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# Inquiry Driven Systems • Part 16

Author: Jon Awbrey

## Philosophical Reflections

### 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.

#### 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 idée 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, ${\displaystyle \operatorname {d} _{0}=\operatorname {disc} _{0},\!}$ as a presentation of examples (POE) can be analyzed as an application of an active instrumental component, a process of presentation, ${\displaystyle \operatorname {p} =\operatorname {pres} ,\!}$ to a passive objective component, a process of exemplification, ${\displaystyle \operatorname {e} =\operatorname {exam} .\!}$ Thus, it can be written as:

${\displaystyle \operatorname {disc} _{0}>\!\!=\{\operatorname {exam} ,\operatorname {pres} \}\!}$

or

${\displaystyle \operatorname {d} _{0}>\!\!=\{\operatorname {e} ,\operatorname {p} \}\!}$

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.

#### 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.

#### 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.

#### 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.

#### Pragmatic Operating Notions

A form of inquiry inaugurated in the light of the pragmatic critique casts no aspersions on the notion of a rational foundation for each domain of knowledge nor does it bear any odium against the very idea of a foundation for itself. Against these desiderata it directs nothing beyond its innocuous reflections on the likelihood of their fallibility.

Work carried out under the guidance of these reflections does not have anything in principle against finding foundations for content or method. Indeed, it continues to look for intellectual standpoints that can operate as relatively stable dwelling places, and it continues to find solid bodies of knowledge and technique that serve as provisional way stations for more or less extensive periods of time. It merely observes that all such foundations are found to be more or less tenuously tethered at the end of a considerable stretch of inquiry, and thus any hope to requisition an immovable anchor at the site of their launch is bound to be a fond hope indeed. Trying to stake the outcome of investigation on such a requirement is tantamount to a conceptual reversion, mistaking the sense of the effective gradient that drives the actual progress of inquiry.

Though the imaginative figure of a "sky hook" can serve as a regulative metaphor to describe the relation of the end of inquiry to its uncertain present, in actuality there is no substantial reality to this mechanism. This means that there must be intrinsically definable properties of the uncertain situation itself that drive it toward its intentional object.

The pragmatic critique of theories of knowledge issues in a pragmatic theory of inquiry that makes positive suggestions about the nature of the process that leads to knowledge and gives definite advice about the best way to proceed in the pursuit of knowledge. The guidelines that come out of this theory are expressed in a number of maxims amd tenets that I will refer to as "pragmatic operating notions" (PON's). These regulative principles have weathered the test of realistic experience and proven their practical utility on all relevant occasions, but however positive and definite they might be, they remain fallible and revisable.

The pragmatic theory of inquiry, in the version currently delivered, is both the mediating platform and the intermediate product of a particular inquiry into inquiry.

Serving as heuristic hypotheses, as conjectures about adequate means of discovery and as recommendations about optimal ways to direct a course of investigation, each of these working assumptions of pragmatic thought can be expressed in terms of the pragmatic theory of signs.

The only way to judge the clarity of a complex indication on intrinsic grounds alone is if it contains one or more independent kinds of signs that are claimed or supposed in their different ways to denote or intend the same overall object. Thus, in order to assess the clarity of any complex symbol, expression, argument, or text solely on the basis of its internal evidence, it must be possible (1) to compile the complete array of separate indications that are found to be declaimed or presupposed in the form, act, and circumstance of its issuance and (2) to evaluate how well this diversity of facets succeeds in cohering toward the same end. To coin a phrase for future reference, I will call this criterion the "test of coherence" (TOC).

The brand of coherence I have in mind here, one that is capable of meeting and passing the TOC indicated above, is subject to confusion with a sundry array of different marks, altogether posing under several inferior brands of coherence, as each of these is assessed by an easier test or weaker instrument called a "test of reductive coherence" (TORC). To claim that one of these inferior brands is a reasonable facsimile for the genuine brand, and a sufficient substitute for all practical purposes, amounts to a stronger claim about the kinds of coherence worth having.

Each opinion, that seeks to strengthen its claim on coherence by making the TOC amenable to replacement by a weakened form of examination, is known by the TORC that supplies its own light on the matter, and thus taken as issuing in a particular "thesis of reductive coherence" (TORC). A TORC is often found employed in various sorts of rhetorical ploys, exchanged with a valid TOC in a "bait and switch" (BAS) operation that ultimately debases the value of the very currency that it pretends to tender with the highest regard. Because each TORC that is properly called reductive fails to measure up to the authentic TOC in one way or another, I will refer to it as a "fallacy of reductive coherence" (FORC).

The valid consideration of coherence needs to be carefully distinguished from the pervasive "fallacy of reductive coherence" (FORC) that bedevils every attempt to achieve a proper understanding of reality and truth. The FORC has two branches, dividing on the issue of which fragmentary aspect of complete coherence is emphasized at the expense of the other.

1. The "denotative", "objective", or "semantic" branch of the fallacy ...
2. The "connotative", "interpretive", or "syntactic" branch of the fallacy would have one believe that a so called "true" expression indicates nothing more than a conformal opinion, in other words, the sort of belief that remains incapable of being distinguished from a comforting illusion or a convenient fiction. Because this form of reductive coherence can be examined solely within the syntactic projection or connotative component of a sign relation, valorizing this aspect of coherence leads one to profess that "truth", as a preferential attribute of everything from signs to theories, breaks down under interrogation to nothing more noble than the expedient form of solidarity that lies in having enough people keep their stories straight for a long enough time.

These two branches of the FORC are nearly able to split up between them the whole enterprise toward authentic types of coherence, simply by deploying, ineptly but exhaustively, the axiomatic instruments they hone from the spurious matter of this manifestly false dichotomy. Paradoxically enough, the lead in to the whole question of coherence is typically posed in such a way that it seems to constitute a dilemma, appearing to force a choice between objective and interpretive concerns, as if there could be any hope of a sensible response to be found within this vein of inquiry.

The partial insights afforded under each single view are revealing as far as they go, and the glamor of each little bit of knowledge that it promises its adherents is fascinating to the point of being captivating, but any light so partial is ultimately deceptive, and if the facts it favors are pursued to the exclusion of the other perspective, then the resulting one sightedness can be damaging to the prospects of ever being able to consolidate a more comprehensive coherence.

As a surrogate criterion for the truth of signs to their objects in reality, the branches of the FORC suggest a battery of alternative tests, each of which mimics the style of truth measured by the TOC, though obscured in a forced and degenerate fashion, and the passing of these tests is often confused with the full coherence of truth to reality, but only within the confines of the various forms of shadow play that an excessive dependence on projective media is bound to limit the mind to.

Various types of reductive coherence, as found to be observable in its dyadic projections, are admirable and interesting qualities for a sign relation to enjoy, and it is probably true that these aspects of coherence are practically necessary properties for the kinds of sign relations that are found to be prevailing in successful inquiries. But reductive coherence is not a sufficient test of useful sign relations, especially when it comes to genuine symbols, and thus the light afforded by the TORC turns out to be inadequate to show the whole truth of the matter.

It needs to be appreciated that the only type of coherence worth having as the end of inquiry is the three dimensional integrity of the unified objective and interpretive situation as embodied in a sign relation. Given this understanding, it should be clear that the various types of reductive coherence that show up in lower dimensional projections are admirable properties of sign relations but are not sufficient to pass the TOC described above.

Degenerate cases:

1. Purely objective coherence, the unreflective copy of things.
2. Purely interpretive coherence, the unrealistic collusion of signs.

Reductive coherence in a sign relation is an admirable and practically indispensable property of expression but not a sufficient test for the qualities of a sign true to a real object that together comprise the object of inquiry.

In spite of the number of times that oracular pronouncements have served as a stimulus to scientific and mathematical inquiry, ...

To suggest that conformal opinion or convenient fiction that the end of inquiry lies in the kind of solidarity that consists merely in having everybody keep their stories straight in every interrogation.

A truly general understanding of a phenomenon or process is both genuine and generative. It implies that one understands the means whereby a phenomenon or result is produced, and if the means happen to fall under one's command, in a way that is controlled, selective, and discriminating enough, then all the variations of the phenomenon can be produced at will. Accordingly, one proof of this kind of understanding, not an absolute test but one that remains contingent on the means being available, is that it enables the conversion of a spectrum of objective possibilities into a repertoire of intentional objectives.

In theoretical inquiry, one is concerned with the ways that a general understanding of a phenomenon or process can be expressed in signs. A conventional name for a phenomenon neither invokes the actuality of its process nor evokes its intended result, but provides the vaguest indication of its object, and instills perhaps the slightest impulse to inquire further into its nature. Even a formula that turns out to be perfectly accurate in the end can find its expression making so obscure a first impression, as regarded on the face of immediate insight, that it supplies the barest inkling of what it portrays and provokes little more than the most inchoate motive toward its own eventual clarification.

A general understanding of a domain of phenomena expresses itself in a "theoretical framework" (TF). The nature of this association is such that a growing understanding both issues in successive stages of a TF's growth and finds itself supported by the TF's structures and resources. This makes it futile to seek any kind of foundational relationship that goes between the form of understanding and the style of its expression. There is no permanent basis, prevailing throughout their long term mutual development, that would serve to assign a generative priority to any fraction of the potentials existing here, in the "chicken and egg" sort of relationship that exists between these two factors.

The TF is intended to combine into an integrated utility the kinds of features and services that were discussed earlier in connection with interpretive and objective frameworks. Toward the expression of this understanding a TF contributes a "medium of description" (MOD), that is, a formal language of descriptive predicates, constrained by logical axioms and regulated by a suitable inference system, that is positively rife with all the ready made terms, propositions, and arguments that are required to form comprehensive theories of specialized phenomena.

A truly general theory of a specialized domain of phenomena, contingent on its being supplemented with the appropriate parameters, ought to be able to generate a proper explanation for any particular phenomenon within its domain, no matter how surprising initially the fact of its happening appears. It does this by providing a suitable collection of "middle terms" that fill out the medium of description and are capable of moderating, through their interventions in the forms of explanations, the degrees of surprise that are initially, and forever otherwise, found to be affecting these happenings.

