Inquiry Driven Systems • Part 9

Author: Jon Awbrey

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• Overview • Part 1 • Part 2 • Part 3 • Part 4 • Part 5 • Part 6 • Part 7 • Part 8 • Part 9 • Part 10 • Part 11 • Part 12 • Part 13 • Part 14 • Part 15 • Part 16 • Appendix A1 • Appendix A2 • References • Document History •

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Reflection on Reflection

Looking Back

Let me review the developments that bring me to this point. I began by describing my present inquiry, $y_{0},$ as an inquiry into inquiry, $y\cdot y.$ Then I focused on the activities of discussion, $d,$ and formalization, $f,$ as two components of the faculty or the process of inquiry, $y>\!\!=\{d,f\}.$ This led me to the present discussion of formalization, $f\cdot d.$ Considered as classes of activities, the collective instances of formalization, $F,$ appeared to be encompassed by the collective instances of discussion, $D,$ thereby yielding the relationship $F\subseteq D.$

I initially characterized discussion and formalization, in regard to each other, as being an “actively instrumental” versus a “passively objective” aspect, component, or “face” of the inquiry $y>\!\!=\{d,f\}.$ In casting them this way I clearly traded on the ambiguity of “-ionized” terms to force the issue a bit. In other words, I used the flexibility that is freely available within their “-ionic” construals, as processes or as products, to cast discussion and formalization into sundry molds, drawing out the patent energies that are manifested by the active process of discussion and placing them in contrast with the latent inertias that are immanent in the dormant product of formalization. In this partially arbitrary way, I decided on the one hand to treat discussion in respect of its ongoing process, the only thing that it has any assurance of accomplishing, but I decided on the other hand to treat formalization in respect of its end product, the abstract image or the formal model that constitutes its chief qualification and thus becomes the mark of what it is.

By casting inquiry into the form $y>\!\!=\{d,f\},$ I made it more likely that my development of its self application $y\cdot y>\!\!=\{d,f\}\{d,f\}$ would first take up the application of discussion to formalization, $f\cdot d,$ and only later get around to the application of formalization to discussion, $d\cdot f,$ that brings the active side of the formalization process into a greater prominence. But the bias that I exploited in these readings does not seem at present to be a property of the incipient algebra that would determine the sense of the applications and the decompositions envisioned here. Thus, if I initially saw a difference between the two presentations $\{d,f\}$ and $\{f,d\},$ then it must have been a purely interpretive and not a substantial one, and the task of giving explicit notice to these interpretive distinctions and working out their algebra or calculus yet remains to be carried out in any sort of convincing fashion.

Still, the casting of discussion and formalization as active and inert, respectively, was not entirely out of character with their distinctive natures, since a process that has an end is more naturally suited to be represented by its result than a process that conceivably never ends. And whereas a discussion was allowed to be a form of discourse that does not need to have an end, with the possible exception of itself, a formalization was sensed to be a form of discourse that has, needs, seeks, or wants a distinct end, not just any end but a form of product that is preferred to satisfy a general description, and one that most likely resides outside the form of a vacuous vanity that simply refers, in a reflexive but hollow echo, to the entirety of its own proceedings.

In this merely penultimate analysis, and to the extent that the question of ends has been analyzed up to the present, it needs to be noted that more than a bit of ambiguity yet remains. When one speaks of a form of discourse each of whose instances necessarily has an end, does one mean that the definition of the form requires each instance to have an end, and does one then mean that each valid instance actually achieves its end, or does one only mean that each instance of some empirically given class of discourses actually reaches some end or another?

The word “reflection” first entered this discussion in what seemed like a purely incidental and instrumental way, as a part of the definition of a “meditation” as “a discourse intended to express its author's reflections or to guide others in contemplation” (Webster's). I converted this term to my own use as a name for a particular class of activities, describing the class of meditations, $M,$ as a brand of measured and motivated discussions that can serve to mediate formalizations within the realm of discussions at large. Thus, I borrowed the term for no better reason than that of interposing a middle term between formalized discussions and discussions in general, thereby yielding the relationship $F\subseteq M\subseteq D.$

In this respect, it seems to be instructive that the issue of reflection first arrived on the present scene, quietly enough, under the aegis of a borrowed term, imported without deliberate design among the components and the connotations of its associated sample of discourse, and involved in a process that seeks to negotiate the conflicting claims that arise between formal and casual discourse. In the simplest sense of the word, an activity of reflection implies only that an agent thinks quietly and calmly about a matter, the etymology of the word suggesting the actions of bending, bounding, casting, folding, giving, turning, throwing, or yielding back again, and hence a pause, a return, or a review. In this regard, the word "reflection" barely alludes to the idea that what the agent turns back to is something that involves itself, its own patterns of activity, and thus the word only hints as yet at the complicities of self reference and self application that are involved in an agent turning back to view its past, its present, or its ongoing forms of conduct.

Whereas I dragged the topics of discussion and formalization somewhat arbitrarily and forcibly into the arena of inquiry, the issue of reflection appeared to develop naturally on its own, without significant foresight on my part, and without deliberation or design gradually forced itself on my attention, as if rebounding from contingent obstacles that exist just beyond my current horizon, reflecting the necessary constraints of a natural law, or echoing the bounds of an inherent capacity that I yet know not of.

When one crosses a critical threshold or a threshold of decision, ...

A notion of reflection, in a more authentically reflexive sense, was implicitly involved in the application of inquiry to itself, $y_{0}=y\cdot y,$ and was eventually encountered on a recurring basis in the application of each newly recognized component of inquiry to itself: $y\cdot y>\!\!=d\cdot d,f\cdot f.$ In a more substantial role, the option of a capacity for reflection was already noticed as a significant parameter in the constitution of an IF.

Often, an IF is founded and persists in operation long before any participant is able to reflect on its structure or to post a note of its character to the constituting members of the framework.

(§ 1.3.3.5, page 14)

More substantially, a notion of reflection was invoked as something necessary …

In other contexts, something called “reflection” was seen as necessary to avoid certain types of unfortunate outcomes, …

To avoid the types of cul de sac (cultist act) encountered above, I am taking some pains to ensure a reflective capacity for the interpretive frameworks I develop in this project.

(§ 1.3.3.5, page 15)

A radical form of analysis &hellip requires interpreters … to reflect on their own motives and motifs for construing and employing objects in the ways they do, and to deconstruct how their own aims and biases enter into the form and use of objects.

(§ 1.3.4.12, page 36)

Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis that can reflect a measure of light on the initially unstated assumptions of their prospective agents.

(§ 1.3.4.12, page 36)

The relationships among the activities and faculties of discussion, contemplation, formalization, meditation, and reflection need to be explored in more detail. In particular, the relationship between formalization and reflection is especially relevant to the task of constructing a RIF.

Unlike a discussion of discussion, $d\cdot d,$ which is easy to start and hard to put an end to once it gets going, it is difficult for a reflection on reflection, $r\cdot r,$ to get itself going with nothing to reflect on but itself. I have just illustrated one way of doing this, namely, by leading a text to reflect on itself, as long as you understand this figure of speech to mean that it leads its interpreters, its writer and reader, without whose agency there would be no reflection at all, to reflect on how it reflects on itself. But I obviously need other ways than this to demonstrate the functions and properties of reflection in anything like their full variety.

