Inquiry Driven Systems : Part 6

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

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6. Reflective Interpretive Frameworks

??? The rest of this Section ???, continuing the discussion of formalization in terms of concrete examples and extending over the next 50 ??? Subsections ???, details the construction of a "reflective interpretive framework" (RIF).  This is a special type of sign theoretic setting, illustrated in the present case as based on the sign relations A and B, but intended more generally to constitute a fully developed environment of objective and interpretive resources, in the likes of which an "inquiry into inquiry" can reasonably be expected to find its home.

This Subdivision of the text begins by presenting an outline of the developments ahead, working through the motivation, the construction, and the application of a RIF that is broad enough to moderate the dialogue of A and B.

The first fifteen Sections (§§ 1 15) deal with a selection of preliminary topics and techniques that are involved in approaching the construction of a RIF.  The topics of these sections are described in greater detail as follows:

The first section (S 1) takes up the phenomenology of reflection.  The next three sections (§§ 2 4) are allotted to surveying the site of the planned construction, presenting it from three different points of view.  An introductory discussion (S 2) presents the main ideas that lead up to the genesis of a RIF.  These ideas are treated at first acquaintance in an informal manner, located within a broader cultural context, and put in relation to the ways that intelligent agents can come to develop characterictic belief systems and communal perspectives on the world.  The next section (S 3) points out a specialized mechanism that serves to make inobvious types of observation of a reflective character.  The last section (S 4) takes steps to formalize the concepts of a "point of view" (POV) and a "point of development" (POD).  These ideas characterize the outlooks, perspectives, world views, and other systems of belief, knowledge, or opinion that are employed by agents of inquiry, with especial regard to the ways that these outlooks develop over time.

A further discussion (S 5), in preparation for the task of reflection, identifies three styles of linguistic usage that deploy increasing grades of formalization in their approaches to any given subject matter.

In the next three sections (§§ 6 8), the features that distinguish each style of usage are taken up individually and elaborated in detail.  This is done by presenting the basic ideas of three theoretical subjects that develop under the corresponding points of view and that exemplify their respective ideals.  The next three sections (§§ 9 11) take up the classes of higher order sign relations that play an important role in reflexive inquiries and then apply the battery of concepts arising with higher order sign relations to an example that anticipates many features of a realistic interpreter.  In the light of the experience gained with the foregoing styles and subjects, the next three sections (§§ 12 14) are able to take up important issues regarding the status of theoretical entities that are needed in this work.

Finally (S 15), the relevance of these styles, subjects, and issues is made concrete by bringing their various considerations to bear on a single example of a formal system that serves to integrate their concerns, namely, "propositional calculus".

A point by point outline follows:

§ 1.	An approach to the phenomenology of reflective experience, as it bears on the conduct of reflective activity, is given its first explicit discussion.

§ 2.	The main ideas leading up to the development of a RIF are presented, starting from the bare necessity of applying inquiry to itself.  I introduce the idea of a "point of view" (POV) in an informal way, as it arises from natural considerations about the relationship of an immanent "system of interpretation" (SOI) to a generated "text of inquiry" (TOI).  In this connection, I pursue the idea of a "point of development" (POD), that captures a POV at a particular moment of its own proper time.

§ 3.	A Projective POV

§ 4.	The idea of a POV, as manifested from moment to moment in a series of POD's, is taken up in greater detail.  

A formalization for talking about a diversity of POV's and their development through time is introduced and its consequences explored.  Finally, this formalization is applied to an issue of pressing concern for the present project, namely, the status of the distinction between dynamic and symbolic aspects of intelligent systems.

§ 5.	The symbolic forms employed in the construction of a RIF are found at the nexus of several different interpretive influences.  This section picks out three distinctive styles of usage that this work needs to draw on throughout its progress, usually without explicit notice, and discusses their relationships to each other in general terms.  These three styles of usage, distinguished according to whether they encourage an "ordinary language" (OL), a "formal language" (FL), or a "computational language" (CL) approach, have their relevant properties illustrated in the next three sections (§§ 26 28), each style being exemplified by a theoretical subject that thrives under its guidance.

§ 6.	For ease of reference, the basic ideas of group theory used in this project are separated out and presented in this section.  Throughout this work as a whole, the subject of group theory serves in both illustrative and instrumental roles, providing, besides a rough stock of exemplary materials to work on, a ready array of precision tools to work with.

Group theory, as a methodological subject, is used to illustrate the "mathematical language" (ML) approach, which ordinarily takes it for granted that signs denote something, if not always the objects intended.  It is therefore recognizable as a special case of the OL style of usage.

To the basic assumption of the OL approach the ML style adds only the faith that every object one desires to name has a unique proper name to do it with, and thus that all the various expressions for an object can be traded duty free and without much ado for a suitably compact name to denote it.  This means that the otherwise considerable work of practical computation, that is needed to associate arbitrarily obscure expressions with their clearest possible representatives, is not taken seriously as a feature that deserves theoretical attention, and is thus ignored as a factor of theoretical concern.  This is appropriate to the mathematical level, which abstracts away from pragmatic factors and is intended precisely to do so.

More instrumentally to the aims of this investigation, and not entirely accidentally, group theory is one of the most adaptable of mathematical tools that can be used to understand the relation between general forms and particular instantiations, in other words, the relationship between abstract commonalities and their concrete diversities.

§ 7.	The basic notions of formal language theory are presented.  Not surprisingly, formal language theory is used to illustrate the FL style of usage.  Instrumentally, it is one of the most powerful tools available to clear away both the understandable confusions and the unjustifiable presuppositions of informal discourse.

§ 8.	The notion of computation that makes sense in this setting is one of a process that replaces an arbitrary sign with a better sign of the same object.  In other words, computation is an interpretive process that improves the indications of intentions.  To deal with computational processes it is necessary to extend the pragmatic theory of signs in a couple of new but coordinated directions.  To the basic conception of a sign relation is added a notion of progress, which implies a notion of process together with a notion of quality.

§ 9.	This section introduces "higher order" sign relations, which are used to formalize the process of reflection on interpretation.  The discussion is approaching a point where multiple levels of signs are becoming necessary, mainly for referring to previous levels of signs as the objects of an extended sign relation, and thereby enabling a process of reflection on interpretive conduct.  To begin dealing with this issue, I take advantage of a second look at A and B to introduce the use of "raised angle brackets" (< >), also called "supercilia" or "arches", as quotation marks.  Ordinary quotation marks (" ") have the disadvantage, for formal purposes, of being used informally for many different tasks.  To get around this obstacle, I use the "arch" operator to formalize one specific function of quotation marks in a computational context, namely, to create distinctive names for syntactic expressions, or what amounts to the same thing, to signify the generation of their godel numbers.

§ 10.	Returning to the sign relations A and B, various kinds of HO signs are exemplified by considering a selection of HO sign relations that are based on these two examples.

§ 11.	In this section the tools that come with the theory of higher order sign relations are applied to an illustrative exercise, roughing out the shape of a complex form of interpreter.

The next three sections (§§ 32 34) discuss how the identified styles of usage bear on three important issues in the usage of a technical language, namely, the respective theoretical statuses of "signs", "sets", and "variables".

§ 12.	The Status of Signs

§ 13.	The Status of Sets

§ 14.	At this point the discussion touches on an topic, concerning the being of a so called "variable", that issues in many unanswered questions.  Although this worry over the nature and use of a variable may seem like a trivial matter, it is not.  It needs to be remembered that the first adequate accounts of formal computation, Schonfinkel's combinator calculus and Church's lambda calculus, both developed out of programmes intended to clarify the concept of a variable, indeed, even to the point of eliminating it altogether as a primitive notion from the basis of mathematical logic (van Heijenoort, 355 366).

The pragmatic theory of sign relations has a part of its purpose in addressing these same questions about the natural utility of variables, and even though its application to computation has not enjoyed the same level of development as these other models, it promises in good time to have a broader scope.  Later, I will illustrate its potential by examining a form of the combinator calculus from a sign relational point of view.