One of the major problems in the evolutionary and developmental study of individual TF's is how each of their MOD's is able to grow over time under the pressure of assimilating and accommodating novel events, how it differentiates and extends its "mesoderm" or "intemediate germ layer" of middle terms, thereby adapting the supply of interpretive mediators to meet the challenge of newly noticed phenomena, problematic impasses, and apparently irresolvable surprises that inevitably and constantly arise as it progresses in its particular form of life.

Against this general background of ideal prospects it is now time to consider how and why the complementary motif of partiality figures in. It happens due to the fact that a "finite and discrete" (FAD) sign is limited in its power to determine (identify or establish) a real object, and thus that the TF's whose syntactic domains are compounded of such FAD components are restricted in their scope and grasp of the realities that lie beyond, in both objective and intellectual directions. As a result, a "finitely informed creature" (FIC) seeking the ideal of a genuine understanding of phenomena has to rest content with partial satisfactions and elliptic realizations of this goal. The theories of information and computability could in large measure be developed out of logical considerations about sign relations simply by imposing a FAD mode of operation and by taking into account the partial determination properties of finite signs and interpreters.

Just as the relation between a genus and a species is reflected in a "specific difference" that distinguishes the species, and just as the relation between a species and an individual is reflected in all the "individual differences" that distinguish the individual, one finds the relation between a general entity and a partial entity is reflected in the "partial differences" that distinguish that form of partial example.

It is often the case that various kinds of ideal examples are imagined to represent their supervening types in an ideal manner, in other words, to belong to each of their natural classes in an especially, particularly, or uniquely exemplary way. In language that is sometimes used, people speak of an actual or imaginary "prototype" that represents the generic or abstract "archetype". Provided an ideal prototype is conceivable, the relation between a general entity and a partial entity can be described as a defect, deficiency, or departure that differentiates the particular.

Depending on whether the exemplary development of the general idea is regarded as achieving its fullness in an order of time or as maintaining its eminence on a scale of quality, examining the relation of general ideas to partial instances will involve looking at relations of successors to predecessors or relations of ends to means, respectively, plus the mixed relations of effects to causes.

#### Defects of Presentation

The immediate focus under this theme deals with the deficiencies of the present presentation of examples in relation to the general principles of inquiry and the general properties of sign relations they are intended to illustrate. Most of the discussion preceding this point has worked to remedy an initial set of "rhetorical defects" in the presentation itself, the lack of understanding it embodied about even the simplest examples. This was addressed to some degree by equipping the discussion with a panoply of formal frameworks for organizing the problematic materials and by applying these frameworks to articulate the iconic and indexical properties inherent in sign relations.

The next task in the examination of concrete examples is to address the "objective defects" of the current set, the conspicuous absence of many properties and structures that one expects to see more fully developed in the kinds of sign relations that are typically involved in authentic processes of interpretation and inquiry. One way to deal with the flaws of a particular example is simply to put it aside and take up another, on each iteration of this procedure trying to use the experience gained in the entire accumulation of precedent cases to overcome their deficiencies in the new essay or trial.

#### Dues to Process

One working out of this theme elaborates the relation of general values to the temporal processes that bring them into actual being. Whether an abiding value is reverenced as immanent or transcendent in relation to its actualizing process does not matter at this stage of discussion, provided that the value is understood to be real, potentially actual, and independent "in the long run" of its particular actualizations.

Each of these last provisos requires a bit of further explanation.

1. A value can be appreciated as real independently of its being actually realized, so long as one understands its reality to consist at least partially in its potential actuality, which means the power it has to become actual in experience.

Whatever abides throughout a domain of activity, constantly pervading a collection of objects or persistently enduring an intervening process, constitutes a value that is amenable to being at least formally associated with any conceived boundary of this domain, even if this boundary is arbitrarily drawn, provided it circumscribes a region within the bounds of the domains's natural limits, that is, within the value's domain of constancy. In short, a constant value across a bounded domain can be "unequivocally projected" (UP'd) to its boundary.

Certainly, much that lies at the boundary of a procedural domain can appear to be transcendent from the point of view of its interior, so long as the whole arena of intervening activity remains transparent enough. This observation permits one to include both immanent and transcendent values under the single heading of "apparently binding" (AB) terminal values, thereby joining both together in a contrast with the temporal processes that actualize them.

A reference to an abiding value neither brings it into actual being nor makes it abide, though it can initiate the process of its realization. Mere reference to a value, however faithfully it devotes a sign of grace to its denotation, does not prove a significant reverence for that value. Only if a grace note's invocation of its denotation issues in the forms of preference and deference that transform actual conduct and inform live performance is there demonstrated a true appreciation of its value.

Mere reference to a value, however faithful in its denotation, does not prove a reverence of that value. Only if the indicated value issues in the preferences and deferences that inform conduct ...

Although its actualization is naturally dependent on time borne events, the value itself is usually recognized to possess a real character, one that makes it logically independent "in the long run" from the numerous inessential accidents of its initial condition and the inevitable peculiar biases that encumber the various stages of its particular instantiations. Therefore, since the independence of this AB terminal value is associated not with its origin but with its end, it is safe to refer to it as an "apparently ultimate" (AU) value.

#### Duties to Purpose

Considered with respect to the preferential standards or canons of value that they embody, each of the sign relations A or B does little more than uphold the distinctions and equalities of its semantic partition. In more complex sign relations one expects to find additional structure within the SEC's, refinements of value that reflect a measure of how well various elements represent their class. A distinguished subset of a SEC that represents its meaning in a recognizably felicitous manner is called a "canonical subset", and its elements are called "canonical forms".

In the order of empirical discovery, as it usually unfolds in complex developments, it often happens that one can gather together a selection of prototypical forms with "nice" properties long before one can articulate a compact set of standards or a definite program of rules that determines its extra measure of felicity. This makes it convenient to speak of the special subsets themselves as constituting the "canons" of their SEC's. Since there are no further differentiations of value within the SEC's of A and B, these examples are tantamount to improper cases that leave each SEC a canon unto itself.

It is obvious that I have loaded this discussion with a lot of excess language, illustrated in a degenerate fashion by the examples presented so far, but all of it is intended to find good use as the sign relations and sign processes become more complex.

### Computational Design Philosophy

To deliver the logical functionality that is required to support inquiry, a computational framework must incorporate the ability to work with both empirical and rational knowledge. To do this it needs to have signs that refer to particular experiences and symbols that represent types of experience, and it needs, not only the capacity to examine the bearings of each on the other, but a means to express the sense of their meeting in an integral form.

This requires forms of expression which can attest to the bearings that each of these two facets of experiential knowledge has upon the other. Finally, the upshot of this whole critique, that balances the divergent contributions to judgment on a scale between opinion and knowledge, by way of recording and reporting the results of its examination in a concerted way, must issue in an articulate observation, in sum, a note whose tone can tell any suitable interpreter just how well an active instance of experience is likened to all that rests in the general mass, or else how acutely one element of experience clashes with the common accord established in the reference class.

Viewed from the standpoint of the pragmatic theory of signs, this design description can be seen to emphasize a certain arrangement of features, one that appreciates the three natural modes of sign functioning and assigns each to the corresponding role in judgment for which it is individually and most naturally suited. Thus, this design recognizes:

1. The role of icons in qualifying the impression of sameness or difference that arises from the critical comparison of particular experience with general experience.
2. The role of indices in pointing to active instances of experience, and thereby, in passing, connecting them with an ongoing context of experience.
3. The role of symbols in capturing whole categories of experience under the unifying cohesion of grammatically singular names, and thus allowing reasoning about things in general to properly begin. Symbols cast in the form of "abstract rational terms" (ART's) or "abstract rational concepts" (ARC's) enable intelligent interpreters to reference the "abstract rational types" (ART's) or "abstract rational categories" (ARC's) that they discover to be revealed in their experience. Notwithstanding their singular features and dual interpretation, the full comprehension of these "reason enabling singular terms" (REST's) or alternatively of these "rationally extended singular types" (REST's) empowers agents of inquiry with capacities for "partially informed reference" or "plural indefinite reference" (PIR) to unspecified multitudes of particular elements that fall within their conceivable extensions.

The very idea of deliberate design involves a reference to the purposes, objectives, or intentions of the designated design agent. In order to reflect on a particular instance of a design process in a critical manner it is necessary to appreciate several features of the agent's situation:

1. First, one has to recognize the ongoing process as a motivated activity of the design agent.
2. Second, one must identify the intended goal or motive purpose toward which end the agent is engaged.
3. Third, one needs to examine the intermediate stages of the design process in relation to the active goals and purposes of the agent, however partially specified or partially satisfied these aims may be at a given moment.

Any intended outcome associated with a design process, whether posed in the guise of a completely specified object, a fully determinate state, or just as selective information about the properties required of objects and states, can be called a "design object" or a "design objective" (DO) of the process. A design object is a special case of what is usually referred to in philosophy as an "intentional object".

#### Intentional Objects and Attitudes

A rule of thumb about "intentional objects" makes them out to be both "inexistent" and "intensional". These adjectives will be explained next, but first it needs to be understood that the sense of this maxim, though genuine, is not absolutely general. As with any heuristic principle, the rule is intended to serve as a guide in practice, to cover the typical cases of recurring interest in applied situations, but not of necessity to deal with the various kinds of degenerate cases that can logically occur. In short, the intention of the maxim is restricted to illuminating the most salient and relevant aspects of intentional objects, as pertains to the ordinary run of situations where a successful application of the concept is reasonably to be expected.

