Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7

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• Contents • Part 1 • Part 2 • Part 3 • Part 4 • Part 5 • Part 6 • Part 7 • Appendices • References • Document History •

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7.

7.1. Divertimento : Eternity in Love with the Creatures of Time

Once again, the discussion has reached a point where so many topics interact, outlining a core where multiple threads converge and diverge and recur again, suggesting a pattern and then fading again, projecting so energetic a mass of confusion that it casts up a shattered image of its own shape, scattered half in light and half in shadow back into the veils of its own convolutions, and eventually unfolding so complicated a tangle that a finitely informed creature like myself is forced to make a selection, to take a chance on any feasible way to fuse the manifold of senseless impressions, and finally to pick out amid the maze of clues a single filament that promises to provide a reasonable way to proceed.

Once again, there arise from the depths of this chaos a few spare forms of mutual ascent, appearing to garner demand all around and to plow it back into the present scene, gradually drawing out emerging aspirations toward an organizing conception and investing the resulting resolutions with the full faith and credit of a manifest destination. But what do these ascendant archetypes really have in their compact to accomplish? While not still mutely ascending to the stylistic fiction of a clean slate, nor quite utterly razing the resurgent need for a symbolic scheme, they do portend a chart that is bold enough in its guiding lines to yield a steady compass for the present direction, while yet they envision a blueprint that remains open enough in its enclosing forms to ready the opportunities of future experience in unforeseen developments of the living subject matter.

In the remainder of the current phase of discussion, concentrating on concrete examples of sign relations, I will continue to glean as much information as possible from the initial examples A and B, gradually bringing a set of considerations that approaches the full power of the pragmatic theory of signs to bear on their case. Of course, the aim of this presentation is directed more to illustrating the analytic capacities and the empirical implications that accompany the use of sign relations, especially as it works out in service to the practical goals of inquiry, than it is attached to any special properties of the examples themselves.

7.1.1. Reflections on the Presentation of Examples

In order to move this discussion forward in the direction of the goals I have for it, I am forced to reflect on its present character and its current state of development, in the light of the aims I have for it. In this light I hope to see to it that the main thrust of the current discussion is aimed toward a "presentation of exemplary models" (POEM), but a critical stance on its means of production entitles the view that it meanwhile remains only a "presentation of selected examples" (POSE). In this subsection, starting from the artificial contrast created between these two forms of construction, the ideal POEM and the typical POSE, I will discuss the differences to be expected between ideal and typical embodiments of abstract intentional concepts, for instance, the programs that implement specified procedures and simulate phenomenal processes.

Because a "willing suspension of disbelief" is not to be asked of readers in a non fiction genre of investigation and ratiocination, I detect an obligation falling on my part at this point to allay a brand of suspicion that may be arising on theirs. I am not insensitive to the circumstance that my constant insinuation of mnemonic acronyms throughout this text is liable to create a running subtext with an often punning sense, and makes it susceptible to riddling forms of interpretation, but this subtext is faithfully intended to support, not subvert, the main purpose of the plain text that covers it. Since the ultimate concern of both accounts is how well they combine to cover an objective topic of interest, it hardly matters which text covers which in the meantime. Ultimately, the only criterion of interest is their common service to single domain of inquiry. Incidentally, even the clang associations can be conducive to alertness, if now and then painfully so.

The best name I can find for a subtext of this kind, having all the characteristics of abbreviated recapitulation, acronymic aphorism, and gnomonic epitome, is to call it a "recipe", thereby putting it in a class with poems, proofs, programs, protocols, prescriptions, and other types of procedural repertories, paradigmatic rubrics, and prevailing refrains that get their most prominent repetends set down in the form of a text. Generally speaking, it is usually best to let the underlying points of the acronymic subtext pass by without extensive notice, and to let their abbreviations recapitulate what they will in passing without remarking or expanding on them any more fully than expressly needed. However, the issue at stake at the present juncture is important enough that I will try to take the pains required to render it more explicit, even if the desired clarity must be purchased at the risk of becoming tedious.