§ 15.	There is an order of logical reasoning that is typically described as "propositional" or "sentential" and represented in a type of formal system that is commonly known as a "propositional calculus" or a "sentential logic" (SL).  Any one of these calculi forms an interesting example of a formal language, one that can be used to illustrate all of the preceding issues of style and technique, but one that can also serve this inquiry in a more instrumental fashion.  This section presents the elements of a calculus for propositional logic that I described in earlier work (Awbrey, 1989 & 1994).  The imminent use of this calculus is to construct and analyze logical representations of sign relations, and the treatment here focuses on the concepts and notation that are most relevant to this task.

The next four sections (§§ 16 19) treat the theme of self reference that is invoked in the overture to a RIF.  To inspire confidence in the feasibility and the utility of well chosen reflective constructions and to allay a suspicion of self reference in general, it is useful to survey the varieties of self reference that arise in this work and to distinguish the forms of circular referrals that are likely to vitiate consistent reasoning from those that are relatively innocuous and even beneficial.

§ 16.	Recursive Aspects

§ 17.	Patterns of Self Reference

§ 18.	Practical Intuitions

§ 19.	Examples of Self Reference

The intertwined themes of logic and time will occupy center stage for the next eight sections (§§ 20 27).

§ 20.	First, I discuss three distinct ways that the word "system" is used in this work, reflecting the variety of approaches, aspects, or perspectives that present themselves in dealing with what are often the same underlying objects in reality.

§ 21.	There is a general set of situations where the task arises to "build a bridge" between significantly different types of representation.  In these situations, the problem is to translate between the signs and expressions of two formal systems that have radically different levels of interpretation, and to do it in a way that makes appropriate connections between diverse descriptions of the same objects.  More to the point of the present project, formal systems for mediating inquiry, if they are intended to remain viable in both empirical and theoretical uses, need the capacity to negotiate between an "extensional representation" (ER) and an "intensional representation" (IR) of the same domain of objects.  It turns out that a cardinal or pivotal issue in this connection is how to convert between ER's and IR's of the same objective domain, working all the while within the practical constraints of a computational medium and preserving the equivalence of information.  To illustrate the kinds of technical issues that are involved in these considerations, I bring them to bear on the topic of representing sign relations and their dyadic projections in various forms.

The next four sections (§§ 22-25) give examples of ER's and IR's, indicate the importance of forming a computational bridge between them, and discuss the conceptual and technical obstacles that will have to be faced in doing so.

§ 22.	For ease of reference, this section collects previous materials that are relevant to discussing the ER's of the sign relations A and B, and explicitly details their dyadic projections.

§ 23.	This section discusses a number of general issues that are associated with the IR's of sign relations.  Because of the great degree of freedom there is in selecting among the potentially relevant properties of any real object, especially when the context of relevance to the selection is not known in advance, there are many different ways, perhaps an indefinite multitude of ways, to represent the sign relations A and B in terms of salient properties of their elementary constituents.  In this connection, the next two sections explore a representative sample of these possibilities, and illustrate several different styles of approach that can be used in their presentation.

§ 24.	A transitional case between ER's and IR's of sign relations is found in the concept of a "literal intensional representation" (LIR).

§ 25.	A fully fledged IR is one that accomplishes some measure of analytic work, bringing to the point of salient notice a selected array of implicit and otherwise hidden features of its object.  This section presents a variety of these "analytic intensional representations" (AIR's) for the sign relations A and B.

Note for future reference.  The problem so naturally encountered here, due to the "embarassment of riches" that presents itself in choosing a suitable IR, and tracing its origin to the wealth of properties that any real object typically has, is a precursor to one of the deepest issues in the pragmatic theory of inquiry:  "the problem of abductive reasoning".  This topic will be discussed at several later stages of this investigation, where it typically involves the problem of choosing, among the manifold aspects of an objective phenomenon or a problematic objective, only the features that are:  (1) relevant to explaining a present fact, or (2) pertinent to achieving a current purpose.

§ 26.	Differential Logic & Directed Graphs

§ 27.	Differential Logic & Group Operations

§ 28.	The Bridge : From Obstruction to Opportunity

§ 29.	Projects of Representation

§ 30.	Connected, Integrated, Reflective Symbols

The next seven sections (§§ 31 37) are designed to incrementally motivate the idea that a language as simple as propositional calculus, remarkably enough, can be used to articulate significant properties of n place relations.  The course of the discussion will proceed as follows:

§ 31.	First, I introduce concepts and notation designed to expand and generalize the orders of relations that are available to be discussed in an adequate fashion.

§ 32.	Second, I elaborate a particular mode of abstraction, that is, a systematic strategy for generalizing the collections of formal objects that are initially given to discussion.  This dimension of abstraction or direction of generalization will be described under the thematic heading of "partiality".

§ 33.	Third, I present an alternative approach to the issue of "degenerate", "defective", or "fragmentary" n place relations, proceeding by way of generalized objects known as "n place relational complexes".  Illustrating these ideas with respect to their bearing on sign relations the discussion arrives at a notion of "sign relational complexes", or "sign complexes".

In the next three sections (§§ 34 36) I consider a collection of "identification tasks" for n place relations.  Of particular interest is the extent to which the determination of an n place relation is constrained by a particular type of data, namely, by the specification of lower arity relations that occur as its projections.  This topic is often treated as a question about a relation's "reducibility" or "irreduciblity" with respect to its projections.  For instance, if the identity of an n place relation is completely determined by the data of its k place projections, then R is said to be "identifiable by", "reducible to", or "reconstructible from" its k place components, otherwise R is said to be "irreducible" with respect to its k place projections.

§ 34.	First, I consider a number of set theoretic operations that can be utilized in discussing these "identification", "reducibility", or "reconstruction" questions.  Once a level of general discussion has been surveyed enough to make a start, these tools can be specialized and applied to concrete examples in the realm of sign relations and also applied in the neighborhood of closely associated triadic relations.

§ 35.	This section considers the positive case of reducibility, presenting examples of triadic relations that can be reconstructed from their dyadic projections.  In fact, it happens that the sign relations A and B fall into this category of dyadically reducible triadic relations.

§ 36.	This section considers the negative case of reduciblity, presenting examples of "irreducibly triadic relations", or triadic relations that cannot be reconstructed from their lower dimensional projections or "faces".

§ 37.	Finally, the discussion culminates in an exposition of the so called "propositions as types" (PAT) analogy, outlining a formal system of "type expressions" or "type formulas" that bears a strong resemblance to propositional calculus.  Properly interpreted, the resulting "calculus of propositional types" (COPT) can be used as a language for talking about well formed types of n place relations.

§ 38.	Considering the Source

§ 39.	Prospective Indices : Pointers to Future Work

§ 40.	Interlaced with the structural and reflective developments that go into the OF and the IF is a conceptual arrangement called the "dynamic evaluative framework" (DEF).  This utility works to isolate the aspects of process and purpose that are observable on either side of the objective interpretive divide and helps to organize the graded notions of directed change that can be actualized in the RIF.

§ 41.	Elective and Motive Forces

§ 42.	Sign Processes : A Start

§ 43.	Reflective Extensions

§ 44.	Reflections on Closure

§ 45.	Intelligence => Critical Reflection

§ 46.	Looking Ahead : The Meta Issue

§ 47.	Mutually Intelligible Codes

§ 48.	Discourse Analysis : Ways and Means

§ 49.	Combinations of Sign Relations

§ 50.	Revisiting the Source

6.1. The Phenomenology of Reflection

This part of the discussion is fair to cast as the phenomenology of reflection.  It aims to amass the kinds of observations that extremely simple reflective agents, as a matter of principal and with a minimal of preparation, can make on the ebb and flow of their own reflective acts.  But this is not the kind of phenomenology that pretends it can bracket every assumption of a sophisticated or a theoretical nature off to one side of the observational picture, or thinks it can frame the description of reflection without the use of formal concepts, such as depend on the bracing and support of a technical language.