With the topic completely hedged about in all these ways, the following things can now be safely said about the notion of a design objective or an intentional object, at least, in the "hard case" of the concept that forms the only case of interest here:

1. An intentional object embodies in a logical sense the aims, ends, goals, or aspirations of a situated agent, but the intended object cannot be regarded as being present in a fully actualized sense so long as the associated intention, or the "intentional attitude" of the agent toward that object, is still maintained as active. In other words:

a. An intentional object is "inexistent" in the actual situation. It is a logical component but not an actual constituent in the intermediate context of the situated agent that actively intends, indicates, makes reference to, or signifies it.

b. An intentional object is not really present in the mediate existential moment (the instigating or non terminal condition) of the agent that is actively involved in maintaining an intentional attitude toward it.

c. An intentional object "models" or logically satisfies the features that a situated agent desires to achieve in a future situation, but these target attributes, by the very nature of its conative state, are qualities it lacks of attaining in its present situation.

d. An intentional object is purely a "potential" object. It is the kind of object of speculative thought that can only be said, and said only somewhat pre figuratively, to lie potentially present within the mediate context or "mean time" situation of the agent that has designs on it or that seeks to accomplish it. An intentional object is present purely as a potential object of the relevant mediating context.

e. When the object is obtained the attitude acquiesces. This means that intentional objects and intentional attitudes, in their dimensions of actualization, are complementary aspects of being, like position and momentum.

f. Often one is tempted to view the "clear and present danger" that is posed by a "design obstruction or non termination" (DON'T) condition to be an example of an intentional object that is really there in the agent's mediate situation, since the obstacle exists as an undeniable presence and the fault exists an actual mode of being. But this clearly involves a mistake about the agent's real agenda. It should be obvious that the actual design objective in such a case is to achieve a condition where the obstacle, fault, or hazard is removed. So the predicate that is a DO in this case is exactly the negation of the objectionable detail.

2. Because the intentional object is not actually present in the situation of the agent that has an active intentional attitude toward it, it can only be said to be represented in the situation in terms of its declared properties, or "intensions", the constraints and requirements it is expected or desired to satisfy. (potential presence)

This analysis of the concept of design objectives or intentional objects, though it trades a bit too heavily perhaps on the stock notions that naive etymology codes into ordinary language, does at least suggest that a study of sign relations could have a significant bearing on the understanding of "design relations", that is, the relationships of design contexts to their intended objects.

#### Imperfect Design and Persistent Error

Participation in an adequately adaptive sign relation affords interpreters with a singular brand of generative capacity for meeting the exigencies of life. An incrementally or recursively developed sign relation, so long as it continues to develop suitably, can provide agents and communities of interpretation with the living form of "sui generis" resource that is demanded to deal with unpredictable changes occurring in both their internal and external environments. In fact, one could well claim that this "je ne sais quantum" measure of utility is indispensable to all forms of intelligent action.

The use of signs in general allows discussion and thought to come into being, permitting agents to stand back in reflection on their objects and to take up a critically aesthetic distance from those pressing forms of engagement that an all too immediate involvement with their objectives can place on the powers of optimal decision. This freedom, this very play in the will, gives agents the tolerance for uncertainty that is essential to the process of inquiry. But even this tiniest bit of detachment, this very modicum of disengagement from the grinding gears of the world, comes at a price.

Philosophic recognition of the risks pertaining to the use of abstract symbols goes back as far as Plato's Socratic dialogues, in particular, to the "Sophist".

There are dangers incurred by the inveterate use of abstract symbols, and the good they do is oft interred with their runes. In this respect it is possible to recognize two distinct, but naturally related, kinds of trouble that can occur whenever the automatic functioning of generic symbols in an interpretive process deteriorates into the carelessly habitual use of meaningless tokens:

1. From the outset there are the ordinary risks of interpretive error that go with the territory of symbolic understanding. No interpreter intrepid enough to take on symbols can avoid undertaking these risks, not while traversing a terrain so littered with fragmentary impressions and inhabitated by indications that are rendered deliberately insufficient to totally and finally determine interpretation. Difficulties of this type make of each symbol an obstacle, of course, but to a purpose. In this more superficial vein of literal obscurity, remarking on the obstinate character of a symbol is only another way of marking the obligatory complement to its implemental utility. The intentional obstruction to interpretation that goes into the formation of a genuinely useful symbol is hardly a matter that one plays at solely for the sake of pitting sheer obliqueness against pure opacity, but it is an enterprise that aims its approach exactly as it does and forms its object precisely as it does because it prizes the beneficial side effects of sharpening particular shapes of instrumental edge.
2. With agents and communities that are capable of more complicated forms of interpretation, symbolic processing incurs a correspondingly more serious danger of going off track and falling into ineffectiveness. Besides the above types of intentional obstruction, there is also a more subtle and invidious brand of liability that is incumbent on the use of symbols. This arises from the power that symbols have to shift the gears of an interpretive process into reverse, as it were, leading discussion and thought in a retrograde or regressive direction and almost always as a consequence onto paths of ineffective diversion. That this is a reversion of the initial drive that goes into the very formation of symbols, no matter whether it is the natural constitution or the beneficial construction of symbols that is seen to be at stake. Somehow, in opposition to the normal regulation of the interpretive process as directed by genuinely beneficial symbols, the avowed direction of symbolic guides becomes subverted and they lead discursive thought down the garden path, back into the very manifold of chaotic sensory impressions from which genuinely useful symbols are intended to rescue the mind in the first place.

Both of these problems with symbolic functioning become aggravated when interpreters yield to the temptation of totally detaching symbols from their real life within sign relations.

Genuine abstractions are not rendered autonomous by disconnecting them from what they abstract from. Detached abstractions lose their elevated status as authentic generalizations, unless one wants to propose what I do not wish to, namely, to take the indications of prepositions for self fulfilling propositions and to count the void as something that categorical features can safely dangle over. But saving this chance of a synthetic a priori, and otherwise unsupported by ongoing experience, the processing of abstract labels expresses no substantial generality, but is just another peculiar form of conduct that the general run of sign bearing agencies can degenerate into. The condition that ensues is something that might be described as "idiosyntactic" behavior.

The only way I know of that interpretive agents and communities can put off devolving into idiosyntactic patterns of cultural degeneracy is by constantly maintaining a critical level of reflective capacity throughout the formation and growth of their interpretive frameworks. The problem is to allow for healthy forms of dependency on the use of abstract symbols without precipitating a precocious fall into the traps of disconnected abstraction. To subsist at this level of self awareness an IF must be steeped in such a pervasive dispensation of the critical disposition that reflective reasoning has become a habitual reflex.

The agents and communities that pursue inquiry must build a slight but non vanishing chance of wariness into every point of their fundamental IF, the one on which they originally found themselves and thereafter continue to find themselves contingent. Then, as a practically necessary consequence, this IF must keep the powers and responsibilities of critical reflection as deeply embedded and as widely distributed as possible throughout the entire medium of the form of life it intends to inculcate. This leaves a life unexamined no place to rest within the desired form of life and thus maintains an ironic suspension of reflexive examination at every turn. When this can be achieved, it keeps alive the habit of examining life as a form of life in its own right. If the entire medium of interpretation is thoroughly steeped in this critical disposition, it makes reflective conduct a constitutional part of the global IF and establishes it as a persistent style of participation on which the continued plausiblity of this very big IF remains contingent.

This makes the reflective critique a constitutional part of the very life of inquiry, keeping the ability to reflect on its own conduct as one form among others as deeply embedded and as widely distributed as possible throughout the medium of its IF, as if in suspension, and impregnating the medium of this living IF with the constant potential and the contingent power to examine its own form of conduct at every turn.

Inquiry, as a form of life, keeps a life examined active as a form of life in its own right and makes the means to examine life a constitutional part of its very form of life.

The worth of a good symbol, one that incorporates a genuinely useful abstraction, is that it lets the mind rise above the individual details of its formation, with all their potential for distraction, and yet all the while it remains connected with their general import and persistently maintains the power to recall some shadow of their particular vivacities back into the evidence of present awareness.

The occupational diseases of symbol spinners are easy to diagnose in the case of isolated individuals, but it is much trickier to detect the warp when whole communities or entire cultures, especially the ones that inform the fabric of one's own frame of reference, are drifting toward the trap of idiosyntactic abstraction or lumbering toward the brink of ethnocentric collapse.

Suppose ${\displaystyle {\text{A}}\!}$ and ${\displaystyle {\text{B}},\!}$ besides just referring to themselves in various ways, want to say something significant about the nature of their interpretive practices. That is, they begin to inquire into the structure of their own systems of interpretation. It can be imagined that the course of this inquiry leads ${\displaystyle {\text{A}}\!}$ and ${\displaystyle {\text{B}}\!}$ to generate a series of models and theories, each of which attempts to summarize in empirical terms or to describe in rational terms the observable varieties of their own interpretive usage.

Tables 88 and 89 illustrate a couple of the many possible ways that the SOIs associated with ${\displaystyle {\text{A}}\!}$ and ${\displaystyle {\text{B}}\!}$ might develop under the impetus of such an inquiry. These Tables present the empirical models of interpretation that ${\displaystyle {\text{A}}\!}$ and ${\displaystyle {\text{B}}\!}$ could conceivably form at a subsequent stage of inquiry, in this case taking the form of the higher order sign relations ${\displaystyle L_{\text{A}}^{\prime }\!}$ and ${\displaystyle L_{\text{B}}^{\prime },\!}$ respectively.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{A}}\\{\text{A}}\\{\text{A}}\\{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\text{B}}\\{\text{B}}\\{\text{B}}\\{\text{B}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{A}}\\{\text{A}}\\{\text{A}}\\{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\text{B}}\\{\text{B}}\\{\text{B}}\\{\text{B}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }&)\\(&{\text{A}}&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }&)\\(&{\text{B}}&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }&)\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\end{matrix}}}$

A sign relation is a higher order sign relation if some of its objects, signs, or interpretants are themselves sign relations. Thus, ${\displaystyle L_{\text{A}}^{\prime }\!}$ and ${\displaystyle L_{\text{B}}^{\prime }\!}$ are classified as higher order sign relations by dint of the fact that some of their objects are elementary sign relations, namely, triples of the form ${\displaystyle (o,s,i)\!}$ coming from the sign relations ${\displaystyle L_{\text{A}}\!}$ and ${\displaystyle L_{\text{B}},\!}$ collectively. Note that this definition allows an arbitrary higher order sign relation ${\displaystyle L\!}$ to have subsets, sections, or subrelations ${\displaystyle K\subset L\!}$ that are not in themselves higher order sign relations, but purely lower order sign relations. Thus, it is often convenient to indicate different subsets of higher order sign relations as being their properly higher order sections or else as being their lower order sections, depending on the evident complexity in each case.