Toward this end, it can also help to illustrate the action of reflection if I find it some material besides itself to reflect off of, in other words, if I supply it with an independently generated and concretely finished text as an argument to exercise its powers of reflection on. Accordingly, in the next part of this discussion I will interleave my text with …

The preview that follows takes up the first stirrings of many subjects that cannot be meaningfully engaged, much less fully formalized, until much later in the investigation. In many cases the ongoing discussion can afford to pause only long enough to toss a provisional name in the direction of a prospective topic, both the name and the place of which promise an eventual return and revision, if not a recurring visitation. If I were forced to give a formal title to my sketch in reconnaissance of this area, I would call it the “phenomenology of inquiry”, but this fine label is already too heavy an emblem for my effort to bear at this point.

This subsection presents a broad overview of the questions raised and the conceptual needs occasioned by the prospects of constructing a RIF. It makes no attempt to completely cover the topics it identifies and does not try to answer the questions it raises or to fill the needs it notices, but it merely points out a selective sample of the most salient concerns that need to be addressed.

The long route which I propose also aspires to carry reflection to the level of an ontology, but it will do so by degrees, following successive investigations into semantics and reflection.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 6]

The subject of reflection is first approached in a topical, paraphrastic, or even periphrastic manner. The notion of a capacity for reflection is submitted to a tentative analysis, as treated in a variety of different modes of conception, by listing the duties that are typically demanded of a reflective agent, by compiling and reconciling the properties that are commonly ascribed to the process of reflection, and by contemplating the responsibilities and the results that the faculty of reflection is supposed to have in the many contexts where it is expected to serve.

“Reflection” is a word that is used with a wide variety of meanings in both ordinary language and technical contexts. Some of these uses have little to do with the sorts of inquiry being pursued here. Other uses, though related to inquiry, refer to processes that are fully as complex as inquiry itself. Neither of these extremes of meaning falls within the present focus of discussion.

The task for this project is to identify a coherent set of operations: (1) that fall within the scope of conceptual analysis and computational modeling, (2) that bear a recognizable and illuminating relationship to what is commonly called “reflection”, (3) that make an operational contribution to inquiry, and (4) that constitute simpler components of the operation of inquiry.

I define “symbol” as any structure of signification in which a direct, primary, literal meaning designates, in addition, another meaning which is indirect, secondary, and figurative and which can be apprehended only through the first.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 12]

The types of reflective operations of interest in this work are best approached and analyzed within a sign theoretic setting. …

Presented in the guise of an allegorical figure, reflection appears as the bailiff or the sergeant at arms who escorts an agent, faculty, or process from the office of power to the dockets of observation, examination, and potential revision. But still, putting all allegory aside, this mode of transport goes nowhere at all, nor travels through any space, but turns on a mere change of views for all that it ushers in. One is perfectly capable of using a power of inquiry of which no account is yet given. But reflection is a part of the inquiry into conduct that gives the conduct in question a description.

He paused and nibbled absentmindedly on his branch for a while, as if gathering his thoughts.

Daniel Quinn, Ishmael, [DQ, 11]

If inquiry is viewed as a process of reasoning, then it takes place in thought, and so in the signs that are the public expression of thought. This means that an inquiry into inquiry has the duty to concern itself with thoughts, signs, and the relationship between them. To do this in an appropriate setting, it has to consider thoughts and signs as things taken apart from, but placed in relation to, their own particular objects. Indeed, the task that distinguishes an inquiry into inquiry, the specific difference that sets it apart, both from all of its object inquiries and again from inquiry in general, is the question of how thought is to be conducted if the goals of inquiry are to be met.

In such places (he went on at last), where animals are simply penned up, they are almost always more thoughtful than their cousins in the wild.

Daniel Quinn, Ishmael, [DQ, 11]

If one considers the formula that characterizes an inquiry into inquiry, $y_{0}=y\cdot y,$ and examines the term $y\cdot y$ that factors $y_{0}$ along the lines of an ostensible self-application, it is evident that any power invoked on the right is instantly echoed on the left and so required to survive the application or else be revoked. If the use of a given power of inquiry, working from the right and serving in the role of an operator, leads to a prospective description of inquiry, worked on the left from the role of an operand to the role of a result, and if the proffered characterization of inquiry is found to be out of accord with significant instances of its actual practice, then either the depiction of inquiry, as it is mediately improvised in progress, or the performance of inquiry, as it is actually conducted in practice, can turn out to be at fault.

This is because even the dimmest of them cannot help but sense that something is very wrong with this style of living.

Daniel Quinn, Ishmael, [DQ, 11]

The philosophical point of view called “pragmatism” takes a particular position on the relation of thoughts to signs, and this determines a particular method of approach to the nature of thinking. To preview here what is presented in detail later, the pragmatic point of view involves: (1) an assertion that thoughts are a special case of signs, (2) a theoretical definition of signs in terms of sign relations, and (3) a corresponding approach to the nature of thought as “praxis”, in other words, of thinking as a process, or inquiry as a form of conduct.

When I say that they are more thoughtful, I don't mean to imply that they acquire powers of ratiocination.

Daniel Quinn, Ishmael, [DQ, 11]

The way that reflection turns action into depiction and description, how it gives a sign to the act and provides a code for its future conduct, is the chief mystery of the whole process of reflection. Expressed in the substantive fashion that the “-ionized” character of “reflection” permits, this riddle arises from wondering how a reflection on the action can be transubstantiated as a sign of the action and resurrect itself in a code of the conduct. In other words, how does a signification calling for an interpretation arise from the very interruption of its full transmission, the comical section of its secular extension, the transient abdication of its permanent tradition, …, or the discrete truncation of a continuous conduction?

But the tiger you see madly pacing its cage is nevertheless preoccupied with something that a human would certainly recognize as a thought.

Daniel Quinn, Ishmael, [DQ, 11]

The way that inquiry obstructs itself, or that each inquiry interferes with every other, is a phenomenon that constitutes a principal target of this investigation. At times it seems as if the present construction is always the main obstruction to the intentions that are embodied in it, forestalling every chance of change, every hope of growth, and every possibility of progress into the future. How do the very processes of analysis, inquiry, and reflection come to have their aims so distorted, their airs so polluted, and their purposes so perverted that the very bodies of their own past effects become the blocks to their moving on?

And this thought is a question: Why?

Daniel Quinn, Ishmael, [DQ, 11]

An inquiry into inquiry can start out so close to the start of its subject that it finds its subject inquiry in a state of inchoate incipience, one where no hint of reflection is yet to be discerned. But once the action of reflection is suspected to lie beneath the manifest activity of the subject inquiry, from the effects of reflection that are discovered to issue from the inquiry in question, the analysis of this reflection can take its charge to such outrageous extremes, breaking down the actual process of reflection to its most inert levels of miniscule details, breaking up the living continuity that is appropriate to a realistic depiction, incrementally revealing the fragments of reflection that are revealed by this analysis, omitting every sense of connection and surgically excising every ligament of extenuating context, or that are incrementally and inspecting revealed by this analysis with such a myopic scope, that no trace of the overriding imagination appears among the pieces that remain, the original aspect of reflection is lost among the residual debris.