On the contrary, the brand of phenomenology being wielded here makes the explicit assumption that there are likely to be an untold number of implicit assumptions that contribute to and conspire in the framing of the picture to be observed, while it is precisely the job of reflective observation to detect the influence of these covertly acting assumptions.  Further, this style of phenomenology is deliberately set free of prior constraints on the choice of descriptive devices, since it can appeal to any formal means or any technical language that serves to articulate the description of its subject.

Certain things need to be understood about the aims, the scope, and the self imposed limits of this phenomenology, especially when it comes to the question of what it hopes to explain.  It is not the task of this phenomenology to explain consciousness but only to describe its course.  This it does by making an inventory of the "contents" that appear in consciousness and by delineating the relationships that appear among these contents.  Along the way, it must take into account, of course, that each moment of taking stock and each moment of charting relations needs to have its resulting list or map, respectively, realized as the content of a particular moment of consciousness.

Already, this lone requirement of the descriptive task raises a host of questions about what it means for something to be counted as a content of consciousness, and it leads, according to my present lights and aims, to a closer examination of a critical relationship, the logical relation "content of", taken abstractly and in general.  Since it does not appear that very extensive lists or very detailed maps can be "wholly realized" as contents within a limited field of consciousness, it is necessary to recognize an extended sense of "realization", where a list or a map can be "partially" or "effectively" realized in a content of consciousness if and when an indication, pointer, or sign of it is present in awareness.

In particular, this tack suggests that some things, that otherwise loom too large to fit within the frame of immediate awareness, can be treated as contents of consciousness, in the extended sense, if only an effective indication of them is present in awareness.  For instance, an effective indication of a larger text is a sign that can be followed to the next, and this to the next, and so on, in a way that incrementally leads to a traversal of the whole.  By extension, a list of contents of consciousness or a map of relations among these contents is "effectively realized" in a single content of consciousness if that content effectively points to it, and if the object to which it points has the structure of an object that pointedly reveals itself in time.  Given the evidence of the sign and the effective analysis of its object, a manifest of contents can be prized for the sake of the items it enumerates or the estates it maps, with each in due proportion to their values.  Both parts of this condition are needed, though, since knowing the name alone of a thing, even if it lends itself to knowing the thing, does not itself amount to knowing the thing itself.

The concepts with which a theory operates are not all objectivized in the field which that theory thematizes.

In short, my philosophical working hypothesis is concrete reflection, i.e., the cogito as mediated by the whole universe of signs.
		Ricoeur, The Conflict of Interpretations, [Ric, 166, 170]

This understanding of the task of phenomenology bears on three features of the approach to consciousness that I am charting here.

1.	It is under the heading of "description", especially as qualified by the adjective "effective", that the rationale of using mathematical models and the strategy of seeking computational implementations of these models can be found to successively fall.

2.	As a rule, I find it helps to avoid hypostatizing consciousness or self awareness as statically constituted entities, but to use the systematic notions of dynamic agency and developing organization.  However, in order to make connections with other approaches to phenomenology I need occasionally to mention concepts and even to make use of language that I would otherwise prefer to avoid.

3.	Finally, it is under the cumulative aims of effective description and systematic dynamics that the utility of sign relations is key.  Sign relations are the minimal forms of models that are capable of compassing all that goes on in thinking along with whatever it is that thinking relates to in all the domains that it orients toward.  The use of sign relations as models, as mathematical descriptions, and as computational simulations of what appears in reflecting on conduct is especially well suited to including in these models a description of what transpires in the conduct of reflection itself.

The type of phenomenology that is being envisioned here depends on no assured power of introspection but only on a modest power to reflect on conduct and thereby to give it a description.  These descriptions, all the better if they are inscribed in external media, can be examined with increasing degrees of detachment and have their consequences projected by deductive means.  In time, the mass of descriptions that accumulates with continuing experience and persistent reflection on conduct begins to constitute a de facto "model of behavior" (MOB).  In common regard this "prescribed code" or "catalog of procedure" (COP) can range from an empirical standard of comparison, through a provisional regulation, to a tentative ideal for future conduct.  However, the status that a COP or a MOB has when it starts out is not as important as its ability to test its prescriptions, along with their deductive and pragmatic implications, against the corpus of continuing observation, reflection, and description.

Reflection and consciousness no longer coincide.  ...

What emerges from this reflection is a wounded cogito, which posits but does not possess itself, which understands its originary truth only in and by the confession of the inadequation, the illusion, and the lie of existing consciousness.
		Ricoeur, The Conflict of Interpretations, [Ric, 172, 173]

It is pertinent at this point to draw a distinction between the power of reflection, that is claimed as a capacity crucial to inquiry, and what is likely to be confused with it, the presumptive power of introspection.  "Introspection", in the sole part of its technical meaning that leads to its being excluded from empirical inquiry, refers to an infallible, and thus incorrigible, power of observation that one is supposed to possess with respect to one's private experiences, matters over which there is imagined to be no higher court of appeal than one's own particular and immediate awareness.  But the horizon of experience that is plotted with regard to this static standpoint fails to reckon with the dynamic nature of an ongoing circumstance, that subsequent experience continually rides a circuit around its antecedents and ever constitutes a higher court for every proceeding and every precedent that falls within its jurisdiction.

The distinction that marks reflection and sets it apart from introspection is its own acknowledged fallibility, which involves its ability to be seen as false in subsequent reflections.  Naturally, this has an import for the status of reflection in empirical inquiry.  Paradoxically, its admission of fallibility is actually a virtue from the standpoint of making reflection useful in science.  If reflection on conduct leads to a description that cannot be falsified by any contingency of conduct, then that description is insufficient to specify any particular conduct at all.  This means one of several things about the description, either (1) it remains a condition of conduct in general, or (2) it resides as a part of a necessary logic at the bounds of all experience, or (3) it rests in a realm of metaphysics that abides, if anywhere, beyond the bounds of purely human experience and thus abscounds altogether from the sphere of empirical inquiry.

In this way the psyche is itself a technique practiced on itself, a technique of disguise and misunderstanding.  The soul of this technique is the pursuit of the lost archaic object which is constantly displaced and replaced by substitute, fantastic, illusory, delirious, and idealized objects.
		Paul Ricoeur, The Conflict of Interpretations, [Ric, 185]

One of the most difficult problems that arises for the phenonenology of reflection, and one that falls under the heading of "fallibility" in a markedly strong way, is the issue of systematic distortion.  Aside from the false idols that are deliberately constructed, there is another host of false images whose generation is so thoroughly systematic that only their lack of consciousness prevents them from being called "deliberate".  All the more naive projects of enlightenment, capitalized or not, are brought down by a failure to recognize this category of human frailty.

If the phenomenology of reflection that is developed and justified from this point on is not to be naive about this brand of fallibility, then it needs to constitute safeguards, a system of checks and balances, if you will, against it.  If no method of remediation can permanently arrest the perpetrator of these schemes from generating distractions in perpetuity, then at least one can hope for ways to arraign the forms of fallibility under various recognizable themes, so that their dangers can be avoided in the future.  In this vein, it is necessary to institute the study of those more opaque obstructions that limit the medium of investigation and to facilitate the analysis of those more refractory resistances to clear reflection, whose names are legion, but whose characters can be diversely noted under the themes of "obstruction", "resistance", the "shadow", the "unconscious", the "dark side of the enlightenment", or even better yet, the "underbrush of the clearing".

In the general scheme of things, the forms of distortion that remain peculiar to particular agents of reflection need garner to themselves nothing outside the incidental degrees of interest.  The best check to counter this species of distortion, to which the isolated individual is likely to fall prey, is the balance of cultural wisdom that is commonly stored up and invested in the living praxis of a reflective community.