In the Tables of ${\displaystyle L_{\text{A}}^{\prime }\!}$ and ${\displaystyle L_{\text{B}}^{\prime }\!}$ I have allowed the separate inquiries of ${\displaystyle {\text{A}}\!}$ and ${\displaystyle {\text{B}}\!}$ to develop in an asymmetric and fragmentary fashion, solely in order to demonstrate the different kinds of structure that can occur. Perhaps the point of these examples is best understood in this way: They serve more as pegs to hang conceptual tools on when these tools are not in use than they function as the objects of actual application. In accord with this organizing role, that gradually hews their features toward complementing rather than imitating the intended characteristics of any real objectives, it is best if these classical and classifying examples are not turned out in too fine a form, and it should not be expected to see in them the same kind of realism that one finds in the prospective subjects or gives to the worked material under discussion. With this purpose in mind, I can now elaborate a number of important structural concepts embodied in the higher sign relations ${\displaystyle L_{\text{A}}^{\prime }\!}$ and ${\displaystyle L_{\text{B}}^{\prime }.\!}$

A syntactic element is "stable" with respect to a process iff ...

A syntactic element is "select" with respect to a purpose iff ...

A syntactic element is "standard" with respect to a <process, purpose> if and only if it is stable and select with respect to the process and the purpose, respectively.

With respect to the connotative component of a sign relation, a syntactic element is said to be "stable" if ...

In the LO sections of A' and B' the SER's that existed in the connotative components of A and B have devolved into less symmetric, more directed dyadic relations.

Con A':	"A" connotes only "i" and "i" connotes only "i",
"B" connotes only "u" and "u" connotes only "u".

Con B':	"u" connotes only "A" and "A" connotes only "A",
"i" connotes only "B" and "B" connotes only "B".


Interpreter A is apparently biased toward using personal pronouns, while interpreter B has a habit of using proper names to refer to everybody in the third person, including himself.

Unless A and B develop suitable fragments of the language of set theory within their SOI's they cannot avail themselves of syntactic elements that can denote the whole sign relations A and B under singular terms. Until then, they are forced to resort faute de mieux to the device of "plural indefinite reference" or "partially informed reference" (PIR), interpreting the same signs in systematically ambiguous ways to denote extended pluralities of objects indifferently. This way of letting an interpreter represent a set in action, by "being the set", as it were, is actually the preferred strategy according to some tastes, since it does not multiply abstract entities beyond necessity. Combined with a proper treatment of "normal forms" for syntactic elements, it leads to SOI's with sufficient power to deal with almost all of their practical set theoretic needs.

#### Dynamic and Evaluative Frameworks

In this subsection I hope to prepare the way for the consideration of more significant examples of sign relations, and to begin demonstrating how this class of formal structures is relevant to the motivated changes or value directed operations of inquiry. In order to see how the rather static and featureless sorts of sign relations considered so far can grow into full fledged examples of inquiry processes it is necessary to develop two additional aspects of their structure.

1. The "dynamic" dimension deals with change, permitting the sequential ordering of state positions in a temporal process.
2. The "evaluative" dimension deals with comparisons, permitting the preferential ranking of state qualities on a scale of values.

Moreover, each of these additional aspects or dimensions of structure needs to be articulated at two levels of application to sign relations, considering the dynamic changes and the evaluative comparisons that can take place either "within" or "between" individual sign relations.

a. "Within" sign relations. This level involves (1) the changes and (2) the comparisons that are possible between the elements of a single sign relation, that is, between its objects or else between its signs and interpretants.

b. "Between" sign relations. This level involves (1) the changes that transform whole sign relations into others, whether these actions are considered to occur dynamically in time or only virtually in contemplation, and (2) the comparisons that go into ranking whole idividual sign relations on various scales of values.

Since I am using sign relations as models of inquiry, that is to say, as models of potential theories of inquiry, ...

The hardest part of the inquiry into inquiry, as I presently see it, comes down to this: Are there rational ways to argue toward a theory of inquiry? That is to say, are there systematic ways of reasoning toward definitions and axioms in any domain, and can these methods be applied to arrive at a definition of inquiry itself, along with the principles that are necessarily true of inquiry? In other words, can definitions and axioms be criticized and evaluated on rational grounds with regard to how well they describe independently given concepts? These are difficult questions for certain models of science to address, namely, those whose image of science accustoms the mind to starting out from received formulations of experience that prior work has tamed into the facile forms of primitive expressions, and whose sense of scientific procedure always seems to argue from a formal basis in definitions and axioms rather than toward them, oblivious to the import of all those processes, rational or otherwise, that initally supply this foundation.

By the end of this subsection I want to have charted a return to my discussion of formalization, proceeding thereafter by way of increasingly complex but nevertheless still concrete examples of formal models. However, in order to get that far I will have to steer a winding course, encountering a diversity of foundational crises and brushing up against a selection of critical obstacles. Luckily, the immediate aims of this discussion demand no more from me than to touch as lightly as possible on the most prominent points of each apparent dilemma as it looms up, and thus I can hope to clear their main obstructions in a passing way. Perhaps the highest priority is to revisit my guiding intuitions about inquiry, to see whether this constellation of methodological hypotheses permanently constrains the models of inquiry that can be entertained, or whether this tentative model of inquiry incorporates a way to recognize when the process of inquiry happens to go astray, and thus leaves room for its own self improvement and a continuing revision of insights.

Successful inquiry into any domain of phenomena is supposed to reduce the level of uncertainty that an interpreter has about the objects or processes in that domain. In future discussions, I will refer to this supposition about the end of inquiry as the "initial description" (ID) of inquiry.

Employing this ID of inquiry in the application of inquiry to itself, it follows that successful inquiry into inquiry is supposed to decrease the uncertainty that an interpreter experiences, expresses, or exhibits with respect to the nature and conduct of inquiry itself. I will refer this supposition about the end of inquiry into inquiry, a corollary hypothesis that is derived from and contingent on the "self employment" of the ID, as the "self expression" (SE) of the ID.

Since it is presumptuous to think that anything definitive can be said about inquiry until after the inquiry into inquiry has achieved its end, the thesis that I identify as the ID of inquiry will have to pass in the meantime as a nominal definition or a topical hypothesis, in other words, as a tentative conjecture about the character of inquiry that arises from the realms of personal intuition and popular opinion and that needs to serve no greater purpose than to get the discussion off and running in a definite direction, along lines of inquiry whose fruitfulness can be tested without loss of generality at any later stage of investigation.

And so a modicum of presumption must be tolerated, since it cannot be avoided in any case, and a measure of arrogance is involved in every interrogation of nature, to think that one's question deserves an answer and that one is perhaps one to find it or make it in time. But the hope that this manner of approach to the object of inquiry can be successful in the long run is tantamount to a regulative principle of inquiry, one whose plausibility depends on certain conditions being fulfilled, and thus its rational use requires one to deal with a variety of potential obstacles that affect its justification in practice.

Although some measure of presumption must be tolerated, since it is not seemly to assume that every measure of it can be avoided, this does not mean that every presumption must remain immune from correction and therefore eternally incorrigible. Any initial assumption remains subject to being criticized from the standpoints of all the casual contexts that it injects itself into. Since these forms of interjection do not found the contexts they interrupt and interpret, and supply at best convenient springboards for discussion but never essential foundations, their defects can always be remedied as the need arises.

In the entire discussion so far, I have let myself be guided by the governing couple of casual intuitions or working hypotheses that are formulated in the preceding ID of inquiry and in its subsequent SE, and especially by the implicit rule of hope that is involved in their use. Consequently, it may seem at this juncture that the utility of the whole discussion hinges on the prior certainty of these two cardinal points. In order to proceed with any degree of confidence along the lines of approach I have chosen, I will have to argue that this is not so, that the apparent force of obstruction presented by the practical necessity of making initial constructions does not prevail against the conceptual possibility of inquiry into inquiry nor against the chances of every simple inquiry simply going forward in accord with its own lights.

It becomes the task of continuing discussion to preserve the mode of guidance identified by the ID of inquiry and to persist in the enterprise staked out by its SE without being pinned down too fast or too fixedly by the patently obvious and hopefully transient limitations that these principles betray on a moment to moment basis. It remains the duty of this project to see whether inquiry constitutes a form of progress that can work toward truer and proper definitions of itself or whether it is terminally limited by the first impressions and incipient reflections that it captures of its own character, no matter how sage or insipid these preliminary guesses at a recipe for inquiry may initially be.

Returning to the refrain: Inquiry into any process or phenomenon is supposed to decrease the uncertainty that an interpreter has about that particular object of interest. Inquiry into the process of inquiry is supposed to decrease the uncertainty that an interpreter endures or evinces with respect to the nature and conduct of inquiry itself.

Expressing everything over again in positive terms: Successful inquiry increases the certainty that an interpreter has about the object of its investigation. Successful inquiry into inquiry increases the certainty that an interpreter possesses or manifests with regard to the process of inquiry itself.

There are many things about the ID of inquiry and its SE that will have to be examined with increasing care at various later stages in this work. If the profile of inquiry and its self application depicted here are to be regarded as useful, then each of the concepts invoked in this picture of inquiry needs to be clarified as much as possible, ideally to the point where it can be accepted as a definition and examined with regard to its potential for formalization and quantification. For the moment, I suggest just a few of the additional points that will undoubtedly arise, and then I return to focus on the topics of immediate concern from the standpoint of developing concrete examples of formalization.

Of central concern, the concepts of uncertainty and certainty that are implied by the ID and its SE need to be analyzed in relation to standard concepts of entropy and information that have already been formalized and quantified to an adequate degree. At first sight, the concept of certainty seems to involve the superabundant qualities of "quick wit": (1) as a feature of a state of intellection, something that enables the exercise of ready decision making powers, and (2) as a feature of signs and expressions, something that increases their clarity and alacrity, or augments the accessibility and usability of their information, all of which seems to add up to facilities and capacities that are not guaranteed by the mere possession of information alone.