When it comes to understanding a living activity, like reflection, or inquiry, or analysis itself for that matter, there are forms of analysis that go too far in their favored or particular directions while failing to take into account the workings of significant “ligaments”, or connective factors, that help to constitute and coordinate both their subjects and themselves, and on which the integrity of both depends. In particular, the purely syntactic analysis of a reflective narrative is liable to be carried to the bounds of such extremities that no trace of reflection is evident within the functional structures of the parts that are obtained or appears beneath the few points of light that the analysis yet throws. At this point, the instrument of reflection is broken so utterly, into so many pieces, and of such a small size that neither a close nor a distant inspection of any fraction of their number reveals any longer the aspect of reflection for which their matter was originally prized and pried into. When this state of analysis is reached, the medium of reflection, though it is still reflective in a certain sense, scatters the ambient light of nature that remains to it and disperses its sense through an evanescent void that presents nothing more illuminating to the imagination than the shimmering opacity of an opalescent haze.

The way that reflection, in adjunction to conduct, leads that conduct to a description of itself, not only in the sense of begetting an image but also in the sense of encountering a design, needs itself to have a name. I dub this turn of reflection, through which it converts the conduct of experience into an experience of conduct, by the name “metamorphism”. The way that a reflection of the action is a sign of the action needs to be investigated further, and is pursued through the rest of this work. An apology is due for continuing to harp on this point, but it remains a crucial point for the whole method of reflection, if it is to be a method.

“Why, why, why, why, why, why?” the tiger asks itself hour after hour, day after day, year after year, as it treads its endless path behind the bars of its cage.

Daniel Quinn, Ishmael, [DQ, 11]

Returning to the formula of an inquiry into inquiry, $y_{0}=y\cdot y,$ it is possible to derive a few of its consequences for the character of the operation that is to be called “reflection”. In general, a formula like $f=g\cdot h$ constitutes a movement of conceptual reorganization, one whose resultant syntactic structure may or may not reflect an objective form of being, that is, an aspect of structure in the being that constitutes its object. If there is a similarity of structure to be found between the formula and the object, then one has what is called an iconic formula, but this is not always the case, and even this special situation requires the proper interpretation to tell in exactly what respect the form of the sign and the form of the object are alike. Whatever the case, the role of the formula as a sign should not be confused with the role of the object in reality, no matter how similar their forms may be.

It cannot analyze the question or elaborate on it.

Daniel Quinn, Ishmael, [DQ, 11]

If one reads the form $y\cdot y$ according to the convention adopted, where a latently but actively instrumentalized inquiry on the right applies to a patently but patiently objectified inquiry on the left, almost as if they were two distinct agencies, faculties, or processes, then it is clear that an inquiry into inquiry can begin with little more than a nominal object, taking the name of “inquiry” in its sights to yield a clue in name only, while it can reserve all the power of an established capacity for inquiry to conduct its review, of which no account, no prescribed code, nor any catalog of procedure has to be given at the outset of its investigation.

If you were somehow able to ask the creature, “Why what?” it would be unable to answer you.

Daniel Quinn, Ishmael, [DQ, 11]

But it is important to remember that the full intention of this factious formulation is more analogous to an interpretive doubling of vision, an amplification of resolving power and a coordination of perspectives, than it is to an objective division of being, a substantial disconnection of essentials or a disintegration of being. Even when the factions of the term $y\cdot y$ are conceived in practice to be implemented by substantially different parts of the same agency, constitutionally they embody but a single power.

Before long I too began to ask myself why.

Daniel Quinn, Ishmael, [DQ, 11]

The form of inquiry into inquiry, $y\cdot y,$ requires that any power assumed on the part of the right is open to be indicted on the part of the left. This entails that any power arrogated for the ends of inquiry has to be given a name, not only under which it is invoked as an executive power, but also by which it is entered on the agenda of issues to inquire into, and finally through which it is indicted for submission to all the powers of inquiry that be. This combination of appellation and supplication, or nomination for and submission to the jurisdiction of a reflexive application, makes up a large part of what is usually called reflection.

Being neurologically far in advance of the tiger, I was able to examine what I meant by the question, at least in a rudimentary way.

Daniel Quinn, Ishmael, [DQ, 11]

Many times, otherwise unrelated uses of the word reflection in the physical sciences can be suggestive. For example, reflection is one of the ways that a continuous appearing phenomenon can be brought into a form of interaction with itself and thereby to exhibit its nature as a pattern of activity with definite features and discrete characteristics. But metaphors like these can be kept from spinning out misleading clues only if the keys to understanding them as analogies can be found.

I remembered a different sort of life, which was, for those who lived it, interesting and pleasant.

Daniel Quinn, Ishmael, [DQ, 11–12]

With respect to the present project, that peers into its own appearances for the sake of seeing what logic lies in the rawness of experience, the analogous question is: How can the continuation of experience be conducted in such a way as to reveal within experience itself the conditions that connect its unconducted to its conducted course?

By contrast, this life was agonizingly boring and never pleasant.

Daniel Quinn, Ishmael, [DQ, 12]

This motion, the kind of movement just put in question or the form of development just wondered about, occurs throughout the whole field of inquiry, making it convenient to find a name for it. Because it steps across a boundary in a state space while keeping its eye on both sides of the displayed distinction, it can be called a circumspect transition or, more dramatically, a peripeteic strophe. At times it appears in lights that earn it the titles of the yoke of knowing existence (YOKE), the conduct of subjectivity (COS), or just the junctive element (JE). It is pertinent in this connection that I am treating the condition of subjectivity as a special case of pragmatic objectivity, as it appears in this instance, one that involves an element of reflection.

Thus, in asking why, I was trying to puzzle out why life should be divided in this way, half of it interesting and pleasant and half of it boring and unpleasant.

Daniel Quinn, Ishmael, [DQ, 12]

So let me dispense for the moment, even if this dispensation has to be carried out for now in the flippant manner and the fugal mannerisms of the foregoing counterpoint of discussion, with what I earnestly desire, all in good time and by means of well tempered arguments, to dispense with once and for all: The notion that individual words, sentences, paragraphs, articles, and so on up the scale can be anything like the final arbiters of thought and anything approaching the units of thought of ultimate interest to inquiry. But I want to do this without giving up the spirit of analysis altogether, merely by looking for forms of analysis that are fit to address the text of inquiry (TOI) in its full integrity.

It was in puzzling out such small matters as these that my interior life began — quite unnoticed.