It is only when the incidence of singular distortions is not damped out by the collective incitement of countermeasures, when the aggregation of local distortions is overlooked by the powers of a general reflection, when the flaws in the individual lights and mirrors of the scientific organon are not taken into account and duly compensated in the shape of the social "panopticon", or when the grinding accumulation and the precipitous mounting up of infinitesimal but significant deviations from accurate reflection are not met with an adequate power of oversight, one that can maintain solely the interests of community integrity at heart, that a truly false ideal begins to hold sway over the very perceptions of every specialized agent of reflection.

When these aberrations and astigmatisms develop unchecked, and when the strain to see things clearly reaches the point of breaking all the instruments thereof, then the most circumscribed faults, the distorted reflections of individual hypocrisy, the strange lack of insight and the missing sense of mutual reciprocity that manifest themselves in the most parochial forms of self interest, then all of these defects, and ills, and shocks begin to "pass through" to the collective strata, to be inherited and propagated by the highest levels of social oraganization, and then a systematic and widespread falsification of the whole conduct of society begins to pervade its view of itself.

On macroscopic scales of organization, with medium sized bodies and bodies of media that extend over considerable distances, with masses of activity that successfully propagate their own forms through vastening expanses of time, the general condition of thoughtfulness cancels out and compensates for all but the most singular of disturbances, namely, those that are peculiar to the microscopic realm of observation.  If the matter is regarded on this grander scale, then it is not hard to find a sufficient reason for the stubborn persistence of the cosmic order, and thus the desirable necessity of doing just this is never far from mind.  In the case of whole societies, a like reason is often enough to explain their inertia, their resistance, and their overall slowness to change.

If there is felt a need to devise an object explanation, a presumptive sources of troubles that is already compact, concrete, and thus confined enough to accuse, apprehend, and hopefully imprison on account of the mass's retarded potential, then resorting to a hypostasis posed in the form of an "archaic object" is a prototypical way of controlling anxiety, and it frequently, if not infallibly, can serve just as well as any other device on which to pin the common blame.  This highlights the question:  What sort of archaic object would account for the general malaise in a community whose dedication to inquiry has become root bound?

I wish to apply a determinate philosophical method to a determinate problem, that of the constitution of the symbol, which I described as an expression with a double meaning.  I had already applied this method to the symbols of art and the ethics of religion.  But the reason behind it is neither in the domains considered nor in the objects which are proper to them.  It resides in the overdetermination of the symbol, which cannot be understood outside the dialecticity of the reflection which I propose.
		Paul Ricoeur, The Conflict of Interpretations, [Ric, 175]

The archaic object of this global aimlessness, that informs the course of the general drift, that the total condition and the specific culture of inquiry revolve about in their orbits, as if they aim to be constantly accelerated toward it, but never quite manage to resolve their situation toward it, as if they fear to dissolve into it, is very likely nothing more than the whole community of interpretation itself, effectively realized as an object of its own devising.

The community of interpretation, whose currency funds the community of inquiry as a going enterprise within its fold, has sufficient reason to preserve itself in its present form as a valuable object, commodity, or resource.  But the dialectical nature of the process that is currently conducted between them, due in part to the dialectrical charges of the "-ionized" terms that pass for information between them.  A term of this charge splits the action from the end and shares it between the parties to an ambiguity, the active and passive objects that together comprise its full denomination.  This division of denotation forces interpretation to vacillate between the two extremes of meaning in a vain and eternal effort to rejoin their senses of value to the realm of the rendered and misspent coin, in hopes of regaining the meaning what was mint in their original condition.  The stowing away of one portion or the other drives the potential that drives both themselves and all the actions that they are meant to convey toward their designate and their destinate ends, but the unstable equilibrium that is their due, especially when it is permitted to be waged by uncontrolled forms of oppositional attraction, does not permit the dialogue to rest.  It continues to remain in doubt and does not fail to renew its ambivalence regarding the maintenance of any fixed form it happens to take, always wondering whether its present form is literally necessary, precisely sufficient, or whether it is but transiently and contingently convenient.  Accordingly and otherwise the whirl of dialogue, for all its own reasons, is always in imminent danger of wasting away into the echo of its own narcissism.

The problem arises of how to bring these systematic distortions under systematic control.  It helps to stand back a bit from the problem and to cast a somewhat wider net.  Accordingly, let the whole category of phenomena that are gathered around this issue be thematized under the family name of an "obstruction to inquiry" (OTI).  This includes as a subordinate genus the panoply of systematic distortions, generated by disingenuous reflections, that can be hypothesized to have their source in protecting the favored assumptions and defending the implicit claims of a particular status quo, no matter whether the implicated propositions are held to be the prerogatives of a privileged POV or whether they are delivered up to indictment as the prejudices of a more widely sanctioned world view.  The archetype of this behavior is appropriately addressed under the mythological or the psychological category of "narcissism".

It is important to note that the family OTI and the genus "narcissus" differ in the levels of hypothesis that are involved in their concepts, both in their speculative formation and in their provisional attribution.  The presence of an OTI is fairly easy to surmise from its distinguishing traits:  the dissipative conduct and the rambling course that affect the inquiry in question.  To the degree that the suspicion of its effect and the verification of its force can be assembled from superficial traces, this makes its maintenance supportable on circumstantial evidence alone.  In a phrase, one says that the wider hypothesis lies "nearer to nature" than the narrower construction, or that it makes its appearance closer to the purely phenomenal sphere.  In contrast, unraveling the precise nature of the obstruction requires a deeper investigation.  There is an additional hypothesis involved in guessing the source of the resistance, no matter how prevalent a particular genus of distortion is found and no matter how likely an individual species of explanation is in fact.

Within this wider setting it may be possible to focus more clearly on the species of threats to accurate reflection that need to be clarified here.  Already, besides the stigma of stubborn error that hangs over the whole refractory horde, there is a germ of paradox that hides within the very folds of this classification.  Namely, it is that the first obstacle one finds to reflection, and hence to every form of reflective inquiry, is a kind of narcissism or self love.  It begins naturally enough, ensconced in the not unnatural desire of every form of life to preserve itself in its present form.  But the simple desire to remain as is can be diverted into a blinded esteem of the self, one that admires its present condition only as reflected in the array of disingenuous reflections and contrived presentations that make up a fixed, idealized, and very selective image.  Finally and strangely enough, this unreflective form of narcissism even comes to prefer the simplistic and beautiful lies to the realistic forms that a veritable mirror would show.

The danger of narcissism, with respect to the prospects of a reflective inquiry, is not in the dynamic attractions and the realistic affections that a person or a society bears toward its truer self, and that in turn inform their respective bearings toward the selves they are meant to be, but in the static character of its attachment to a fixed, idealized, and partial image of that self.

Once again, the quality that distinguishes reflection from introspection, its fallibility, is a trait that sufficiently reflective agents can find reflected in their own conduct of reflection, and needless to say, their conduct in general.  This quality of fallibility, thus cognized and thus converted, that is, once its application to oneself is acknowledged and its consequences for one's experience are recognized, becomes a type of self recognizant character, an internalized trait that leads reflective agents to become more corrigible, more docile, and thus more educatable.  This makes it possible for reflective agents to build up their images of reality from scratch materials, to proceed through steps that are always revisable and edifiable, and to leave the finishing of their forms to the work of future editions.  In the final analysis, while this mannerism of aesthetic distance and tempered discretion prevents any affection or any impression from becoming too "immediate", in the strictest sense of that word, it is just this mode of detachment that assures the sensible image of its eventual remediation.

The nature and use of reflection in inquiry, as it currently appears, can be described as follows.  Reflection on conduct leads to a description of that conduct, posed in terms of a reflective image.  Over an interval of time or an extended period of investigation, these descriptive images are accumulated into exhaustive theories and compiled into compact models of the conduct in question.  To be useful in science, or empirical inquiry, these theories and models must be capable of being false with respect to their intentions, amenable to being tested in further experience, and subject to being amended on subsequent reflection.