As always, in carrying out the analysis of a vaguely given idea in relation to a known concept, assuming there really is something to the idea, one has the options: (1) of extending the precursory term to incorporate additional meanings, or (2) of limiting the term of the paradigm to its established senses and inventing distinctive names for the extra components of meaning. The choice between these options is usually decided by how much continuity is perceived along the series of related concepts, as they come to be analyzed.

Until the terms it invokes are formalized, or at least clarified to a greater extent than they are at present, the ID that I presented on behalf of inquiry and the SE that I employed for the sake of inquiry into inquiry will provide little more assistance toward understanding the character of their subject than the vague indication already supplied in the nominal invocation of "inquiry", and even that much progress is purchased at the cost of no small measure of distraction.

Axiomatic presentations, that arrange their subjects as if freshly sprung from undefined terms and unproven axioms, are extremely useful for the purposes of retrospective exposition and rhetorical justification, but they rarely do justice to the actual order and process of discovery or fairly represent with any degree of realism the evolution and growth of their living subject matters. Not even logic and mathematics are such purely deductive enterprises as to remain for long entirely captivated by their still life forms and aesthetically distanced styles of depiction.

Since nothing about inquiry makes sense outside the framework of sign using agents, the ID and SE are able to refer, without loss of generality, to an "interpreter" as forming the generic agent of inquiry, instead of the "agent" or "observer" that might be expected to appear in seemingly more general formulations. The pragmatic theory of signs, that naturally develops in parallel with the pragmatic theory of inquiry, is presented in large part simply to explain what is meant by this "interpreter". As a bonus, the extra dimension of relationship involved in the pragmatic theory of signs can be turned toward the beneficial purpose of constantly maintaining a critical perspective on one's own conceptual constructions.

The vast abstraction schematized by means of the single word "has" — that I sought to flesh out in a highly selective sample of its senses: via the conditions an interpreter "experiences", "expresses", "exhibits", ranging in meaning through all the categories from passive to active modes, from "endures" to "evinces", from "possesses" to "manifests" — this is a complex of interpretive possibilities that will take some time to develop and clarify, not the least because it resonates with the twin themes of the "fugitive canon" that I alluded to early on in this study. In quick order, within a framework that permits the creation of artificial mediations between sequences of experiential states, between successions of felt conditions such as pain or relief, doubt or belief, what kinds of formally effective models could possibly be subtle enough to convey the substance of these persistent general categories while working within the limitations of transient particular states?

Certainty = Information + Clarity + Alacrity + ...

One of the ways that the supposed information can be expressed is in the form of propositions that the interpreter observes about its object. Thus, different states of information about an object can be constituted or represented by different collections of propositions about that object. In logic, an arbitrary collection of propositions is called a "theory", a title of no particular significance until one has examined the consistency and validity of the supposed theory.

Using this form of description, an interpretive agent can be conceived as moving through a space of information about an object, whose points are characterized by different amounts of uncertainty versus information about an object, and where each state of information with regard to an object is associated with a theory about that object.

#### Discussion of Examples

At this point, in order to make further use of the pragmatic theory of signs without distorting its character too severely, I am forced, even for the sake of this simple example, to broach a difficult and potentially controversial topic that, for good or ill, can no longer be avoided. For future reference, let me entitle this issue as a question about "the general versus the restricted theory of sign relations". The problem for pragmatic theory and practical application is how to steer a middle course between the riptide of vague generalities and the narrow idols of reductive procedure.

In general, questions about the relationship of signs and interpretants, both inside and outside a computational framework, form a major concern of the pragmatic theory of signs, and will continue to be revisited throughout this discussion. Time and time again, questions about the true character of the interpretant role are found to abide at the heart of the problem, forming the cardinal points of investigation on which everything else hinges. The reason for this appears to be yet another brand of recursion or self similarity affecting the domain of inquiry. Namely, interpretants fill a role within their individual sign relations that is analogous to the role that sign relations used as formal models fill within the larger inquiry, providing a controlled mediation between the wide open domains of phenomena and language.

In the general theory of sign relations, which concerns itself with the formal properties of thinking processes, the interpretant domain is meant to encompass the full variety of mental impressions and affections: ideas, concepts, intuitions, intentions, impulses and dispositions to act, and every sort of intellectual construct, both cognitive and affective. This heady brew is not yet on the table for current consumption, but all of it imbues the aspirations of artificial intelligence with a measure of essential enthusiasm, and a spirit to which even those whose scope is focused on the objective dynamics of intelligent systems cannot turn down a glass.

Working within the constraints of formally effective descriptions (FED's), this project can explore nothing more than pale scattered shadows of these connotative and ideational dimensions of meaning. In the pragmatic theory of signs, it is held that all thought takes place in signs. Ideas, concepts, and other mental constructs are regarded as signs in the mind, in other words, as modifications of their peculiar medium that affect the states of their conducting agents. But with regard to their pertinent formal structure, namely, the sign relations that shape their action as signs, mental signs are no different from the generic brand of signs. In sum, all signs are defined as signs precisely in terms of their relative associations and formal operations, and not according to the marks of any absolute material essence.

Still, there falls within the sweep of this enlarged scope an element of crucial importance to all forms of pragmatic thinking. This is the notion that a solid store of meanings for signs and ideas can be found, not quite in the individual actions of an agent that come and go with the moment, so transient and irrepeatable in themselves, but in the agent's conative character, informed conduct, and consummate disposition to act. This realm includes both inborn and borne in patterns of inclination, broadly conceived plans of action, and generalized contingent resolutions to act in definite ways under prescribed conditions.

If this description sounds familiar, it is with good reason. The formal realm that shares these features is precisely the domain of operational definitions and effective programs whose use in clarifying concepts is being explored in this project. The upshot is, that whatever vague signs are allowed into the sign domain simply on the chance that they might mean something to somebody sometime, there is a more critical property demanded of the interpretant domain that is intended to play a role in deliberate inquiry. For a sign relation to serve inquiry in a positive way its interpretant domain ought to make available to its agent explicit expressions of program like entities that can define with maximal clarity the imports of its signs and ideas.

#### Information and Inquiry

Given my initial description of inquiry as a process that reduces the uncertainty of an inquirer (any observant agent or interpretive system) about the state of an object system, and combining this with the characterization of interpreters in concrete form as sign relations, there arises an obvious question that must be addressed by this project: How is the state of uncertainty of an agent about an object system to be defined from the data present in a sign relation?

In spite of the bare construction of the A and B dialogue it is possible to elaborate a few scenarios on its basis that illustrate the relevance of sign relations to inquiry situations. To devise motivating stories for these inquiries and still be able to obtain the needed variations from such sparce materials, I will be forced to re use many elements of the sign relations A and B in non standard ways. Because they lack most of the analytic refinements that will be needed for complete clarity, these inventions risk the introduction of a few confusions. However, the exercise of untangling potential confusions in a simple example can provide useful practice, highlighting problems before they grow too complex to tackle, and training the attention to detect what features really matter in defining a situation of inquiry.

One type of inquiry might begin with A having no idea what B will say next, except for the certain knowledge that it must be confined to the syntactic domain S = {"A", "B", "i", "u"}. I will refer to this as a "syntactic" type of inquiry, since the object system appropriate to the inquiry situation, as described, is identical to the syntactic domain S. As a rough approximation, this inquiry can be viewed as a degenerate spin off from the original dialogue, one in which the true object domain has been lost, and attention has devolved to mere banter over signs. More carefully regarded, the relationship of the syntactic inquiry to the original situation could be described as deriving new sign relations Syn (A) and Syn (B) from the old sign relations A and B, in each case replacing O with S and splitting the stock of ordered triples in a corresponding fashion, as shown in Tables ** and **.

In this sort of "syntactic inquiry", the state of uncertainty on the part of A about the state of the object system S is a condition of maximum entropy with respect to the outcomes in S and can be represented as a uniform distribution of probabilities over S. In this scenario, A has log2|S| = log2(4) = 2 bits of uncertainty about what B will say next. If A hears B say "A" next, say, then A has no remaining doubts about the issue. As a result of receiving this sign, A comes to reside in a state with 0 bits of uncertainty about the question now past. The same reasoning applies to each of the other signs in S. Altogether, each sign in S conveys 2 bits of information to the interpreter A with respect to the prior condition of maximum uncertainty about the state of the object system S. The "average uncertainty reduction per symbol", in this case 2 bits, is called the "capacity of the information channel", as this channel is defined by the entire set up of the inquiry situation.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\text{A}}\\{\text{A}}\\{\text{A}}\\{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }{\text{A}}\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }{\text{B}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\text{B}}\\{\text{B}}\\{\text{B}}\\{\text{B}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }{\text{B}}\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }{\text{B}}\end{matrix}}}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{A}}\\{\text{A}}\\{\text{A}}\\{\text{A}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{A}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{u}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\text{B}}\\{\text{B}}\\{\text{B}}\\{\text{B}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{B}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{i}}{}^{\prime \prime }\end{matrix}}}$

Another type of inquiry might begin with A wondering what object B will denote next. Here, the object system referred to as a part of the inquiry situation is identical with the object domain O of the sign relations A and B.

Fragments

To deliver the logical functionality that is required to support inquiry, a computational framework must incorporate the ability to work with both empirical and rational knowledge. To do this it needs to have signs that refer to particular experiences and symbols that represent types of experience, and it needs, not only the capacity to examine the bearings of each upon the other, but a means to express the gist of this result in an integral form. If these references and representations are to avoid the various ways of violating the bounds of sense — something they can do either by failing to have sufficient denotation from the outset or by exceeding the bounds of consistency and tractability at any stage of attempting to process their indications — then ...