Daniel Quinn, Ishmael, [DQ, 12]

In the process of elucidating the pragmatic point of view and applying it to the present array of problems, it soon becomes useful to examine the very notion of a point of view (POV). As reflections on the idea of a POV gradually mount up, the analysis of the general conception of a POV begins not only to take on a definite shape for itself, that is, with respect to the conditions it needs for its continued progress, but also to give a determinate, if slightly schematic, form to its object. Eventually, a sufficient confidence in the accumulated developments of the concept of a POV can lead this analysis to the point of suggesting provisional definitions and even to the point of attempting a specific formalization of POVs in general. This series of developments occurs concurrently throughout the construction of the current or any RIF, the necessity of which ought to be clear from the fact that the sequence of POVs from which one reflects is critical to the result and the success of any process of reflection.

A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and finds the testimony confirmed in a striking way. Thus, he becomes aware of ignorance, and it is necessary to suppose a self in which this ignorance can inhere. … In short, error appears, and it can be explained only by supposing a self which is fallible. Ignorance and error are all that distinguish our private selves from the absolute ego of pure apperception.

(Peirce, CP 5.233–235)

Peirce makes the point that one's first awareness of a personal existence arises in reaction to the brute impact of experience and is ultimately compounded by way of reflection on its imports. Taking this to echo the exchange between Brutus and Cassius, I have the points that I need to stake out and to sound out a significant portion of the RIF that I intend to discuss.

Before passing over the subject of the JE, in order to continue with a sketch of reflection, it is useful to notice a couple of features that affect this style of movement, as recapitulated in this strophe, and that determine the prospective turns of events, as predicated on its action. In one sense the motion is reversible, since the boundary in the basic state space, once crossed, is easily crossed again. In another sense the transition is irreversible, since what is learned from a single crossing, assuming the agent is capable of acquiring knowledge in the process, is neither so quickly forgotten nor so easily lost.

It is the usual thing, in contemplating the forms of development that are epitomized by the figure of the JE, to find the images of winding gyres and helical ascents coming to mind, in other words, the trajectories of open curves in an extended space that project onto closed curves in a more basic space. In anticipation of later developments, I propose to attribute the basic and the extended aspects of this strophic segue to its dynamic and its symbolic components, respectively.

If it is important, at first sight, to recognize the JE as an irreducible primitive, inscribing its expression of its own being in the self signed tokens of a uniquely traced but perfectly typical autograph, all along personalizing its form of possession with an irrepressible panache, and leaving its legacy in an otherwise irreproducible style of paraph, it is just as important, on second thought, to try various schemes of analysis on it, with the aim, however artificially, of articulating, approximating, or explaining its form.

A number of questions arise at this point, concerning the justification of these moves, not just to justify the initial JE but to rationalize all of the ensuing action that is predicated on it. Just to name a few:

1. What justifies a particular way of leading experience to reflect on itself?
2. What justifies a particular way of causing reflection to comment on itself?

If it is asked, with respect to the legitimacy of all such questions, what is the justification for imposing extraneous ventures and superimposing foreign notions on the otherwise natural course of things, the answer has to be that, otherwise, it could not be articulated at all, and that, once reflected, the naturalness of expression that affected the original intention cannot be recovered without some risk of artificiality.

The object example of a strophic transition is the action of inquiry itself. For instance, if an inquiry is something that strives to move from a state of uncertainty toward a state of certainty about its object, then an inquiry into inquiry is something that proposes to move from a state of uncertainty toward a state of certainty about the identifiable elements and features of inquiry itself, including the natures of doubt and certainty, and of the distinction or the relationship between them. Distributing the terms a bit, this means that an inquiry into inquiry tries to move from a state of doubt about doubt toward a state of knowing about doubt.

To deal with the relationship between the dynamic and the symbolic aspects of the JE, I try a couple of strategies, ranging in character from the casual to the formal.

1. To start, I adapt an informal distinction between the matter of a thought and the manner of thinking it. For example, in the effort to think about uncertainty one hopes to develop a certain concept of it. So, even though one continues to think about uncertainty, one hopes to become fairly certain about it. Here, the matter or content of one's thinking is fixed on uncertainty while the manner or conduct of one's thinking is hoped to change from the dubious to the certain.
2. Eventually, it is necessary to develop a formal concept and even a mathematical model of this relationship. To do this, I adopt the intuitive notions of a point of view (POV) and its point of development (POD), gradually turning them into formal concepts of a very general character. This requires distinguishing between two kinds of propositions that are associated with POVs and PODs, namely: (a) the propositions that are attached to or contained in them, and (b) the propositions that are applied to or maintained about them.

Just to give a rough idea of how these two distinctions relate to each other, the matter of a thought corresponds to an attached proposition, in a POV or at a POD, while the manner of a thought corresponds to an applied proposition, on a POV or about a POD. Employing this language to describe the case of an inquiry successfully self-applied, one can say the following things. An agent of inquiry has a POV that changes from one POD to the next in a series of developments, and this can be a POV that concerns itself with the question of inquiry, among other things, and thus with the topics of uncertainty and certainty, or doubt and belief. In such a case, as the POV moves from an initial POD to a terminal POD, a part of its matter stays fixed on doubt, while its whole manner is transformed from one of doubt toward one of belief.

It is not always necessary to distinguish a POV from each of its PODs, except when one needs to emphasize the dynamic aspect of these ideas, especially the fact that a single POV can pass through or incorporate many different PODs in the course of its development. It is legitimate to say that the POV is present at each of its PODs, or that the PODs are incorporated in their overall POV. Accordingly, it is not always necessary to lose sight of the successive PODs in a series, so long as they are amenable to being incorporated in the last POD, or final POV.

When one says that a POV is associated with a particular proposition, whether containing it or instancing it, one always means a POV as it exists at a particular POD, or through a particular range of its PODs. For example, if I say ${}^{\backprime \backprime }J~{\text{thinks}}~K~{\text{is smarter than}}~L{}^{\prime \prime },$ then I am implicating a POV that $J$ has at a particular POD, assumed to be capable of specification. Moreover, I am relying on the specific information inherent in this POD to index the particular persons $K$ and $L$ that I am assuming $J$ has in mind at that POD. In technical terms, this requires the “intentional context” that is signaled by the verb thinks, normally “opaque” to all distributions of contextual information from any point outside its frame, to be treated as “transparent” to the packet of information that is assumed to be represented by the POD in question.

In the application of mediate interest to this project, a POV corresponds to a computational system, while a POD corresponds to one of its states. It is desirable to have a way of referring to the system as a whole, but in ways that are implicitly quantified by the relevant classes of states. For example, I want to have a system of interpretation in place where it is possible to write ${}^{\backprime \backprime }j:x=y{}^{\prime \prime }$ to mean that ${}^{\backprime \backprime }j~{\text{sets}}~x~{\text{equal to}}~y{}^{\prime \prime },$ to read this as a statement about a system $j$ and two of its stores $x$ and $y,$ and to understand this as a statement that implicitly refers to a set of states that makes it true. Further, I want to recognize this statement as the active voice, attributed account, or authorized version of the more familiar, but passive, anonymous, or unavowed species of assignment statement ${}^{\backprime \backprime }x:=y{}^{\prime \prime }.$

The rudimentary parallels between these different distinctions should not be treated too rigidly, as a number of finer points about their true relationship remain to be sorted out. The next few remarks are given just to provide a hint of what is involved.