In sum, the very feature of reflection that seems to be its chief defect, the fact that it can generate false images, casting reflections that are false to the actions they intend to represent and even leading to wholly distorted perspectives on the objectified scene of activity, is the very characteristic that saves its appearance in experience and the very trait that permits it to show its face at the court of inquiry, which all along admits that distortions acknowledged to be imperfect images can still be disclosed to subsequent experience and remedied in future reflections.

6.2. A Candid Point of View

This section discusses, in a general and informal way, the objectives inspiring and the requirements surrounding the elaboration of a RIF.  This is approached, in part, by taking up the intuitive notions of a "point of view" (POV) and a "point of development" (POD), as they stake out, respectively, the intellectual repertoire and history of a typical agent of inquiry.  Initially, these ideas serve in a familiar manner to characterize the intellectual skills and growth of agents, in particular, as they redound on the cultivation of the agents' reflective resources.  Increasingly, these concepts are subjected to formalization, partly by analyzing their relations to each other and gradually by relating their inherent structures and referent involvements to the already formalized concepts of objective frameworks, genres, and motifs.

As I reflect on signs and texts, I am led to enumerate more and more phenomena associated with the process of interpretation and with the models of it that I find in sign relations.  Some of the deepest and subtlest of these phenomena, at least, that I am able to observe and recount, take their theme from a certain "intermingling of categories" that is found at the basis of every real phenomenon.  This issue comes to prominence and makes itself evident as topic of inquiry whenever one tries to organize the original chaos of phenomena through the imposition of a suitable scheme of categories.

What is the typical outcome of setting out such a scheme for nature?  No sooner does one institute a provisional scheme of categories for organizing phenomena than one discovers every system with a stamp of reality to it steadfastly ignoring the lines of one's naive imagination.  And yet it soon becomes clear that this seeming "perversity of nature" arises from an error of attribution on the part of the mind that casts the aspersion.  Ultimately, it stems from the fact that every scheme of categories that the mind can forge and foist on nature, for instance, "sign" and "object", "self" and "other", remains, after all, the scene of a mere abstraction, implicating the "pallid" and the "shadowy" sides of the same dissention, but all the while circling about and turning on the complex but unitary reality that underlies the phenomenon in question.

In view of these complexities, that interfere with applying even the simplest of organizational paradigms to the material of signs and texts, it is necessary for me to pause a while and carefully contemplate how I can rehabilitate their use, at least, for the ends of this investigation.  First, I examine the distinction between "sign" and "object".  Then, I consider the duality between "self" and "other", or what amounts to the same thing, the relation between a "first person" and a "second person" POV.  In each case, the task is to discover how a distinction that seems so easy to subvert can ultimately be developed into a useful instrument of analysis and articulation.

There's nought but care on ev'ry han',
	In every hour that passes, O;
What signifies the life o man,
	An 'twere na for the lasses, O.
		Robert Burns, Green Grow the Rashes, O

Any object, anything grasped as a whole, can be a sign.  Indeed, the entire life of a person or a people can serve as sign unto itself or others and take on a significance all its own.  In converse fashion, every sign token is an object in the world.  In this role, a sign is forced to obey the ruling and relevant natural laws and empowered to take on a dynamics all its own.

In the contention between signs and objects, the answer initially given by the pragmatic theory of signs is that anything can potentially serve in any role of a sign relation.  In particular, the distinction between "sign" and "object" is a "pragmatic" distinction, a mark of use, not an "essential" distinction, a mark of substance.  This is the right answer as far as the beginning of the question goes, where it is the possible character of everything that is at issue.  The pragmatic approach makes it possible to begin an investigation that would otherwise be obstructed by a futile search for non existent essentials, as if it were necessary to divine them from prior considerations before any experience has been ventured and before a bit of empirical evidence has been collected.

Reason alone teaches us to know good and evil.  Therefore conscience, which makes us love the one and hate the other, though it is independent of reason, cannot develop without it.
		Rousseau, Emile

But the form of answer that is sufficient to begin a study is not the form of answer that is necessary to end it.  Even though it is useful for a general theory of signs to provide a patently indifferent form of answer at the preliminary phases of its investigation, this style of response is ultimately judged to be facile when it comes to questions about the good of a sign, the end of an inquiry, or the suitability of each thing to the role it is assigned.  In the end, an all purpose brand of conceptual scheme, allowing for the equipotential coverage of every conceivable option, however useful or necessary to the task, is likely to be found insufficient for wrapping up these goods and delivering them into the service of the mind.  Thus, by the round about way of this objection, one brings to mind the other meaning, the underlying nuance and the ultimate sense, of the word "object", which suggests the end, the goal, or the good of something.

Questions about the good of something, and what must be done to get it, and what shows the way to do it, belong to the "normative sciences" of aesthetics, ethics, and logic, respectively.  Aesthetic knowledge is a creature's most basic sense of what is good or bad for it, as signaled by the experiential features of pleasure or pain, respectively.  Ethical knowledge deals with the courses of action and patterns of conduct that lead to these ends.  Logical knowledge begins from the remoter signs of what actions are true and false to their ends, and derives the necessary consequences indicated by combinations of signs.

In pragmatic thought, the normative disciplines can be imagined as three concentric cylinders resting on their bases, increasing in height as they narrow, from aesthetics to ethics to logic, in that order.  Considered with regard to the plane of their experiential bases, logic is subsumed by ethics, which is subsumed by aesthetics.  And yet, in another sense, logic affords a perspective on ethics, while ethics affords a perspective on aesthetics.

That is about all I can say about normative considerations at this point.  Further discussion is put off until this text has developed either the intuitive insight or the theoretical power to say something more definite.

Because a sign, so far as it can tell in the time it passes, addresses an unknown future interpretant, that is, an indefinite futurity of potential responses, there is always an aspect of dialogue about the sign relation, especially insofar as it is subject to extension.  This is true no matter who, whether self or other, is ostensibly addressed by the sign or text at issue, and never mind what the chances are of a literal return in the communication.  In this regard, it is recognizance enough for a sign to be issued or a text to be written in anticipation of its future result.  And though it is never certain, it is always possible that the author of a text partially anticipates the use that others make of what is signed.

It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be.
		G.W. Leibniz, Theodicy, paragraph 360

	When these prodigies
Do so conjointly meet, let not men say
"These are their reasons", "they are natural",
For I believe they are portentous things
Unto the climate that they point upon.
		Julius Caesar:  Casca—1.3.28–32

Indeed it is a strange disposed time;
But men may construe things after their fashion,
Clean from the purpose of the things themselves.
		Julius Caesar:  Cicero—1.3.33–35

In order to recover the faculties supported by one's favorite categories and to maintain the proper use of their organizational schemes, it is incumbent on the part of the wary, conscientious, and duly circumspect schemer to recognize in every case how each part of the contention is implicated in the action of the other.  In this connection, a triumvirate of closely related aspects of sign relations comes to the fore:

1.	There is an aspect of "futurity", marking the openness of signs to interpretation and the extensibility of sign relations in multitudes of novel but meaningful ways.  This dimension of regard is staked out in anticipation of the possibility that perfectly fitting but previously unsuspected interpretants can be discovered within or added to any given sign relation, whether passed or present.

2.	There is a factor that contemporary theorists call "alterity", noting the quality of radical and reciprocal otherness that is involved in the dialogue of one self with another.  Besides its invocation of the wholly other, this term subsumes all the ways that one being can be alien and unknown to itself, and it even suggests the host of alterations, errors, deviations, distortions, and transmutations that accompany all acts of record keeping and interpretation.

3.	There is a feature that C.S. Peirce called "tuity", acknowledging the aspect of "thouness" or the prospect of a second person POV that is brought into play whenever one self addresses another.  Along with the perspective of a genuine other, this recognizes all the referrals and deferrals that an interpretive agent can make to a past, present, or potential self.

All of these dimensions of concern focus on the circumstance that signs, especially written or recorded signs, moderate a complexly integrated sort of relationship between self and other, or between "first person" and "second person" POV's, in such a way that they render the paired categories of each scheme inextricably involved in one another.