Poems, proofs, and programs of procedures, whether by provision of etymology or by virtue of tried and true principles revealed in their practice, all share a common form of "apheuristic definition", to wit:

“Just the words that do”

This means that the creation of each form of text is carried out in terms of primitive symbolic elements and requires for the height of its art the selection of exactly those that are fit to do the job intended for them.

Now it probably appears that the present discussion, to the degree I am responsible for conducting it, is designed to deliberately violate this maxim in every conceivable way. But its apparent sins against the rule can be mitigated if one considers its true intention, whether there is the space to avow it or whether it resorts to a tacit understanding. The aim for the present moment is not directly, not just yet, to write a program for inquiry, but only to examine the feasibility of doing so, and perhaps to prepare the grounds for its eventual possibility.

This indirect tactic and extenuating purpose of the current discussion explains why its prevailing drift seems to proceed in a direction that opposes all the senses of the poetic rule and the programmatic maxim. Working under typical conditions, even the tersest exegesis of a recipe, in order to develop and explain the hidden implications of its previously compressed formulations, needs room to unpack and elaborate its terms. Ordinarily, the text that is fit to serve as a recipe is not the same as the text that is fit to explain a recipe. In short, there is usually a wide line to be observed between the terms that are found suitable to supply a recipe and those that are called for to supplement a recipe.

Finally, a word to the wise: These formulations of the typical case have been expressed in carefully guarded clauses for a good reason. When it comes to ideal conditions, with suitably intelligent or well designed IF's, then one cannot exclude the possibility of ideal cases cropping up in the relationship between recipes and what they recapitulate. If enough information is prestored in the "cognitive yolk" of an intelligent IF, then there is a good chance of finding the occasional idee fixe (IF), that is, a fixed point under the contraction and expansion mappings that serve at first to create a recipe and then to re express it, respectively.

Though its referential ellipses and circles can obsess and even oppress, the form of contingency represented by an IF is not essentially vicious in and of itself. Given the right opportunities, an IF can work out its consequences for itself in beneficial ways. Though brevity is the soul of wit, abbreviation can make hash out of codes that only an intelligent or just plain lucky style of non deterministic interpretation can restore to their senses. Though words collide, they have no effect on the world outside until an interpreter acts, freely choosing whether to compound or to dispell the always inherent potential for confusion. Finally again, waking to the final truth that I can find in the matter, none of these possibilities need unduly disturb the composure of any interpreter who is accustomed to the idea that a medium can also be a message, or that the blank slate may indeed be the innate idea.

Since it is obvious that a "finitely informed creature" (FIC) will seldom achieve anything approaching perfect success on the first, or second, or third, or … any one of many successive tries, the deceptively innocuous nuance that separates an "exemplary model" from a "mere example" finds itself settling in a place that is very near the heart of the issue here. There it precipitates a cloud of doubt that can grow to overshadow all hope of grasping the necessary connection between a POEM and a POSE. Accordingly, it becomes incumbent on this inquiry to ask: What is it about the connotation of the word "exemplary" that speaks with so much more authority, conviction, and emphasis than the denotation of the randomly chosen "example" is capable of indicating?

In order to tell which is which, and which applies to the present case, I need to make it my object to examine the process of "exemplification", the initial phase that carries out and achieves the selection of a model. Indeed, careful attention to this phase is needed to tell if there exists, in the first place, any difference of import between a POEM and a POSE, as the thing will find itself deemed in a retrospective judgment, and whether there is anything that exists from the beginning that can go toward making the POEM turn out in a substantially distinctive style, one that is even the least bit more remarkable than just another POSE, somewhat peculiar and somewhat typical, among the many possible.

Reviving the form of annotation that I introduced in the initial analysis of inquiry, the constitution of the current discussion, d0 = disc0, as a "presentation of examples" (POE) can be analyzed as an application of an active instrumental component, a process of "presentation", p = pres, to a passive objective component, a process of "exemplification", e = exam. Thus, it can be written as: disc0 >= {exam}{pres}, or d0 >= {e}{p}.

Parceling out the various responsibilities of the current discussion from a logical point of view, the exemplification process appears to be a necessary preliminary to the presentation process. This order of logical precedence can be maintained in spite of how interwoven the two phases may be from dialectical and dynamic perspectives.