The distinction between matter and manner of thought is correlated with the distinction between object and sign, so long as these are recognized as distinctions of momentary use and not as distinctions of fixed nature. In the beginning, these distinctions also coincide with the distinction between dynamic and symbolic aspects of inquiry. A typical instance of this is when a change of physical configuration is needed to carry out an experiment, while what is learned as a result of that experience is tantamount to a change in the organization of one's thought, and where this includes changes in the signs, texts, and other sorts of records that form one's knowledge base as well as changes in the ideas, or signs in the mind, that make up one's mental configuration.

Nevertheless, it is important to appreciate that all of these distinctions can become increasingly and divergently relativized as higher orders of reflection on the initial domain of objects turn wider circles of signs around it and heap higher towers of ideas upon it. When this happens, any initial portion of the objective and lower order syntactic domains can form the matter of a thought, while any final portion of the higher order syntactic domains can embody the manner of a thought.

Here is the critical point. A conceptual distinction is not absolute, but relative to the POV that sees it, makes it, draws it, or uses it. Indeed, one of the reasons for introducing the concept of a POV is to formalize this general insight and thereby to permit reflection on specific POVs. But the intention of this move is to include any distinction that can be made in the process of an inquiry and found essential to its progress. Accordingly, the aim of this insight marks an intention to comprehend, not just the distinctions between previously identified predicates, like the attributes dubious and certain already mentioned, but also any future distinctions that might be discovered as necessary to inquiry. Almost immediately, for instance, the distinction just made by way of formalizing the concept of a POV, between the propositions at and the propositions about a POV, falls into the category of distinctions in question, at least, put under examination for the purposes of a review.

Consciousness is a movement which continually annihilates its starting point and can guarantee itself only at the end. In other words, it is something that has meaning only in later figures, since the meaning of a given figure is deferred until the appearance of a new figure.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 113]

In a sense, knowledge shrinks as wisdom grows: for details are swallowed up in principles. The details of knowledge which are important will be picked up ad hoc in each avocation of life, but the habit of the active utilisation of well-understood principles is the final possession of wisdom.

Alfred North Whitehead, The Aims of Education, [ANW, 46] cited in Stephen R. Covey, First Things First, [CMM, 71]

If I reflect on my own POV, it becomes evident that the critical focus and main interest of this inquiry is on the kinds of inquiry that cross a certain threshold, that of becoming deliberately conducted and critically controlled. But in order to remain critical and reflective I have to be interested in both sides of this distinction. This is the usual pattern of the circumspect transition that I just personified in the form of the JE. But here it seems to lead to the disconcerting conclusion that reason is founded on unreason, and that this reason is justified by the end that it leads to, not by the state that it starts in. This sounds ominous and dangerous, but I think that the difficulties it raises are partly verbal, the fault of ambiguities that are quick to right themselves on reflection, but more seriously, partly due to misleading theory of what constitutes a foundation, a theory that tends to be applied on the modern scene as an uncritical reflex of that very same and everyday modern POV.

The general problem encountered here can be expressed in the question: How can reason rationally address its other, the real irrationality of unreason that it finds in its experience, not only in and of the world but at the beginnings of its own being? If reason addresses unreason as its founder, then it seems to founder in its justification of itself. This is how the question and its puzzing echo first present themselves, but in order to approach a genuine answer it seems more likely that a transformation of the question is demanded, perhaps recasting it so: How can one form of reason rationally address another, whether it is wholly and radically other or complementary to and continuous with its own being? Other versions of this question, and other attempts to respond to it, appear throughout the remainder of this work.

One thing is apparent: If reflective inquiry, based on the rationality of the intellectual share of reason, addresses instinctive inquiry, based on the sensibility of the affective, emotional, and motivational portion, as something wholly other, indeed, as its logical opposite, then it obstructs the eventuality and even precludes the possibility of discovering their compatibilities and continuities, and it interferes with the chances of seeing how each form of inquiry completes and extends the other.

The Light in the Clearing

Thus we can understand that “the entire sensible world and all the beings with which we have dealings sometimes appear to us as a text to be deciphered”.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 222] quoting Jean Nabert, Elements for an Ethic, [Nab, 77]

Before this discussion can proceed any further I need to introduce a technical vocabulary that is specifically designed to articulate the relation of thought to action and the relation of conduct to purpose. This terminology makes use of a classical distinction between action, as simply taken, and conduct, as fully considered in the light of its means, its ways, and its ends. To the extent that affects, motivations, and purposes are bound up with one another, the objects that lie within the reach of this language that are able to be grasped by means of its concepts provide a form of cognitive handle on the complex arrays of affective impulsions and the unruly masses of emotional obstructions that serve both to drive and to block the effective performance of inquiry.

Once the differentiation between sheer activity and deliberate conduct is comprehended on informal grounds and motivated by intuitive illustrations, the formal capabilities of their logical distinction can be sharpened up and turned to instrumental advantage in accomplishing two further aims:

1. To elucidate the precise nature of the relation between action and conduct.
2. To facilitate a study of the whole variety of contingent relations that are possible and maintained between action and conduct.

When the relations among these categories are described and analyzed in greater detail, it becomes possible forge their separate links together, and thus to integrate their several lines of information into a fuller comprehension of the relations among thought, the purposes of thought, and the purposes of action in general.

It is possible to introduce the needed vocabulary, while at the same time advancing a number of concurrent goals of this project, by resorting to the following strategy. I inject into this discussion a selected set of passages from the work of C.S. Peirce, chosen with a certain multiplicity of aims in mind.

1. These excerpts are taken from Peirce's most thoughtful definitions and discussions of pragmatism. Thus, the general tenor of their advice is pertinent to the long-term guidance of this project.
2. With regard to the target vocabulary, these texts are especially acute in their ability to make all the right distinctions in all the right places, and so they serve to illustrate the requisite concepts in the context of their most appropriate uses.
3. Aside from their content being crucial to the scope of the present inquiry, their form, manner, sequence, and interrelations supply the kind of material needed to illustrate an important array of issues involved in the topic of reflection.
4. Finally, my reflections on these passages are designed to illustrate the variety of relations that occur between the POV of a writer, especially as it develops through time, and the POV of a reader, in the light of the ways that it deflects its own echoes through a text in order to detect the POV of the writer that led to its being formed in that manner.

Pragmatic Maxim 1

The first excerpt appears in the form of a dictionary entry, intended as a definition of pragmatism.

Pragmatism. The opinion that metaphysics is to be largely cleared up by the application of the following maxim for attaining clearness of apprehension: "Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object."

(Peirce, CP 5.2, 1878/1902).

The second excerpt presents another version of the pragmatic maxim, a recommendation about a way of clarifying meaning that can be taken to stake out the general POV of pragmatism.

Pragmaticism was originally enounced in the form of a maxim, as follows: Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.

(Peirce, CP 5.438, 1878/1905).

