relations, one has to use signs to do it, and this requires one's taking part in what can be called a "higher order" (HO) of sign relations. By way of definition, a sign relation is a HO sign relation if some of its signs refer to objects that are themselves sign relations or classes of sign relations.
So long as one expects to deal with only a few sign relations at a time, managing to use only a few conventional names to denote each of them, then one's concomitant participation in a HO sign relation hardly ever becomes too problematic, and it rarely needs to be formalized in order for one to cope with the duties of serving as its unofficial interpreter. Once a reflective involvement with HO sign relations gets started, however, there will be difficulties that continue to lurk and grow just beneath the apparently conversant surface of their all too facile fluency.
By way of example, a singular sign that denotes an entire sign relation refers by extension to a class of elementary sign relations, or a set of "transaction triples" <o, s, i>. So far, this is still not too much of a problem. But when one begins to develop large numbers of conventional symbols and complicated formulas for referring to the same classes of sign transactions, then considerations of effective and efficient interpretation will demand that these symbols and formulas be organized into semantic equivalence classes with recognizable characters. That is, one is forced to find computable types of similarity relations defined on pairs of symbols and formulas that tell whether they refer to the same class of sign transactions or not. It is almost inevitable in such a situation that canonical representatives of these equivalence classes will have to be developed, and a means for transforming arbitrarily complex and obscure expressions into optimally simple and clear equivalents will also become necessary.
At this stage one is brought face to face with the task of implementing a full fledged interpreter for a particular HO sign relation, summarized as follows:
1. The objects of Q are the abstract classes of transactions that constitute the sign relations in question.
2. The signs of Q are the collection of symbols and formulas used as conventional names and analytic expressions for the sign relations in question.
3. The interpretants of Q ...
But a generic name intended to reference a whole class of sign relations is another matter altogether, especially when it comes into play in a comparative study of many different orders of relations.
</pre>
===6.30. Connected, Integrated, Reflective Symbols===
===6.30. Connected, Integrated, Reflective Symbols===