1. Operating on corrupt arguments or initially senseless indications. Attempting to start out from a state of empty nonsense, from a logically pointless or impoverished point of view, and trying to pursue a moment of semantic irreference on the impulse of a direction with null import. Drawing on resources that are logically empty and following instructions that are semantically nil.
2. Transgressing the bounds of consistency or tractability at any subsequent stage of computation and thereby becoming logically empty or effectively vacuous, conceptually inconsistent or computationally intractable at an intermediate stage of investigation.

Even though the present discussion is focussed on isolated cases of sign relations, it cannot illustrate the properties of these examples in an adequate way without considering extended multitudes of other relations, both those that share the same properties and those that do not. Thus, to get the comparative study of sign relations started on a casual basis, something that is helped in addition by placing sign relations within the larger field 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.

dimensions of temporal evolution and deliberate evaluation

coordinating temporal evolution with directed evaluation

partial specification: approximate, deficient, imperfect, incorrect

partial satisfaction: approximate, deficient, imperfect, incorrect

## Overview of the Domain : Interpretive Inquiry

Interpretive Stance, Initial Theory, Concrete Examples

### Interpretive Bearings : Conceptual and Descriptive Frameworks

In this section I review the conceptual and descriptive frameworks that I will deploy throughout this work. In passing, I explain my overall attitude toward the use of any theoretical outlook (scaffold or catwalk), namely, that it needs to be as flexible and as reflective as possible.

#### Catwalks : Flexible Frameworks and Peripatetic Categories

In order to have a term that expresses both the conceptual and the descriptive aspects of these perspective standpoints, I have chosen to call them "interpretive frameworks". When analyzed in depth and fully formalized they might be recognized as "theoretical frameworks". But not every manner of intuition (or slant on the world) can survive the reflective process and persist under examination as a viable style of interpretation. And I need a term to underscore the fact that these heuristic frameworks are already in operation, shunting attention and shifting selection on an automatic and informal basis, long before anyone thinks to articulate their axioms in theory or to criticize their biases in action.

The reason I refer to interpretive frameworks rather than "ontologies" is to emphasize that many of the categories listed in these systems are inclusive or overlapping in their scopes. Thus, the circumstance that the same object can be contemplated under several different headings of the framework is not of necessity intended to say anything substantive about the object itself.

The reason I refer to interpretive frameworks rather than "hierarchies", even though I will often settle on a standard sequence for considering the attributes of a contemplated object, is that there is in general no uniquely best order for taking up these properties.

This may seem like a trivial point, taken for granted by everyone as a part of understanding the use of language, but it serves to highlight an important issue, one still lacking in universal agreement.

I will say that a logical distinction is "interpretive" to mean that it depends on the choice of an interpreter to determine how anything is classified with respect to it. This does not mean that every option of consideration will always be found equally fitting, but only that it is possible to contemplate the alternatives in a form of mental experiment.

As much as possible I will try to exploit the available degrees of interpretive freedom to view all conceptual and descriptive distinctions as being in relation to a framework of interpretation. For ease of discussion, if not for any more substantive reason, interpretive frameworks are often depicted as enacted by interpretive agents or embodied by interpretive communities, all of which conditions of practice can be summed up in a parametric reference to a single "interpreter".

##### Eponymous Ancestors : The Precursors of Abstraction?

As one application of the flexible attitude just proposed, consider the following issue.

An important problem in the evolution or development of intelligence is the question how genuine concepts (categorical abstractions and hypothetical constructions) can be derived from particular percepts. The gap between individual acquaintance and comprehensive description always seems too vast to explain how incipient minds can vault it with any sense of security.

In formal language theory, this distinction corresponds to the difference between "terminal" and "non terminal" symbols in a formal grammar. That is, it signifies the contrast between lexical items with narrowly defined extensions and atomic instances as opposed to grammatical categories with infinite extensions and complex constituencies. Asking the question in this setting: How does a burgeoning language facility make the transition from finite state grammars, where terminals yield handles on non terminal symbols that obviate the need for a parser to backtrack, to higher level grammars, where a strategy of hypothetical trial and error is inevitable?

One way of visualizing a continuity in this transformation is by supposing that the potential to serve as an abstract sign is already available to interpreters in the flexible use of concrete signs. This suggests that generative categories and genuine hypotheses may arise by degrees in a gradual turning of phrases from fixed meanings to functional roles. Thus, authentic concepts can be derived from the interpretive recycling of individual names and nominal idioms into paradigmatic and schematic senses.

Peripatetically speaking, this illustrates a way that fledgling interpreters might pace themselves itself through the steps of this jump (the leap of abstraction) and trace a smooth progress over the intervening space: first, let them reposition discrete names in paradigmatic and schematic senses; then, allow them enough sense to recapture terminal and formulaic stereotypes as newly productive archetypes.

##### Reticles : Interpretive Flexibility as a Design Issue

As separate objects and independent constructs in and of themselves, interpretive frameworks are like the templates that observers impose on the scenes viewed through a reticle. Outside the slim chance of a pre-established harmony among them, there is no guarantee that the forms of intuition permitted by these instruments are essentially designed to fit the objects surveyed. Any notion of the world is a compromise between the specious and the factitious and yet supplies the mind with its only available grasp on reality.

The artifactual nature of the mind's handle on things is a commonplace observation of most philosophies, but there is a job here that remains to be carried out. Descriptively, the task that falls to this project is to consider how computational models of interpretive systems can be designed to take this factor into explicit account. Instrumentally, it is a design goal of this project to reflect this aspect of interpretive frameworks in the implementation of their supporting software, and thus to recognize and incorporate a feature in the artifact that seems unavoidable in the natural case.

Later, in making use of formal calculi, I will propose that the distinction between constants and variables can be treated as interpretive and need not be a fixture of the syntactic specification. This means it will be part of the meaning that is left up to the interpreter which symbols have fixed interpretations and which are taken as surrogates for a variety of substitutions.

#### Heuristic Inclinations and Regulative Principles

This discussion involves itself in a relationship with objective systems, linguistic and mathematical signs and descriptions, and a broad span of mental bearings that range through the following list: sensations and impressions, percepts and intensions, concepts and ideas, affects and irritations, actions and impulses, purposes and intentions.

### Features of Inquiry Driven Systems

I have described inquiry as a process of determination that takes an agent from a state of uncertainty to a state of relative certainty or increased information, of a kind and to a degree sufficient for action, ...

I am operating on the assumption that / If inquiry is a process of determination that leads from uncertainty to the kind of certainty, sufficient for action, that an agent experiences as a state of belief or knowledge, then I need to say something about / articulate / examine the underlying epistemology, the implicit theory of knowledge and belief, that I employ / is employed in this project.

... then I need to say something about the kind of certainty that can be the goal of inquiry, and how I intend to use words like "belief" and "knowledge" in this discussion / understand concepts like belief and knowledge.

I do not believe I know of any difference in my immediate experience between belief and knowledge. To be more precise, I do not think I can tell a difference/ I detect no difference, from any quality present in the moment of experience itself, between an experience of believing something to be true and an experience of knowing something to be true. I do not think that, by itself, any agent can tell a difference between what it believes and what it knows.

By myself, I do not see how I can draw a distinction / tell a difference between what I believe and what I know. The distinction posed between them is not essential, but serves rhetorical and statistical functions, as a measure of intensity and commonality.

To say I "know" something is true is to mean that I really believe it. To say that someone else "knows" something is to say that the other believes the same as oneself.

Within the moment / I believe momentary experience has no quality in itself that distinguishes/ In the moment of experience /

The distinction made between belief and knowledge serves a largely / is partly rhetorical and partly statistical. The word "knowledge" operates as an intensifier, to say that one "really" believes something and to measure / as a modifier to indicate the intensity of belief or the measure of commonality / shared belief across a community/ to say that one has checked a belief by various means, verified it with others, including one's recollective former and preconceivable future selves, and found it to be a widely shared belief across this group.

There is nothing about the experience itself that distinguishes a state of belief from a state of knowledge. The distinction of knowledge serves as an intensifier, to say that one "really" believes something, or as a statistical function, to say that one has checked this belief by various means, with others, including one's past future selves.

For my purposes, I can see no difference present in the quality of the state itself between an agent "believing" a sign (expression or indicator) to be true and the same agent "knowing" the sign to be true.

If there is a difference between belief and knowledge, then it must have something to do with the way that one state of experience can refer to other states of experience outside of itself. In other words, it has to do with global and relational properties of the manifold of experience, and with the possibility that information about these constraints can be reflected and articulated within the individual moments of the manifold itself.

Thus, the distinction of "knowledge" is not essential or phenomenal, but incidental and epiphenomenal. That is, it has to do with the way that relations between basic levels of phenomena can reflect themselves within/ The way I use these words is not perjorative, but taxonomic. It neither diminishes the reality of epiphenomenal features and accidental attributes nor excuses me from the task of analyzing the geometry of their incidence/ but merely classifies / and does not diminish the importance of epiphenomena or the reality of accidental events ...

For my purposes, I can see no difference in the state itself between an agent believing a sign (statement or indicator) to be true and that agent knowing that sign to be true.

The intention of this section is to discuss in some detail two examples of inquiry driven systems that have already been implemented in the form of computer programs.

The goal of this section is to present in concrete detail significant examples of two different kinds of inquiry driven system which have already been implemented in the form of computer programs.

In this section I describe two examples of inquiry driven systems that have already been implemented as computer programs. The basic terms of description are taken from the pragmatic theory of signs, which I introduce as briefly as possible.

In this section I describe two examples of inquiry driven systems that have already been implemented as computer programs. The description is cast within the pragmatic theory of signs, which I review briefly and only to the extent necessary for discussing the examples.

#### The Pragmatic Theory of Signs

The treatment of inquiry to be developed in this project makes constant use of a philosophical perspective on thinking and communication known as the "pragmatic theory of signs". The subject matter of the theory of signs is a class of three place relations called "sign relations". These relations can be understood as set theoretic objects, as sets of ordered triples, and it is often useful in building concrete intuitions to consider elementary examples of this sort. But the sign relations of ultimate interest have infinite extensions and extremely complex internal structures.