Pragmatic Maxim 2

Over time, Peirce tried to express the basic idea contained in the pragmatic maxim (PM) in numerous different ways. In the remainder of this work, the gist of the pragmatic maxim, the logical content that appropriates its general intention over a variety of particular contexts, the common denominator of all of its versionary approximations, can be referred to with maximal simplicity as “PM”. Otherwise, subscripts can be used in contexts where it is necessary to mention a particular form, for instance, referring to the versions just given as “PM₁” and “PM₂”, respectively.

Considered side by side like this, any perceptible differences between PM₁ and PM₂ appear to be trivial and insignificant, lacking in every conceivable practical consequence, as indeed would be the case if both statements were properly understood. One would like to say that both variants belong to the same pragmatic equivalence class (PEC), where all of the peculiarities of their individual expressions are absorbed into the effective synonymy of a single operational maxim of conduct. Unfortunately, no matter how well this represents the ideal, it does not describe the present state of understanding with respect to the pragmatic maxim, and this is the situation that my work is given to address.

I am taking the trouble to recite both of these very close variants of the pragmatic maxim because I want to examine how their subsequent interpretations have tended to diverge over time and to analyze why the traditions of interpretation that stem from them are likely to develop in such a way that they eventually come to be at cross-purposes to each other.

There is a version of the pragmatic maxim, more commonly cited, that uses we and our instead of you and your. At first sight, this appears to confer a number of clear advantages on the expression of the maxim. The second person is ambiguous with regard to number, and it can be read as both singular and plural, since the …

Unfortunately, people have a tendency to translate our concept of the object into the meaning of a concept. This displacement of the genuine article from the object to the meaning obliterates the contingently indefinite commonality of our manner of thinking and replaces it with the absolutely definite pretension to the unique truth of the matter // changing the emphasis from common conception to unique intention. This apparently causes them to read the whole of our conception as the whole meaning of a conception … // from thee and thy to the and our //

The pragmatic maxim, taking the form of an injunctive prescription, a piece of advice, or a practical recommendation, provides an operational description of a certain philosophical outlook or frame of reference. This is the general POV that is called pragmatism, or pragmaticism, as Peirce later renamed it when he wanted more pointedly to emphasize the principles that distinguish his own particular POV from the general run of its appropriations, interpretations, and common misconstruals. Thus the pragmatic maxim, in a way that is deliberately consistent with the principles of the POV to which it leads, enunciates a practical idea and provides a truly pragmatic definition of that very same POV.

I am quoting a version of the pragmatic maxim whose form of address to the reader exemplifies a second person POV on the part of the writer. In spite of the fact that this particular variation does not appear in print until a later date, my own sense of the matter leads me to think that it actually recaptures the original form of the pragmatic insight. My reasons for believing this are connected with Peirce's early notion of tuity, the second person character of the mind's dialogue with nature and with other minds, and a topic to be addressed in detail at a later point in this discussion.

By way of a piece of evidence for this impression, one that is internal to the texts, both versions begin with the second person POV that is implied by their imperative mood.

Just as the sign in a sign relation addresses the interpretant intended in the mind of its interpreter, PM₂ is addressed to an interpretant or effect intended in the mind of its reader.

Pragmatic Maxim 3

The third excerpt puts a gloss on the meaning of a practical bearing and provides an alternative statement of the pragmatic maxim (PM₃).

Such reasonings and all reasonings turn upon the idea that if one exerts certain kinds of volition, one will undergo in return certain compulsory perceptions. Now this sort of consideration, namely, that certain lines of conduct will entail certain kinds of inevitable experiences is what is called a "practical consideration". Hence is justified the maxim, belief in which constitutes pragmatism; namely, In order to ascertain the meaning of an intellectual conception one should consider what practical consequences might conceivably result by necessity from the truth of that conception; and the sum of these consequences will constitute the entire meaning of the conception.

(Peirce, CP 5.9, 1905).

Pragmatic Maxim 4

The fourth excerpt illustrates one of Peirce's many attempts to get the sense of the pragmatic POV across by rephrasing the pragmatic maxim in an alternative way (PM₄). In introducing this version, he addresses an order of prospective critics who do not deem a simple heuristic maxim, much less one that concerns itself with a routine matter of logical procedure, as forming a sufficient basis for a whole philosophy.

On their side, one of the faults that I think they might find with me is that I make pragmatism to be a mere maxim of logic instead of a sublime principle of speculative philosophy. In order to be admitted to better philosophical standing I have endeavored to put pragmatism as I understand it into the same form of a philosophical theorem. I have not succeeded any better than this: Pragmatism is the principle that every theoretical judgment expressible in a sentence in the indicative mood is a confused form of thought whose only meaning, if it has any, lies in its tendency to enforce a corresponding practical maxim expressible as a conditional sentence having its apodosis in the imperative mood.

(Peirce, CP 5.18, 1903).

I am including Peirce's preamble to his restatement of the principle because I think that the note of irony and the foreshadowing of comedy intimated by it are important to understanding the gist of what follows. In this rendition the statement of the principle of pragmatism is recast in a partially self-referent fashion, and since it is itself delivered as a "theoretical judgment expressible in a sentence in the indicative mood" the full content of its own deeper meaning is something that remains to be unwrapped, precisely through a self-application to its own expression of the very principle it expresses. To wit, this statement, the form of whose phrasing is forced by conventional biases to take on the style of a declarative judgment, describes itself as a "confused form of thought", in need of being amended, converted, and translated into its operational interpretant, that is to say, its viable pragmatic equivalent.

Pragmatic Maxim 5

The fifth excerpt, PM₅, is useful by way of additional clarification, and was aimed to correct a variety of historical misunderstandings that arose over time with regard to the intended meaning of the pragmatic POV.

The doctrine appears to assume that the end of man is action — a stoical axiom which, to the present writer at the age of sixty, does not recommend itself so forcibly as it did at thirty. If it be admitted, on the contrary, that action wants an end, and that that end must be something of a general description, then the spirit of the maxim itself, which is that we must look to the upshot of our concepts in order rightly to apprehend them, would direct us towards something different from practical facts, namely, to general ideas, as the true interpreters of our thought.

(Peirce, CP 5.3, 1902).

If anyone thinks that an explanation on this order, whatever degree of directness and explicitness one perceives it to have, ought to be enough to correct any amount of residual confusion, then one is failing to take into consideration the persistence of a particulate interpretation, that is, a favored, isolated, and partial interpretation, once it has taken or mistaken its moment.

Pragmatic Maxim 6

A sixth excerpt, PM₆, is useful in stating the bearing of the pragmatic maxim on the topic of reflection, namely, that it makes all of pragmatism boil down to nothing more or less than a method of reflection.

The study of philosophy consists, therefore, in reflexion, and pragmatism is that method of reflexion which is guided by constantly holding in view its purpose and the purpose of the ideas it analyzes, whether these ends be of the nature and uses of action or of thought. … It will be seen that pragmatism is not a Weltanschauung but is a method of reflexion having for its purpose to render ideas clear.

(Peirce, CP 5.13 note 1, 1902).