As I currently parse the matter, the exemplification process is logically a necessary preliminary to the presentation process. This order of precedence can be regarded as being true, from a logical point of view, whatever the order of procedure in actual point of fact.

This order of precedence can be regarded as being true, from a logical point of view, whether or not in point of actual fact the phase of finding a model must be finished completely before the submission of the chosen model to presentation can begin, or whether it is practically always necessary to interleave exemplification with the development of its own presentation.

As a text that is put forth in a conceit filled attempt to illuminate a conceptual subject matter, having aims that by deliberate design must always reach beyond the fading grasp of its "finite and discrete" (FAD) significance, the question remains for any POEM, no matter how humble its implicit focus or its explicit orbit, whether the relations among its intrinsic elements will conceivably approach proportions in the common regard that are "epic" in relation to the scope of its intended topic. Of course, this question becomes all the more poignant in relation to topics so exalted as intelligence and inquiry, where "elliptic" and "parabolic" figures of speech are just "hyperbolic" ways of eulogizing the necessary failures of approach.

Now that this form of discussion has gotten under way, it is possible to turn a portion of its acquired momentum toward the task of sharpening its initial portrayal, exploiting for this purpose the technical concepts that are exemplified clearly enough in the presentation up to this point. Drawing on the parallel concepts from the pragmatic theory of signs, it makes sense to classify the "presentation" and "example" components of this discussion in line with the "syntactic" and "objective" domains, respectively, of a sign relation. In this way, it becomes possible to acknowledge the following correspondences:

1. The presentation component constitutes an active involvement in the realm of signs and ideas that, collectively and severally, are being invoked to carry the current discussion.
2. The example component constitutes a passive representation of the open subject matter or the patent object of discussion, selecting for presentation a simple enough sample to begin addressing the intended domain of objects, but providing that these examples are understood as essaying nothing more than a preliminary sample, a sketchy lot, or a paradigm few that have been drawn out of the many objects conceivable within the full scope of the intended topic of discussion.

Before this presentation of examples can continue in a useful way I need to stop and think for a moment, to reflect on the broader purposes that concrete examples of sign relations are meant to fulfill as a part of the overall inquiry into inquiry. If examples are presented and perceived in a purely isolated fashion, then nothing of general utility can be learned from them. Even the most "finite and discrete" (FAD) example, properly conceived, is able to enjoy various forms of continuity with the extended collections of its ilk that fall under the same general concepts.

And yet FAD examples are liable to particular kinds of misunderstanding, precisely because their descriptions in terms of general concepts can be individualized to the point of becoming idiosyncratic. As remarkably well defined entities FAD examples have so many properties that not all of them are likely to be relevant to any given topic, focus, or current of discussion. The problem of identifying the appropriate dimensions of inclusion for a FAD example, placing it under the right general concepts and staking out the right dimensions of variation passing around and through its vicinity, is a task called "searching for parameters".

7.1.2. Searching for Parameters

A genuine search for parameters does not initially present itself as a straightforward search, in other words, as a simple matter of searching (1) a known space of objects for (2) the unknown set of objects that fit (3) a known description according to (4) a known measure of suitability. While it persists as a genuine problem, it does not appear in the form of one that can be solved in a simple and direct fashion by systematically traversing the points of a known space, a space already described by identified parameters and generated along established dimensions of variation, until a point passing the given tests is found.

A genuine search for parameters initially presents itself to be more like a matter of searching for an unknown space in which to place a known set of objects in a suitable but otherwise vaguely determinate manner. Thus, the criterion of suitability has to be developed along with the spaces tried. In general, the number of conceivable spaces, given all the qualitative dimensions of quantitative variation that can be imagined, seems to make this such a vastly different order of search that it no longer seems feasible to think it can ever be rendered systematic. However, there are selected situations in which objects and spaces can be treated on a par with each other and placed upon an inclusive basis, so it is useful next to specialize this discussion and consider the formal conditions under which these inclusions are possible.