There are well known dangers of paradox, but not so well acknowledged risks of distortion, that arise in the interrogation of any reflection.  Although its outward signs are obvious, the source of the difficulty is remarkably difficult to trace.  Perhaps it can be approached as follows.  Without trying to say what consciousness is, I can still speak sensibly of its contents, and talk of their structures in relation to each other.  These contents, whether percepts or concepts or whatever, are all signs.  And so I can study the effects of reflection in the medium of its texts and develop a model of reflection as a process that evolves these texts.

What generally happens when one tries to model reflective consciousness and to formalize the reflective discourses that signify its public life?  In reaching for the available languages of logic and set theory, one is likely to use them as reductively as possible on the first attempt, and thus to state the relation of anything to awareness directly in terms of membership, in sum, by means of a globally overarching dyadic relation.  What does this picture of reflection pretend about the relation of the world to the mind, or conversely, the relation of awareness to anything?  Although it confuses the relation of "content" to "consciousness" with the relation of "object" to "concept", this degree of play in the imagery is a forgivable, occasionally useful, and a probably inescapable analogy.  In any case, it does not amount to the most serious distortion in the picture as a whole.

What is really wrong with the dyadic picture of reflection is the fact that it treats both of the relations it surveys, of minds to ideas and of ideas to things, on the model of a consummation and a containment, as if to place everything being related in an all embracing hierarchy and in opposition to all forms of reciprocal participation among its entities.  This image renders a consciousness of contents and a concept of objects each in the likeness of a set and its elements, rather than presenting them as they most likely are, a relationship of systems or agents and of texts or signs to the ideals or objects that motivate them, constituting mutually embracing forms of participation in a unified textual activity.  In all, the initial attempt at explaining reflection lays it out according to a conception that grasps it prey, and loses the creature in the process, rather than a conception that releases the potential of what it imprisons.

One of the reasons for bringing the pragmatic theory of signs to bear on this discussion is deal with just these problems, constellated by the need for reflection and made acute by the defects of the dyadic picture.  By means of triadic sign relations, and given a capacity to create and modify the interpretant signs that fill out its original set of semantic equivalence classes, an interpretive agent has the "elbow room" needed to stand aside from the ongoing process of interpretation, to reflect on its present determinants, and to consider its possible developments.

An inquiry that cannot clearly and completely comprehend itself as an object can at least inquire into the succession of signs that record its progress.  The writer of a text can use that text to describe, at least partially, the process of writing and using it so.  The reader of a text can understand that text to describe, at least partially, the process of reading and understanding it so.  Further, a discussion can generate a record that describes, more than just the transient proceedings of that discussion, the principles and parameters that determine its creation.  In each of these ways, a text can address the qualities that determine its intended character, comment on the context in which it takes a part, and act on behalf of its pretended objectives.

The procedural distinction just recognized, between the passing traces of a process and the permanent determinants of its generic character, informs a significant issue, on which is staked nothing less than the empirical feasibility of an inquiry into inquiry.  From this point on, a certain figure of speech can be used to mark this distinction, when it is relevant to the course of discussion, and to signal a deliberate turn in the direction of consideration, when the corresponding exchange of its dialectical roles is intended.  According to the nuances of this paradigm, one can distinguish a process intended in the "substantive generative" sense from a process intended in the "genitive gerundive" sense, and address oneself selectively, at turns, to the "process that achieves" versus the "process of achieving" any contemplated activity or result.

An inquiry at such a point of development that it cannot entirely grasp its ongoing process of inquiry as an object of thought, namely, as the "process that inquires", can at least try to capture a representative sample of the signs that record its "process of inquiring".  Speaking metaphorically and with the proper apology, every thus generated and thus collected "text of inquiry" (TOI) can be addressed as a partial reflection of the generative process of inquiry.  Moreover, it is not irredeemably illegitimate to say that a TOI can partly describe itself, since this merely personifies the circumstance that a process of inquiry can describe itself partly in the form of a TOI.

O jest unseen, inscrutable, invisible
As a nose on a man's face or a weathercock on a
	steeple.
My master sues to her, and she hath taught her suitor,
He being her pupil, to become her tutor.
O excellent device!  Was there ever heard a better?—
That my master, being scribe, to himself should write
	the letter.
		Two Gentlemen of Verona:  Speed—2.1.127–132

When I write out my thinking in the form of a text, a critical thing happens:  It faces me as the thought of another, and I start to think of what it says as though another person had said it.  Almost unwittingly, a critical process comes into play.  In regarding the text as expressing the thought of another, I begin to see it from different POV's than the one that led to its writing.  As I find my own inquiry reflected in one or another TOI, it addresses me afresh as the question of another and I encounter it again as a novel line of investigation.  This time around, though, the topic of concern and the style of expression become subject to directions of criticism that would probably not occur to me otherwise, since the angles of attack permitting them do not open up on their own, neither on first thinking nor ever, most likely, while merely speaking.  This can be the beginning of critical reflection, but it can also stir up destructive forms of interference that inhibit and obstruct the very flow of thought itself.

If I can be granted the license to continue saying that a text says this or that about itself when what I really mean is that a person or process employs its text to say the corresponding thing about itself or its text, then I can begin to introduce a variety of descriptive terms and logical tools into this text that can be used to talk about what this or another TOI "thinks" or "believes" at various points in its development, that is, in order to detail what I or its proper author thinks or believes at the corresponding points of discussion.

Fourteen, a sonneteer thy praises sings;
What magic myst'ries in that number lie!
Your hen hath fourteen eggs beneath her wings
That fourteen chickens to the roost may fly.
Fourteen full pounds the jockey's stone must be;
His age fourteen – a horse's prime is past.
Fourteen long hours too oft the Bard must fast;
Fourteen bright bumpers – bliss he ne'er must see!
Before fourteen, a dozen yields the strife;
Before fourteen – e'en thirteen's strength is vain.
Fourteen good years – a woman gives us life;
Fourteen good men – we lose that life again.
What lucubrations can be more upon it?
Fourteen good measur'd verses make a sonnet.
		Robert Burns, A Sonnet Upon Sonnets

One of the main problems that the present TOI has to address is how a TOI can address the problems of self reference that an inquiry into inquiry involves.  If a sonnet can say something true about sonnets, then a TOI, far less limited in the number and measure of its lines, ought to be able to say something true about TOI's in general, unless the removal of these limitations takes away the only things whereof and whereby it has to speak, the ends and means of its own form of speech.

Using the pragmatic theory of signs, the forms of self reference that have to be addressed in this project can be divided into two kinds, or classified in accord with two dimensions of referential involvement.  Roughly speaking, reference in the broader sense can suggest either a denotative reference to an object or a connotative reference to a sense.  Therefore, a projected self reference can be classified according to the ways that its components of reference propose to recur on themselves:  how much pretends to be a self description along denotative lines and how much purports to be a self address in the connotative direction.

Under suitably liberalized conditions of interpretation, then, what is meant by "a self referent text", whether one that denotatively describes or connotatively addresses itself?  Apparently, it can mean a text that addresses, describes, refers to, or speaks to either one of two issues:  (1) the outwardly passing features of its own succession of signs, or (2) the inwardly relied on properties of its own regenerative sources.

It is one thing for a text to be generated according to the laws laid down in another.  This takes place, for example, in devising or following a proof according to the axioms and rules of inference that are recorded in a proof system.  It is another thing entirely for a text or a corpus of texts to derive or induce the very principles of their own generation and then return to disclose the process of derivation or induction itself according to which the whole text or corpus is divined or drafted.

What the discussion of reflection has so far been leading up to, if I stop to reflect on what might be the implicit project behind its scheme of development, is tantamount to a "monadology", a project of a complete and total provision for a system of perfect but virtual self reflections.  But I suspect that such a project is unsupportable in reality outside the realm of infinite resources and pre established harmonies, while my present aim is to see what can be done with finite and empirical means.  A monadology, if it entertains itself with any form of investigation at all, addresses the task as a sheer masquerade, styling its inquiry after the fashion of a "complete logical analysis" (CLA).