Pragmatic Maxim 7

The seventh excerpt is a late reflection on the reception of pragmatism. With a sense of exasperation that is almost palpable, this comment tries to justify the maxim of pragmatism and to reconstruct its misreadings by pinpointing a number of false impressions that the intervening years have piled on it, and it attempts once more to correct the deleterious effects of these mistakes. Recalling the very conception and birth of pragmatism, it reviews its initial promise and its intended lot in the light of its subsequent vicissitudes and its apparent fate. Adopting the style of a post mortem analysis, it presents a veritable autopsy of the ways that the main truth of pragmatism, for all its practicality, can be murdered by a host of misdissecting disciplinarians, by its most devoted followers. This doleful but dutiful undertaking is presented next.

This employment five times over of derivates of concipere must then have had a purpose. In point of fact it had two. One was to show that I was speaking of meaning in no other sense than that of intellectual purport. The other was to avoid all danger of being understood as attempting to explain a concept by percepts, images, schemata, or by anything but concepts. I did not, therefore, mean to say that acts, which are more strictly singular than anything, could constitute the purport, or adequate proper interpretation, of any symbol. I compared action to the finale of the symphony of thought, belief being a demicadence. Nobody conceives that the few bars at the end of a musical movement are the purpose of the movement. They may be called its upshot.

(Peirce, CP 5.402 note 3, 1906).

There are notes of emotion ranging from apology to pique to be detected in this eulogy of pragmatism, and all the manner of a pensive elegy that affects the tone of its contemplation. It recounts the various ways that the good of the best among our maxims is "oft interrèd with their bones", how the aim of the pragmatic maxim to clarify thought gets clouded over with the dust of recalcitrant prepossessions, drowned in the drift of antediluvian predilections, lost in the clamor of prevailing trends and the shuffle of assorted novelties, and even buried with the fractious contentions that it can tend on occasion to inspire. It details the evils that are apt to be done in the name of this précis of pragmatism if ever it is construed beyond its ambition, and sought to be elevated from a working POV to the imperial status of a Weltanshauung.

Postscript A

The next three elaborations of this POV are bound to sound mysterious at this point, but they are necessary to the integrity of the whole work. In any case, it is a good thing to assemble all these pieces in one place, for future reference if nothing else.

When we come to study the great principle of continuity and see how all is fluid and every point directly partakes the being of every other, it will appear that individualism and falsity are one and the same. Meantime, we know that man is not whole as long as he is single, that he is essentially a possible member of society. Especially, one man's experience is nothing, if it stands alone. If he sees what others cannot, we call it hallucination. It is not "my" experience, but "our" experience that has to be thought of; and this "us" has indefinite possibilities.

(Peirce, CP 5.402 note 2, 1893).

Nevertheless, the maxim has approved itself to the writer, after many years of trial, as of great utility in leading to a relatively high grade of clearness of thought. He would venture to suggest that it should always be put into practice with conscientious thoroughness, but that, when that has been done, and not before, a still higher grade of clearness of thought can be attained by remembering that the only ultimate good which the practical facts to which it directs attention can subserve is to further the development of concrete reasonableness; so that the meaning of the concept does not lie in any individual reactions at all, but in the manner in which those reactions contribute to that development. … Almost everybody will now agree that the ultimate good lies in the evolutionary process in some way. If so, it is not in individual reactions in their segregation, but in something general or continuous. Synechism is founded on the notion that the coalescence, the becoming continuous, the becoming governed by laws, the becoming instinct with general ideas, are but phases of one and the same process of the growth of reasonableness.

(Peirce, CP 5.3, 1902).

No doubt, Pragmaticism makes thought ultimately apply to action exclusively — to conceived action. But between admitting that and either saying that it makes thought, in the sense of the purport of symbols, to consist in acts, or saying that the true ultimate purpose of thinking is action, there is much the same difference as there is between saying that the artist-painter's living art is applied to dabbing paint upon canvas, and saying that that art-life consists in dabbing paint, or that its ultimate aim is dabbing paint. Pragmaticism makes thinking to consist in the living inferential metaboly of symbols whose purport lies in conditional general resolutions to act.

(Peirce, CP 5.402 note 3, 1906).

Postscript B

The final excerpt touches on a what can appear as a quibbling triviality or a significant problem, depending on one's POV. It mostly arises when sophisticated mentalities make a point of trying to apply the pragmatic maxim in the most absurd possible ways they can think of. I apologize for quoting such a long passage, but the full impact of Peirce's point only develops over an extended argument.

There can, of course, be no question that a man will act in accordance with his belief so far as his belief has any practical consequences. The only doubt is whether this is all that belief is, whether belief is a mere nullity so far as it does not influence conduct. What possible effect upon conduct can it have, for example, to believe that the diagonal of a square is incommensurable with the side? … The proposition that the diagonal is incommensurable has stood in the textbooks from time immemorial without ever being assailed and I am sure that the most modern type of mathematician holds to it most decidedly. Yet it seems quite absurd to say that there is any objective practical difference between commensurable and incommensurable. Of course you can say if you like that the act of expressing a quantity as a rational fraction is a piece of conduct and that it is in itself a practical difference that one kind of quantity can be so expressed and the other not. But a thinker must be shallow indeed if he does not see that to admit a species of practicality that consists in one's conduct about words and modes of expression is at once to break down all the bars against the nonsense that pragmatism is designed to exclude. What the pragmatist has his pragmatism for is to be able to say: here is a definition and it does not differ at all from your confusedly apprehended conception because there is no practical difference. But what is to prevent his opponent from replying that there is a practical difference which consists in his recognizing one as his conception and not the other? That is, one is expressible in a way in which the other is not expressible. Pragmatism is completely volatilized if you admit that sort of practicality.

(Peirce, CP 5.32–33, 1903).

Let me just state what I think are the three main issues at stake in this passage, leaving a fuller consideration of their implications to a later stage of this work.

1. Reflective agents, as a price for their extra powers of reflection, fall prey to a new class of errors and liabilities, any one of which might be diagnosed as a reflective illusion or a delusion of reflection (DOR). There is one type of DOR that is especially easy for reflective agents to fall into, and they must constantly monitor its swings in order to guard the integrity of their reflective processes against the variety of false images that it admits and the diversity of misleading pathways that it leads onto. This DOR turns on thinking that objects of a nature to be reflected on by an agent must have a nature that is identical to the nature of the agent that reflects on them.

An agent acts under many different kinds of constraints, whether by choice of method, compulsion of nature, or the mere chance of looking outward in a given direction and henceforth taking up a fixed outlook. The fact that one is constrained to reason in a particular manner, whether one is predisposed to cognitive, computational, conceptual, or creative terms, and whether one is restrained to finitary, imaginary, rational, or transcendental expressions, does not mean that one is bound to consider only the sorts of objects that fall into the corresponding lot. It only forces the issue of just how literally or figuratively one is able to grasp the matter in view.

To imagine that the nature of the object is bound to be the same as the nature of the sign, or to think that the law that determines the object's matter has to be the same as the rule that codifies the agent's manner, are tantamount to special cases of those reflective illusions whose form of diagnosis I just outlined. For example, it is the delusion of a purely cognitive and rational psychology, on seeing the necessity of proceeding in a cognitive and rational manner, to imagine that its subject is also purely cognitive and rational, and to think that this abstraction of the matter has any kind of coherence when considered against the integrity of its object.