If the discussion is ruled by an OF in which search spaces themselves are able to become focal objects of discussion and thought (DAT), and if there is an ample enough variety of search spaces that constitute the corresponding topic of DAT to make this whole construction worthwhile, and if there is at bottom the same FAD space of generators that is found responsible for constructing every search space as an object of DAT, ...

It is not really the asymmetric identification of some things as objects (of spaces) and other things as spaces (of objects) that constitutes the nature of the problem.

One of the most deceptive things about any genuine problem is the fact that after the problem is solved it can always be described in several alternative ways, some of which recast the matter in a form that makes it look like no problem at all, that is, like there never was a problem. A study of problem solving that views every problem from its terminal end (the telos end of the scope) is bound to falsify the nature of the whole subject. To arrive at a truer description of problems it is necessary to find ways of accurately characterizing the problematic state that exists at the outset of the problem.

The sign relations A and B were deliberately chosen to be as simple as possible without falling into complete triviality, and they clearly lack development in many properties that would be expected of sign relations involved in inquiry processes. One way to deal with a defective example is simply to put it aside and pick up another, but this can be wasteful and ultimately exhausting. Besides, there are probably lessons to be learned from the growing accumulation of examples that can better guide the selection of successive trials. Before I can grasp the relation of these paltry examples to the exalted concepts they are meant to suggest, it will be necessary to spend a considerable amount of time reflecting on the purpose in general that a presentation of examples is meant to serve in any inquiry and, if possible, developing general tools and heuristic rules for getting the most instruction out of each incidental case.

Before I can develop better examples of sign relations, conceivably approaching the orders of sign processes that constitute significant parts of inquiry, I will need to spend a long time considering the conceivable dimensions of variation that are relevant to this search. But look at the problem I am faced with here. Searching for examples is itself a special type of inquiry process. Presentation of examples is itself a special type of sign process, directed toward the representation and communication of abstract ideas by means of the selection of objects that are indicated to fall under these ideas. But my immediate interest in locating apt examples and presenting them in a lucid manner is only a small part of a larger concern, which cannot be allowed to depend solely on the elements of personal luck and skill that I may or may not bring to bear in this process.

In the large scale project that subsumes this discussion of examples, I am trying to develop programs that can support the conduct of inquiry, hoping to bridge the barriers of odium and tedium that affect the current scene and interfere with the practical job of inquiry (JOI). Obviously, this effort on my part takes off from whatever skill in inquiry I can personally muster and bring to bear in the task, but its potential for success is no longer, not once I realize it has already begun and perhaps always been beginning this way, solely a matter of what kind of luck any individual might have in the quest.

In order to write a program for any significant component of inquiry, it becomes necessary to render one's personal engagement in inquiry much more reflective and deliberate and much less determined by sheer luck. Finding good examples of inquiry processes is not just a matter of searching known spaces of sign relations for more significant examples of established concepts, but more a question of finding meaningful spaces in which to place the collections of examples already found.

One is never at a loss for ways to generate an all too generous bounty of concrete examples, but a random "hunt and pick" (HAP) approach that hazards a trip through all the spaces of cases that can be generated on set theoretic grounds alone is not a happy choice in the present case. At any stage in the search for examples, one needs to derive a sense of direction by looking at the samples of examples that are found in view. Further, one needs to develop a means of locomotion that will permit the search for a sample space to roam about in ample enough rooms to have a hope of success, but a medium also that trains itself to gradually limit its lines of inquiry to explore the most fruitful and likely directions.

For all these reasons, I plan to establish at this point in the discussion a separate, parallel, and reflective (SPAR) track for standing apart and looking back on whatever mainstay of inquiry is currently in the fore. Obviously, there are dangers as well to aimless reflection, perhaps even more debilitating than the simple frustrations of uncontrolled search, as anyone will appreciate who has lost a measure of time in the funhouses of philosophic speculation. Consequently, to prevent this discussion from devolving ad nauseum into navel contemplation exercises, I will limit the extent of its reflective tack to a single additional track.