On principle, there is nothing inherently the matter with the form of the CLA itself, but it does not embody all by itself the spirit of suspense that accompanies a genuine human inquiry.  A real inquiry cannot know before it starts what the answer is and how the end will be achieved, and it cannot, if it wishes, merely trick out the foils of an already completed and pre arranged survey, parading them as a passing series of plotted and transient complications in the guise of an honest quest.  Some types of completeness are far more complete than others, however.  Taken with respect to a properly limited and workably modest context, and treated as "relatively complete" rather than "absolutely complete", the ideal substrate of the CLA forms a suitably plastic material for modeling many forms of concretely reasonable inquiry.

Invoked with a spirit of moderation, the idealized model envisioned in the CLA can nevertheless serve as virtual guide for practical inquiries, highlighting the space of conceivable models and projecting a standard against which to measure every approximate, likely, and partial result.  An inquiry of this self controlled kind, that considers in addition the logical alternative to every hypothesis it finds itself making, if it is addressed appropriately to the conditions of its constraining resources, can achieve complete success only within a tightly circumscribed sphere of action.  Thus, the ideal of CLA informs a workable genre of inquiry, but the experimental variations that it enables and permits an agent to contemplate are bound up with the experiences that can be expressed in a language of finite and discrete signs, and exactly to the extent that they are in fact expressible.

In principle and in effect, an inquiry pushing the envelope of CLA is restricted to a "universe of limited marks".  For all practical purposes, it must keep its remarks to a finite universe of discourse, and a small one at that.  Beyond these bounds, every inquiry is forced to take its chances on a pure hypothesis, unmitigated by any consideration of the opposite case.  Communities of inquiry, however, are likely to embody a distribution of individual inquiries that have placed their bets on opposing options.  Diversity of interpretation leads to disjunctions of opinion that can render many heads much smarter than one, but it also engenders forms of disagreement, discord, and duplicity that, for all their practical inevitability, are not essentially necessary.

Engaging in practical inquiry in a community of partially informed and presumptively constrained reasoners, then, is a task that leads to the recognition of several critical needs, not only for ways of synthesizing fragmentary interpretations of the presumptive truth and for reconciling divergent accounts of the objective world, but also for strategies that make these methods of negotiating differences and resolving conflicts more commonly available to all the inquirers in a putative community.  Finally, an agent attempting to be reasonable under these conditions needs to be permitted to exercise a number of "editorial" prerogatives.  For example, there needs to be a way to "retract projections", that is, to recognize the alienated aspects of oneself that appear to crop up in others and to reconsider the rejected options for thought and action that nevertheless are capable of leading to bona fide values.

In a striking analogy with visual perception, it is the reflections in the ambient flow of energy that make it possible for one complication in the medium, a living being, to see another variation in the density of the medium, animate or otherwise, as an object.  Reflection permits one to render an experience as due to a separate entity, to regard its occasion as the appearance of an object, and to respond to its cause as a reality.  The analogy is broken at the junctures where an agent attributes these reflections to the passive "reflectances" of the object itself rather than perceiving them as the active responsibility of every participant in the process as a whole.

In accord with this visual analogy, two factors frustrate the prospects of indefinitely extending and smoothly finishing any project of inquiry that works in a medium of CLA:

1.	The "transparent obstruction" (TO), or "obstacle of transparency", is due to an initial inability to discover and to render visible every assumption, category, or distinction that one automatically and implicitly acts according to.

2.	The "opaque obstruction" (OO), whether it presents itself in the guise of an obvious or an obscure obstacle, arises on account of a final incapacity to consider both sides of every question posed.  This can amount to either one of two shortcomings:  (1) failing to identify a logical alternative to every presumption or thesis that one identifies with, or (2) failing to evaluate a logical alternative to every assumption or hypothesis that one does in fact identify.

In short, a "finite information creature" (FIC) is required to keep the contents of its forms within the range of a definite set of figures and to rest the forms of its contents within the scope of a certain cast of characters.  To be sure, these are precisely the characters that can be modeled and the figures that can be cut within a circumscribed theater of operations that everyone calls a "partial logical analysis" (PLA).

6.3. A Projective Point of View

A necessary connection between signs and reflection gives the TOI its critical function as a transitional object in the development of inquiry.  In the form of a TOI, I address my reflection as if it were the reflection of another.  On the off chance that it renders me a bit more critical, as I eye both its sources of authority and its styles of presentation, I can regard the record of this reflection as a partially alienated object, an artifact of unknown origin, or a work of uncertain provenance.  And so the very existence of a sign, that takes after another in a search for its meaning and ultimately takes its place in tracing the traces of that process of inquiry, is intimately bound up with the act of reflection.

There is, moreover, a connection between the act of reflection and the psychological mechanism called "projection" that is useful to notice here.  As it happens in practice, the effect of reflection is frequently achieved, not directly, by means of a deliberate effort to observe and to evaluate one's own conduct, but more indirectly, through the initial observation and the subsequent criticism of another's behavior, finally followed up by the often delayed afterthought and usually reluctant insight that the properties ascribed to the other's behavior can also apply to one's own.

The relationship between the isolated components of behavior in this sort of "projective" situation amounts to a familiar kind of sign relation.  In regard to the properties possessed in common, the other's pattern of behavior is an icon, at first unrecognized, of one's own form of conduct.  The introspective act of recognizing and assimilating the significance of such a relationship is referred to as "retracting" or "re owning" the projected attributes and descriptions.  To sum things up in these terms, the retraction of a projection can bring about, in its composite fashion, the ultimate effect of a critical reflection, namely, the elicitation and application of a valid description to one's own conduct.

Before the usefulness of this insight can be appreciated, it is necessary to resolve an interdisciplinary conflict over the use of the term "projection" and to sort out the relationship between the psychological and the mathematical concepts of "projection".

O time, thou must untangle this, not I.
It is too hard a knot for me t'untie.
		Twelfth Night:  Viola—2.3.39-40

There are a couple of contingencies surrounding the trials of learning from one's own experience, issuing from and bearing on the complexity of that very experience, that appear to be tangled up with each other.  Echoing the mythology of the Gordian knot, the Herculean Hydra, the Laocoonian serpert, and the Persean Medusa, each of which accounts of perverse polymorphism seems to reflect a variant aspect but to capture a sheer fragment of the underlying archetype, these two factors can be addressed by means of the following allegory:

1.	The Knot.  It is frequently difficult to learn anything at all from the encounter with one's own experience, especially while one is still faced with the full complexity of that experience.

2.	The Knife.  One tends to establish a personal array of mental or conceptual "frames", "planes", or "sections" that one can reliably and reductively "chart", "map", or "project" one's experience on.

The relationship between these two factors is such that the Knot leads to the Knife as its adaptive or expedient remedy, but that the Knife affords only a transitory relief for the problems bound up in the Knot, and further, an excessive reliance on any fixed array of armaments and stratagems under the emblem of the Knife has the contrary tendency to worsen the troubles experienced under the category of the Knot.

Thus, it is fair to say that the difficulty of learning from the full complexity of one's own experience is a problem condition that partly leads to and partly arises from the very configurations of artificial sections and arbitrary coordinates that one contrives to project one's experience on and to judge one's experience by, respectively.  Although one's idealizations, simplifications, and other pet schemes of reductive representation can serve to render one's experience initially manageable, they can ultimately and adversely interfere with seeing the obvious.

In this setting, it is possible to bring about an accommodation between the mathematical and the psychological concepts of "projection" and to reconcile their discordant uses of the term within a concerted paradigm.  For example, in dealing with the joint configuration space of a multiple agent system, one considers this "yoked extension space" (YES) to fall within a "common extension" (CE) of all the single agent state spaces.  Each agent involved in such a system "projects", in a geometric sense, the total action of the system on its own "section" of the whole CE, its "local outlook", "mental plane", personal "frame of reference" (FOR), or "point of view" (POV).