Thus it develops that significant examples of sign relations are typically described and analyzed indirectly, by referring to a postulated agent that enacts or embodies the three place transactions involved in a particular case. The agent of sign relation is commonly called an "interpreter", who is variously said to partake in, embody, enact, compute, implement, execute, or carry out the sign relation in question. This brand of personification and its idioms serve a narrative function, supplying the observer in theory with an identifiable character and a point of view that reflects incidental variations in attitude toward the subject, but their purpose at heart remains one and the the same, which is merely to indicate or convey a particular sign relation.

Because inquiry systems will be described as special types of sign relations, inquiry driven systems and inquiry agents will be treated respectively as sign relations and interpreters that enjoy certain types of additional features.

Viewed within the pragmatic theory of signs, inquiry driven systems come at the end of a chain of incremental specification and increasing specialization. Starting from the bare conception of a triadic relation, notions of determination and correspondence are added to obtain the definition of a sign relation. To the static form of a sign relation, a notion of dynamic change is added to reach the idea of a sign process. To the aimless flow of a sign process, a notion of value is added that gives the succession of signs a motive, a direction, and a goal. Altogether, a system with non trivial values specified for each of these attributes constitutes an inquiry driven system.

What I just gave is a convenient order for taking up the attributes of an inquiry driven system. There is nothing unique about this approach, in particular, it is often useful to consider the dimension of value before discussing the dynamics of change. The most important thing about this list of properties is that it makes it possible to discuss the extent to which the changes of the system are in accord with the values of the system. A major part of the work remaining in this project is concerned with analyzing these global attributes into more detailed features, examining their relationships to one another, and ultimately translating their potential qualities into operational terms.

In this description inquiry driven systems are viewed as special cases of sign systems, those to which a notion of value has been added, by which a particular interpreter distinguishes what it considers to be better and worse signs of a given object.

This is a comparative dimension along which a particular interpreter distinguishes / recognizes better and worse signs of a given object, and differentially measures the quality of messages that otherwise have exactly the same meaning / along which a interpreting agent assesses a measure of quality among expressions, a comparative dimension of better and worse representations / signs of an object to a particular interpreter has been added, a comparative dimension of better and worse representation.

##### Sign Relations

Conceived in logical terms, a "sign relation" R is a certain kind of three place relationship that exists among the elements of three domains: the object domain O, the sign domain S, and the interpretant domain I. To qualify as a sign relation in this setting, a three place relation R is required to satisfy a few additional properties to be named later.

Expressed in terms of its set theoretic extension, a sign relation R is associated with a set of ordered triples <o, s, i> that forms a subset of the cartesian product OxSxI. The notation R = Set(R) c OxSxI can be used to single out this interpretation.

Expressed in terms of its computational intension, a sign relation R is associated with a predicate or program that values ordered triples <o, s, i> according to their fitness for the logical functions of the intended sign relationship. The notation R = Fun(R) : OxSxI > B, where B = {0, 1}, can be used to single out this interpretation.

Ways of Knowing a Relation

Knowledge by acquaintance:		extension or enumeration;
Knowledge by description:		intension or comprehension;
Knowledge by regulation:		intention or competence.


When the extension of a concept is infinite, or for any reason inconvenient/ or inconvenient for pragmatic reasons to enumerate in detail, then knowledge of its objects must be achieved by means of description rather than acquaintance.

When the extension of a concept is infinite, or inconvenient for pragmatic reasons to enumerate in final detail, then a finite agent's comprehension of it is required to be knowledge by indirect description rather than knowledge by direct acquaintance (Russell). That is, the objects of the concept are known by means of the concept's intensions, the common properties of its objects as expressed in symbolic reminders. But the intensions of a concept can be still more numerous than the objects of its extension, and even when a finite selection of these intensions is enough to specify the extension uniquely, there can always be many different collections which do so, and many different ways of approaching the concept by proceeding through a sequence of features in the subset chosen.

Thus, knowledge by description is approximate knowledge, knowledge whose quality and character can depend on the current stage and overall manner of approach. This sort of knowledge is contingent on and biased by each agent's particular way of approaching the objective, or the objects of the concept in question.

Due to the inclusion of these secondary facets in the character of the knowledge cut out, not every aspect of it is invariant over changes in the means of approach. The artifacts of the resulting knowledge that are not indifferent to the path of approach are called intensional features of the method, procedure, or computation. For example, programs that effectively compute the same function, the same set of ordered pairs in extension, but do it with non identical profiles of efficiency are said to differ in their intensional properties. Here, it is not the intensions of the functions as objects which differ, but the intensions of the programs as objects which do. The intensions of a program are related to the intensions of a function in the complex way that information about functional domain elements is traded for information about functional range elements throughout the progress of a computation.

Sometimes our grasp of the objects coming under a concept is even more tentative and tenuous.

Sometimes the mind's reach toward an objective is still more tentative and tenuous, exceeding the grasp of any present concept or familiar description, but represented only in the hope that certain rules of procedure or regulative principles are bound to converge on it in time. Thus, the object of knowledge is the object of an intention, and so is the hopeful knowledge itself. This kind of epistemological stance or orientation toward knowledge can be called "intentional knowledge" or "knowledge by intention", but is really more like an "intention to know".

To the extent that the computational intentions of this project are successful, more and more of the theoretical concepts employed in the unformalized parts of the inquiry will be operationalized as computable functions, serving to accomplish the actions or recognize the objects intended by each concept. In practical terms, this means that the functional interpretation of relational concepts, including the notion of a sign relation that founds the whole enterprise, will become paramount to the approach I have chosen. However, ...

The letters "o", "s", and "i" are examples of identifier names (variables or constants) that are used in discussing sign relations. They denote elements of the relational domains that fill the object, the sign, and the interpretant roles of the sign relation in question.

When the object is a formal system then its elements are regarded as signs (words or phrases, terms or formulas, pixels or pictures).

When the object is a dynamic system then its elements are regarded as states (points, moments, positions, vectors, configurations).

In general, the only constraint placed on a sign relation is the following definition.

(Peirce, NEM)

To complete this definition, it would be necessary to say what is meant by the notions of "determination" and "correspondence" that it invokes. This I defer to a later discussion. For now, I can limit discussion to the kinds of sign relations that are useful in systems theory and that occur in the computational representation of formal systems.

For the purposes of systems theory, and staying within the frame of computable representations, a number of additional restrictions and simplifying assumptions can be attached to the generic specifications of a sign system.

Because this discussion will stay within the framework of systems theory and limit its scope to the computational representation of formal systems, a number of restrictions and simplifications can be imposed on the general definition of a sign relation.

The roles of the sign relation are filled by systems or states of systems.

The object system o is a member of the object domain O.

In the cases of interest here, the object name (variable or identifier) "o" refers to a system or a state of system.

### Examples of Inquiry Driven Systems

#### “Index” : A Program for Learning Formal Languages

The program "Index" actualizes an inquiry driven system that learns formal languages, operating under a restricted notion of learning that is explained next.

To specify an inquiry driven system I can first describe it in static terms as a sign relation, and then elaborate the more dynamic aspects of its sign process. In this example the role of the object is played by a special kind of mathematical object, a formal system known as a "two level formal language".

The object o is a two level formal language over a finite alphabet A. The object domain O is the set of all such languages over the same alphabet.

A two level formal languge o is specified by giving its words and its phrases, o = <W, P> = <o.lex, o.lit>, two sets that comprise its "lexical" and "literal" levels, respectively.

The words of o are finite sequences of letters from the alphabet A, collectively forming a set W called the "lexicon" of o. In symbols, W(o) = o.lex c A*.

The phrases of o are finite sequences of words from the lexicon W, collectively forming a set P called the "liturgy" of o. In symbols, P(o) = o.lit c W*.

As mathematical objects, not to mention objects that are potentially infinite in their extension and presumably unknown to the agent at the beginning of inquiry, o and O have the status of "external objects". This means they do not inhabit the minds or computers, the original or extended media, of inquiry agents. External objects never have their being in the locus of representation but become known to the agent only by means of the signs that gradually come to inhere in its being.

Because the agent of inquiry has a limited capacity for taking up information, the process of becoming informed about an external object cannot be any form of direct instruction on the part of the object or perfect intuition on the part of the agent. It is always a matter of stepwise approximation to better representations of the object. The progress of inquiry accumulates the tokens of the object's features that successively impress themselves on the agent's medium of attention and integrates them into the ongoing process that constitutes a particular agent's total activity.

#### “Study” : A Program for Reasoning with Propositions

The "Study" module implements an inquiry driven system that helps the user reason with expressions in propositional calculus.

The "Model" function within this program is a generic routine that implements a type of interpreter for propositional calculus. It takes in a proposition expressed in a particular syntax for propositional calculus and generates a data structure that is tantamount to the Disjunctive Normal Form (DNF) of the proposition. I will use the function notation "DNF(P)" and "Model(P)" to indicate the output of this routine for the proposition P. The DNF of a proposition P, as expressed in the data structure Model(P), is in a sense the clearest expression of the proposition P relative to the particular class of purposes that are embodied in a given interpreter.

The Study module contains several functions which compute different kinds of normal forms for propositions. These procedures constitute "modelers" or "interpreters" of propositional syntax in the sense that they generate the logical "models" or satisfying "interpretations" of propositions.

Any procedure that computes a normal form exemplifies an important kind of inquiry driven system. The dimension of value, or motivation, associated with the process can be regarded as a measure of "clarity". In computing a normal form the interpreter passes from an arbitrary representation of an indicated objective, one that can be as obscure as possible within the bounds of acceptable syntax, to a standardized formulation, one that manifests a patently clear and readily readable expression of the same objective. Thus, the operation is one that preserves meaning while maximizing clarity and ease of application.

In computing a normal form the system passes from an arbitrarily obscure representation of a propositional objective to a maximally clear expression of the same objective.

Need to clarify that a normal form is defined relative to a particular class of purposes or questions. For example, a sorted list is a normal form for questions about the multiplicity of items on the list, that is, about the existence and the number of occurrences of given items on the list.