One of the tasks assigned to this reflective track is to throw a more critical light on the operating notions and working assumptions that I have been using more or less implicitly in the discussion so far. Engaging in critical reflection of this sort eventually brings up the "question of foundations" (QOF), an attempt to make an explicit review of the sets of ideas that are fundamental in practice to whole domains of thinking about experience, whether it concerns the bases of an external body of knowledge or the springs of one's ongoing stream of thought. Since it is not so much a question of whether there are sets of ideas that get called "foundations" as a question of how these ideas are used, I will distinguish between "static" foundations, those that are used in such a way that they cannot be questioned, and "mobile" foundations, those that can be identified, examined, criticized, and changed when necessary.

To maintain a focus on the kinds of questions that are relevant to concrete examples of sign relations, the spectrum of issues arrayed over the next few subsections is designed to be subsumable under a single integral theme, with each of its leading terms pointing to a series of simple questions about the relationship of "generality" to "partiality".

To introduce this theme, "the relation of generality to partiality", I will first tease out a series of tensions that inhere beneath its intentionally disarming semblance of unity, and then I plan to unravel how this array of hidden dimensions not only makes room for novel features in formerly formal grammars but also helps to set the stage for concrete contents that can fill out the abstract patterns of purely formal languages, in a fashion, dressing up their bare and immodest forms with the logical modalities of tense, intension, intention.

In the process of elaborating this unifying theme, I will also begin directing attention toward a set of issues that interweave with its topic. These questions concern the design characteristics of a software system that is intended to assist the study of n place relations in general and sign relations in particular.

7.1.3. Defect Analysis

The various threads of discussion taken up here can be sorted out as follows. Considered with respect to the larger scale of involvement and the longer term of investigation, I continue to be engaged in analyzing the task of inquiry from a pragmatic point of view. Pursuant to this broader purpose, I am more immediately concerned with illustrating the process of interpretation by detailing the structures of sign relations, in particular the examples A and B. It is clear that both of these aims are only partly satisfied at this point, and this leads me to contemplate what remains to be done. In terms of analytic procedure, this is a case of "analyzing the remainder", or of detailing the defects of the present state of knowledge with regard to the intended state of understanding.

Defect 1. There is no reason to think that even the possibility of an integral relationship between inquiry and interpretation is thoroughly understood at this point.

Defect 2. The bare fragments of sign relational structure and the pale shadows of their objective and interpretive potentials presented so far suggest no more than a glimmer of how a static sign relation can give rise to an actual dynamic process, much less generate and regulate a motivated process like inquiry.

Therefore, in continuing to analyze the task of inquiry as it presents itself in practical terms, and in continuing to illustrate the process of interpretation by means of concrete sign relations, more attention needs to be directed to the relationship between these two components.

In order to learn the most that is possible from examples that are deliberately chosen to approach the least amount of complexity and the fewest properties of interest, I will need a way of reflecting on their evident deficiencies in a constructively critical fashion. Inaugurating this method of reflection requires me to draw on the available clarity, the ambient light and the tenuous knowledge that makes apparent what little I can already discern, however dimly in the offing, both about the general phenomenon of interpretation under review and also about the ideal process of inquiry at stake.

As I attempt to treat the objective defects of these examples and the rhetorical defects of their presentation, it brings me to a general reflection on the role that examples are meant to serve, not just in presenting an exposition but in the very process of discovery itself. What develops in the sequel is that a suitable form of reflection on impoverished examples can serve a double purpose. Persistent operation as a reflective investigator demands that I, more or less intermittently, keep awake to the opportunities and the duties that lie on both sides of this task, and to realize that a dual pair of procedural descriptions can often be realized in one and the same process.

These reflections on the double duties of discursive processes have an immediate bearing on the conduct of the critiques to be taken up here. Namely, a discussion that presents my analysis of defects in my current choice of examples is also a discussion that exemplifies my choice of methods for analyzing my current presentation. Depending on how the abstract form of this procedure manages to get itself interpreted in concrete actions, the presentation of analytic results can appear to be interlaced with specific illustrations of a particular method of analysis. This general method, called "defect analysis" (DA), is designed to extract a maximal amount of information from deficient examples, and it has close affinities with the types of differential analysis that are used to form iterative series of approximations to mathematical objects and functions.