What does the POV of an agent consist in?  Generally speaking, agents are not dumb.  They are not limited to a single view of their situation, nor are they restricted to a single scenario for its ongoing development.  They can entertain many different possibilities as candidates for the so called and partly self describing "objective situation" and they can envision many different ways that these potential situations might be developing, both before and after their passage through the moment in question.  Furthermore, under circumstances favorable to reflection, agents can invoke POV's that help them to contemplate many different possible developments in the constitution of these very same POV's.

Now, it is conceivable that all the POV's entertained by a single agent are predetermined as having the same collection of generic characters, and thus that this invariant constitution is what really limits the range of all possible POV's for the agent in question.  If so, it leads to the idea that this invariant constitution defines a "uniquely general POV", a "highest order meta POV", or a "consummate POV" of the agent involved.  Still, the only points of access and the only paths of approach that an agent can have to its own consummate POV, if indeed such a goal does make sense, are through the agency and the medium of whatever POV's it happens to have at each passing moment in its developmental history.  Consequently, a persistent enough search for a good POV opens up the investigation of each agent's prevailing "point of develoment" (POD).

In the best of all possible worlds, then, being under the influence of one POV does not render an agent incapacitated for considering others.  Of course, there are practical limitations that affect both the capacity and the flexibility of a particular POV, and there can be found in force both logical constraints and resource constraints that leave a POV with a narrowly fixed and impoverished character, one that the agent opting for it can fail to represent reflectively enough within the scope of this POV itself.  In particular, the "finite information constructions" (FIC's) that are accessible from a computational standpoint are especially limited in the kinds of POV's they are able to attain.

This means that POV's and POD's have recursive constitutions and recursive involvements with one another, calling on and referring to other POV's and POD's, both for the exact definitions that are needed and also for the more illuminating elaborations that might be possible, both those belonging to the same agent, reflexively, and those possessed by other agents, vicariously.  A large part of the task of building a RIF is taken up with formalizing POV's and POD's, in part by analyzing their intuitive notions in terms of their implicit recursive structures and their referential involvements with each other, and in part by exploring their potential relationships with the previously formalized concepts of "objective concerns" (OC's).

In settings where recursion is contemplated, it is possible to conceive of a distinction between "well founded" recursions, that lead to determinate definitions of the entities in question, and "buck passing" recursions, that lead one down the "garden path" to an interminable "run around".  The catch, of course, is that it is not always possible to implement an effective procedure that can accomplish what it is possible to conceive.  Thus, there are cases where the imagined distinction does not apply and times when the putative difference is not always detectable in practice.

In this connection, there are two or three fundamental questions that need to be addressed by this project:

1.	What makes a POV or a POD "well founded"?

2.	Can "buck passing" POV's and POD's be tolerated?

3.	How should they be treated and regulated, if tolerated?

A tentative approach to these questions is tendered by the pragmatic theory of sign relations, where the "definitive" and the "elaborative" aspects of recursion correspond to the denotative and the connotative components of reference, respectively.  Although it is always useful to organize the connotative realm in the species of a determinate ordering or a well founded hierarchy, there is found in these parts generally a greater tolerance for the baroque proliferation of circuitous references and a broader acceptance of provincial, dialectic, and private coinages.

If all thought takes place in signs, as a tenet of pragmatism holds, then mental space is a space of signs and their interpretants, in other words, it is a connotative realm.

In this perspective, that is to say, in the POV of the present project and in the current opinion of its author, a POV is associated with an abstractly defined, but concretely embodied and frequently distributed, "section of memory" (SOM), where the signs constituting it are stored.  In this rendition, a SOM is a curve, surface, volume, or more general subspace of the total memory space, in other words, a subset of memory that can be treated, under the appropriate change of coordinates, as being swept out by a set of variables, and ultimately addressed as being generated by a list of binary variables or bits.  Working under the assumption that agents can engage in non trivial developments, it must be granted that they have the ability to change their POV's in significant ways between the successive POD's in their progress, and thus to move or jump from one SOM to another, as dictated by will or as constrained by habit.

In this comparison, what is visualized as the geometric structure of a "cone" is commonly implemented through the data structure of a "tree", that is, a set of memory addresses (along with their associated contents) that are accessible from a single location, namely, the "root" of the tree, or the literal "point" of the POV.

Typically, but not infallibly, an agent can reduce the complexity of what is projected on its personal POV by employing a reductive hypothesis or a simplifying assumption.  Often, but not always, this idealization is arrived at by picking one agent to treat as "nominal", in other words, whose actions and perceptions are regarded as "natural", "normal", or otherwise unproblematic.  Usually, especially if one is a "mature" agent, this nominal agent is just oneself, but a "novice" agent, unsure of what to do in a novel situation, can chose another agent to fill the role of a nominal guide and to serve as a reference point.

It would be nice if one could ignore the sharper edge of knowledge that is brought to light at this point, and fret but lightly over the smooth and middling courses that gloss the conformal plateaus of established knowledge.  However, it is the nature of the inquiry into inquiry that one cannot forever restrict one's attention to the generic, nominal, or unexceptional case, well away from the initial conditions of learning and the boundary conditions of reasoning.  Still, for the purposes of a first discussion of POV's and POD's, I limit my concern to the nominal case, where the reductive strategy indicated is useful to some degree and where the nominal agent of choice is none other than oneself.

Under default conditions of operation, then, each one's POV embodies the reductive assumption that one's own particular actions and perceptions are "nominal", that is, natural, normal, or otherwise "not a problem".  Relative to this ordinary setting, each one's POV is normally configured for tracking the more problematic courses of other agents and the drift of the residual system as a whole.  Therefore, the natural setting of a POV can be pictured in terms of the perceptual "gestalt" it facilitates.

In unexceptional circumstances one always takes one's own agency and one's own experience for granted.  This is tantamount to assuming that a synthetic balance is already in effect between the claims of conduct and the trials of bearing.  Given this much free reign in arranging the play of forces, the artificial state of accord that results can present itself to be a neutral context of interpretation and the superimposed scene of rapport that prevails can pretend itself to be the unquestioned background of instrumental activity that is implicated in every notable objective contemplated or observation performed.  Cast in the role of a stationary stage for the action, there is a whole body of interactions that reside in dynamic equilibrium with each other and that make this proving ground appear to be at rest, but the whole contrivance merely acts to place in relief and to render more obvious whatever else in the way of phenomenal experience is thereby permitted to figure against it as representing an object worthy of inquiry.

Loosely speaking, and operating under the usual anthropomorphism, one can say that an agent projects the joint state trajectory, the course that the whole system takes through a sufficiently well defined CE, onto a trajectory through its own proper space, the residual state space that is encompassed by its chosen POV.  Strictly speaking, in another sense, all that is known of an agent is just what is projected on its space, and thus one can say that an agent is wholly constituted by this projection.

The difference between the two senses of "projection" can now be rationalized as follows.  A psychological projection begins when a mathematical projection is employed to deal with a complex experience, that is, an overwhelmingly complicated trajectory of the total system.  But the default assumption that one's own actions are not significantly implicated in what happens can occasionally turn out to be unjustified.

In a case of "psychological" or "transverse" projection, the significant aspects or motivating features of a problematic situation are attributed to the other actors, while one's own collusion in the relevant character of the total situation is ignored, denied, or otherwise relegated to the peripheral background of the configuration kept in focal awareness, the figure that is currently being attended as a content of consciousness.  This form of strategic reorganization usually occurs reflexively among the automatic processes of perception, in spite one's full knowledge or token recognition of the times when it is just as likely that the salient quality of the situation is due to one's own conduct, and even when it is equally possible that the complexion of the moment cannot be resolved into separate components and rendered accountable to individuals at all.

6.50. Revisiting the Source

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

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