It needs to be understood that the cpncept of a canonical form is defined relative to a particular purpose, a purpose which is embodied in a particular interpreter, or which a particular interpreter is intended to realize. Often this purpose can be expressed as a task of answering a particular class of questions about the object domain.

For the purposes of this discussion, I will draw a distinction between "canonical forms" and "normal forms". Distinquish canonical form in a semantic equivalence class, the intentional concept, from normal form of a transformation, the operational concept. A canonical form is an expression that is especially well suited to represent its equivalence class. A normal form is a fixed point of a grammatical transformation, that is, a stable point of a rewrite procedure that acts on the space of expressions. When the intentional canon/ canonical intention is rendered operational/ put into operation by a particular interpreter, then the two notions coincide, but only then.

To illustrate how the Model program actualizes an inquiry process, I will treat two examples in detail, …

Example 1:  P(x, y)  =
"x implies y".

Table 101.1  Standard Truth Table for P(x, y)
x	y	P
1	1	1
1	0	0
0	1	1
0	0	1

Table 101.2  Variant Truth Table for P(x, y)
P
x	y	1
x	(y)	0
(x)	y	1
(x)	(y)	1

Table 101.3  Model Tree for P(x, y)

___.____ x ___ y     *
|     |
|     |____(y)    -
|
|____(x)___ y     *
|
|____(y)    *

Table 102.1  Logical Input for P(x, y)
File:  "P.log"	Translation
( x ( y ))	 Not x without y.

Table 102.2  Model Output for P(x, y)
File:  "P.mod"	Model Value
x
y *	*
(y ) -	-
(x ) *	*

Table 102.3  Tenor Output for P(x, y)
File:  "P.ten"	Model Count
x
y *	1
(x ) *	2

Table 102.4  Disjunctive Normal Form for P(x, y)
DNF	Translation
((    x    y	 Either x and y
)(  ( x )	 or not x
))	 .

Table 103.1  Structure of the Sign Relation Rel(P)
Object	Sign	Interpretant
o1	s1	s2
o2	s1	s2
o3	s1	s2
o1	s2	s3
o2	s2	s3
o3	s2	s3
o1	s3	s3
o2	s3	s3
o3	s3	s3

Table 103.2  Contents of the Sign Relation Rel(P)
Element	 Description
o1	 Point " x  y "   =   <1, 1>
o2	 Point "(x) y "   =   <0, 1>
o3	 Point "(x)(y)"   =   <0, 0>
s1	 Parse "(x (y))"
s2	 Parse "(x y, (x))"
s3	 Parse "(x (y, ()(y)), (x))"

Example 2:  Q(x, y, z)  =
"just one false of x, y, z".

Table 104.1  Standard Truth Table for Q(x, y, z)
x	y	z	Q
1	1	1	0
1	1	0	1
1	0	1	1
1	0	0	0
0	1	1	1
0	1	0	0
0	0	1	0
0	0	0	0

Table 104.2  Variant Truth Table for Q(x, y, z)
Q
x	y	z	0
x	y	(z)	1
x	(y)	z	1
x	(y)	(z)	0
(x)	y	z	1
(x)	y	(z)	0
(x)	(y)	z	0
(x)	(y)	(z)	0

Table 104.3  Model Tree for Q(x, y, z)

___.____ x ___ y ___ z     -
|     |     |
|     |     |____(z)    *
|     |
|     |____(y)___ z     *
|           |
|           |____(z)    -
|
|____(x)___ y ___ z     *
|     |
|     |____(z)    -
|
|____(y)___ z     -
|
|____(z)    -

Table 105.1  Logical Input for Q(x, y, z)
File:  "Q.log"	Translation
( x , y , z )	 Just one false
among x, y, z.

Table 105.2  Model Output for Q(x, y, z)
File:  "Q.mod"	Model Value
x
y
z -	-
(z ) *	*
(y )
z *	*
(z ) -	-
(x )
y
z *	*
(z ) -	-
(y ) -	-

Table 105.3  Tenor Output for Q(x, y, z)
File:  "Q.ten"	Model Count
x
y
(z ) *	1
(y )
z *	2
(x )
y
z *	3

Table 105.4  Disjunctive Normal Form for Q(x, y, z)
DNF	Translation
((    x    y  ( z )	 Either  x  &  y  & -z
)(    x  ( y )  z	   or    x  & -y  &  z
)(  ( x )  y    z	   or   -x  &  y  &  z
))	 .

Table 106.1  Structure of the Sign Relation Rel(Q)
Object	Sign	Interpretant
o1	s1	s2
o2	s1	s2
o3	s1	s2
o1	s2	s3
o2	s2	s3
o3	s2	s3
o1	s3	s4
o2	s3	s4
o3	s3	s4
o1	s4	s4
o2	s4	s4
o3	s4	s4

Table 106.2  Contents of Rel(Q):  Objects
Element	 Description
o1	 Point " x  y (z)"   =   <1, 1, 0>
o2	 Point " x (y) z "   =   <1, 0, 1>
o3	 Point "(x) y  z "   =   <0, 1, 1>

Table 106.3  Contents of Rel(Q):  Signs
Element	 Description
s1	 Parse "(x, y, z)"
s2	 Parse "( x (y, z)
,(x) y  z
)"
s3	 Parse "( x ( y (z)
,(y) z
)
,(x)( y  z
,(y)()
)
)"
s4	 Parse "( x ( y ( z ()
,(z) *
)
,(y)( z  *
,(z)()
)
)
,(x)( y ( z  *
,(z)()
)
,(y)()
)
)"

Table 107.1  Normal Form Expansion of Q(x, y, z):  Version 1
Sign	 Expression	 Translation
s1	 (x, y, z)	 Just one false of x, y, z
s2	 ( x (y, z)	 Either x & (y, z)
,(x) y  z	   or  -x &  y  z
)
s3	 ( x ( y (z)	 Either x & either y & (z)
,(y) z	              or  -y &  z
)
,(x)( y  z	   or  -x & either y &  z
,(y)()	              or  -y & false
)
)
s4	 ( x ( y ( z ()	 Either x & either y & either z & 0
,(z) *	                         or  -z & 1
)
,(y)( z  *	              or  -y & either z & 1
,(z)()	                         or  -z & 0
)
)
,(x)( y ( z  *	   or  -x & either y & either z & 1
,(z)()	                         or  -z & 0
)
,(y)()	              or  -y & false
)
)

Table 107.2  Normal Form Expansion of Q(x, y, z):  Version 2
Sign	 Expression	 Translation
s1	 (x, y, z)	 Just one false of x, y, z.
s2	 ( x (y, z)	 Either x & (y, z)
,(x) y  z	 or not x &  y  z
)	 .
s3	 ( x	 Either x &
( y (z)	   either y & (z)
,(y) z	   or not y &  z
)	   ;
,(x)	 or not x &
( y  z	   either y &  z
,(y)()	   or not y & false
)	   ;
)	 .
s4	 ( x	 Either x &
( y	   either y &
( z ()	     either z & false
,(z) *	     or not z & true
)	     ;
,(y)	   or not y &
( z *	     either z & true
,(z)()	     or not z & false
)	     ;
)	   ;
,(x)	 or not x &
( y	   either y &
( z  *	     either z & true
,(z)()	     or not z & false
)	     ;
,(y)()	   or not y & false
)	   ;
)	 .


### Discussion and Development of Objectives

#### Objective 1a : Propositions as Types

In this component I investigate an important relationship that exists between two kinds of formal systems, called applicational calculi (AC's) and propositional calculi (PC's).

Expressions in an applicational calculus are called "terms" and are built up from a supply of primitive symbols called "basic terms" through the use of a binary operation called "application".

Expressions in a propositional calculus are called "propositions" and are built up from a supply of primitive symbols called "basic propositions" through the use of a stock of k ary operations called "connectives".

Exact formalization of symbolic calculi is absolutely necessary, especially if we want computers to serve as interpreters, or at least to lighten the burdens of interpretation by taking up the bit parts of formal routines. Because the problem environments where calculi develop show no signs of stopping in their growing complexity, it becomes inevitable that we turn to computers as auxiliary interpreters of formal systems, to secure their operational significance and manage the increasing complications of their practical use. But a formalized syntax, however necessary, is not enough to demonstrate utility.

A calculus is never a finished object, complete in itself, but a tool shaped to the end of interpretation.

I am using the word "interpretation" to denote the whole complex of activities through which signs acquire practical meaning. For human beings the process of interpretation is a largely automatic and usually unanalyzed affair, but it can also be highly flexible and unusually adaptive. Human language users or symbol manipulators have powers they hardly reflect on and barely understand, to entertain novel associations between signs and whatever it is that signs convey, to examine habitual assumptions about the meaning of symbols in practice.

One person can simply invite another to entertain new associations between signs and ideas or to examine old assumptions about their meaning in practice, and the other is somehow able to comply, if only for the sake of experiment and argument. But the need to supply a formal system with a computational basis, involving exact syntax, effective semantics, and computerized "pragmatics" (that is, a computer supported operational basis) requires us to analyze the process of interpretation in minute detail and on new grounds.

In use, AC's and PC's take on meaning according to a variety of interpretive rules. I am adopting an interpretation on either side that highlights the relation of interest between these two kinds of calculi and that brings the intended correspondence into sharper relief.

In both kinds of calculus the primitive symbols are distinguished as "constants" and "variables". A constant is a name for a definite object of thought, and is intended to maintain a fixed meaning throughout a given discussion. A variable is a symbol of indefinite reference, or a token without a pre assigned meaning, but is used as a site for the substitution of other expressions or as a placeholder for a multitude of conceptual objects and logical values.

Semantics. Meanings are provided or attached to symbols by means of:

1. Contexts of occurrence: the facts or rules of distribution.

2. Action induced on other symbols by means of rewrite rules:

generators and relations, or paraphrastic definitions.

3. Synonymy: membership in semantic equivalence classes.

4. Arbitrary fiat, external designation, or special convention.

#### Objective 1b : Proof Styles and Developments

${\displaystyle <\cdots >}$

#### Objective 1c : Interpretation and Authority

${\displaystyle <\cdots >}$