One way to derive the maximum benefit of instruction from even the sparest examples and roughest approximations that are essayed toward a general concept is to thoroughly analyze the deficiencies of each attempt in relation to a prospectively ideal illustration of the intended idea. Because of its analogy to iterative methods of approximation, this mode of analyzing declinations from a target idea or intended object can be regarded as a logical form of differential analysis. Even without an exact idea of the general concept being addressed, and long before the notion of distance between ideas, rough or refined, can be made precise, it is nevertheless possible to use one's casual intuitions about a concept and one's sense of direction toward the final idea to search out ways of improving each trial or draft of the paradigm.

7.1.4. The Pragmatic Critique

The general idea behind this form of differential approach is extremely important to the pragmatic theory of inquiry, which cannot avail itself of any infallible foundations or absolute certainties at the outset of inquiry, but must say how it is possible to begin inquiry as it always does begin, forever starting out in the middle of the action from a mixed condition of partial ignorance and partial knowledge, with a small number of active doubts and a greater multitude of contingent beliefs, and yet still arrive at improvements in the understanding of phenomena.

The basic problem for a pragmatic theory of inquiry can be expressed as follows. The critical judgments to be made at the end of inquiry, though they rely in an incidental sense on the context of unexamined judgments that are always present at the beginning of inquiry, must acquire a degree of certainty that becomes independent in a logical sense from the purely apparent securities of their tentative origin. Otherwise, the claim of inquiry to lead from ignorance to knowledge merely begs the question, redundantly iterating those sheer opinions that already prevailed at the outset, that clothed the undertaking in a series of arguments but were never fairly examined in the investigation.

Regarded in the light of this pragmatic critique, a candidate theory about the development of knowledge needs to identify a realistic model for the conduct of inquiry, the kind of guiding paradigm that can serve in actual practice to direct a genuine search for knowledge, not merely a scheme for summarizing the results after the quest is over and done. This has serious import for the image of inquiry that one really uses. It means that the kind of foundational approach commonly portrayed in axiomatic developments of deductive theories does not provide a viable or accurate picture of the discovery process that prevails in science, not even so often one might think within the realm of mathematics itself, but typically amounts to a put up job, a post hoc reconstruction and a rationalized exposition of the end result only.

On due reflection, it appears that the proper placement of the deductive phase within inquiry and the actual function of the explicative work it means to embody does not rest with the initial motivation of inquiry but fills a need for the intermediate staging and testing of tentative results. This permits axiomatic presentations and deductive developments to find a useful role for themselves within the actual progress of inquiry, sandwiched between the original creation of experimental ideas and the eventual probation of hypothetical concepts.

Another way to express the heart of this problem is in terms of the admittedly rather tenuous distinction between formal and casual contexts of discussion. One is being asked to justify how it is possible for an honest inquirer to draw on the natural human resources of prior belief, tacit knowledge, and casual intuitions without having the whole ensuing progress of inquiry be undermined by this personal way of starting out. This threat to the validity of inquiry can be averted only if one of the feasible ends of subsequent inquiry is to question the self evidence and the practical utility of the prior dispensations referred to as axioms.

If one desires to say that the putative knowledge is merely "potential", hidden, or implicit at the beginning of inquiry and becomes "kinetic", actual, or articulate via its pursuit, then this can probably be accepted as a valid manner of speaking, since it does not disparage the character of the effort that is required to manifest effective knowledge by means of authentic inquiry. But the pragmatic critique puts one on guard for the circumstance that the progress of inquiry is often less like falling off a log and rolling down a hill than it is like hollowing out a canoe and striking out upstream. Its headway is often achieved against the formidable gradients of resistance that are already established in the informal contexts of thought and discussion, put up not only by natural obstructions in the objective environment but also by habitual flows of learned associations parading as reasoning in the interpretive setting. It is only fair that every pretense of tacit and prior knowledge must bear the burden of proof against the forms of prejudice to which its claims are constantly liable.

7.2. Computational Design Philosophy

7.2.6. Information and Inquiry

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• Contents • Part 1 • Part 2 • Part 3 • Part 4 • Part 5 • Part 6 • Part 7 • Appendices • References • Document History •

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