2. The general rule of pragmatism to seek the difference that makes a difference has its corollaries in numerous principles of indifference. Not every difference in the meantime makes a difference in the end. That is, not every difference of circumstance that momentarily impacts on the trajectory of a system nor every difference of eventuality that transiently develops within its course makes a difference in its ultimate result, and this is true no matter whether one considers the history of intertwined conduct and experience that belongs to a single agent or whether it pertains to a whole community of agents. Furthermore, not every difference makes a difference of consequence with respect to every conception or purpose that seeks to include it under its "sum". Finally, not every difference makes the same sort of difference with regard to each of the intellectual concepts or purported outcomes that it has a bearing on.

To express the issue in a modern idiom, this is the question of whether a concept has a definition that is path-dependent or path-invariant, that is, when the essence of that abstract conception is reduced to a construct that employs only operational terms. It is because of this issue that most notions of much import, like mass, meaning, momentum, and number, are defined in terms of the appropriate equivalence classes and operationalized relative to their proper frames of reference.

3. The persistent application of the pragmatic maxim, especially in mathematics, eventually brings it to bear on one rather ancient question. The issue is over the reality of conceptual objects, including mathematical "objects" and Platonic "forms" or "ideas". In this context, the adjective "real" means nothing other than "having properties", but the import of this "having" has to be grasped in the same moment of understanding that this old schematic of thought loads the verb "to have" with one of its strongest connotations, namely, that nothing has a property in the proper sense of the word unless it has that property in its own right, without regard to what anybody thinks about it. In other words, to say that an object has a property is to say that it has that property independently, if not of necessity exclusively, of what anybody may think about the matter. But what can it mean for one to say that a mathematical object is "real", that it has the properties that it has independently of what anybody thinks of it, when all that one has of this object are but signs of it, and when the only access that one has to this object is by means of thinking, a process of shuffling, sifting, and sorting through nothing more real or more ideal than signs in the mind?

The acuteness of this question can be made clear if one pursues the accountability of the pragmatic maxim into higher orders of infinity. Consider the number of "effects" that form the "whole" of a conception in PM₁, or else the number of "consequences" that fall under the "sum" in PM₂. What happens when it is possible to conceive of an infinity of practical consequences as falling among the consequential effects or the effective consequences of an intellectual conception? The point of this question is not to require that all of the items of practical bearing be surveyed in a single glance, that all of these effects and consequences be enumerated at once, but only that the cardinal number of conceivable practical bearings, or effects and consequences, be infinite.

Recognizing the fact that "conception" is an "-ionized" term, and so can denote an ongoing process as well as a finished result, it is possible to ask the cardinal question of conceptual accountability in another way:

What is one's conception of the practical consequences that result by necessity from a case where the "conception" of practical consequences that result by necessity from the truth of a conception constitutes an infinite process, that is, from a case where the conceptual process of generating these consequences is capable of exceeding any finite bound that one can conceive?

Postscript C

It is may be helpful to append at this point a few additional comments that Peirce made with respect to the concept of reality in general.

And what do we mean by the real? It is a conception which we must first have had when we discovered that there was an unreal, an illusion; that is, when we first corrected ourselves. Now the distinction for which alone this fact logically called, was between an ens relative to private inward determinations, to the negations belonging to idiosyncrasy, and an ens such as would stand in the long run. The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of a definite increase of knowledge.

(Peirce, CP 5.311, 1868).

The real is that which is not whatever we happen to think it, but is unaffected by what we may think of it.

(Peirce, CE 2:467, 1871).

Thus we may define the real as that whose characters are independent of what anybody may think them to be.

(Peirce, CP 5.405, 1878).

Having read these exhibits into evidence, if not yet to the point of self-evidence, and considered them to some degree for the individual lights they throw on the subject, let me now examine the relationships that can be found among them.

These excerpts are significant not only for what they say, but for how they say it. What they say, their matter, is crucial to the whole course the present inquiry. How they say it, their manner, is itself the matter of numerous further discussions, a few of which, carried out by Peirce himself, are already included in the sample presented.

Depending on the reader's POV, this sequence of excerpts can appear to reflect anything from a radical change and a serious correction of the underlying POV to a mere clarification and a natural development of it, all maintaining the very same spirit as the original expression of it. Whatever the case, let these three groups of excerpts be recognized as forming three successive levels of reflection (LORs) on the series of POVs in question, regardless of whether one sees them as disconnected, as ostensibly related, or else as inherently the very same POV in spirit.

From my own POV, that strives to share this spirit in some measure, it appears that the whole variety of statements, no matter what their dates of original composition, initial publication, or subsequent revision, only serve to illustrate different LOR's on what is essentially and practically a single and coherent POV, one that can be drawn on as a unified frame of reference and henceforward referred to as the pragmatic POV or as just plain pragmatism.

There is a case to be made for the ultimate inseparability of all of the issues that are brought up in the foregoing sample of excerpts, but an interval of time and a tide of text are likely to come and go before there can be any sense of an end to the period of questioning, before all of the issues that these texts betide can begin to be settled, before there can be a due measure of conviction on what they charge inquiry with, and before the repercussions of the whole sequence of reflections they lead into can be brought to a point of closure.

If one accepts the idea that all of these excerpts are expressions of one and the same POV, but considered at different points of development, as enunciated, as reviewed, and as revised over an interval of many years, then they can be taken to illustrate the diverse kinds of changes that occur in the formulation, the development, and the clarification of a continuing POV.

The Face in the Mirror

We cannot proceed in the question of the who without introducing the problem of everyday life, self-knowledge, the problem of the relation to the other — and, ultimately, the relation to death.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 232]

It is the business of this preview to take up the initial stirrings of many subject matters that cannot hope to be completely developed, even clearly engaged, and much less fully formalized at the present stage of discussion. At many points I can afford to pause only long enough to toss a provisional name in the direction of a subject I plan to address more fully later on, and at times I can merely indicate in cursory terms a topic that I intend to return to at several later points in this work.

There are aspects of inquiry that are difficult to address from a purely cognitive point of view, that is, from a standpoint that expects agents of inquiry to behave in a strictly rational fashion. At times it appears that there are complexities in the phenomenology of inquiry that are impossible to compass, comprehend, deal with, fathom, grasp, or tackle by means of a purely cognitive or strictly rational method of approach. Nevertheless, it is not that the manner of proceeding ought to be anything other than what it aims to be, but merely that it cannot expect its subject matter to mirror nothing beyond its own manners of limitations, principles, and scruples.

The reason that these issues have to be discussed at this particular point of this particular inquiry is simply that it cannot proceed beyond this point without facing up to them and facing them down again, that is, without addressing them in some measure and reducing the force of their obstruction. In short, these issues present a real obstacle to the progress of this inquiry.

It is such a rarity for this theme of “internal opposition” to find a clear expression in the light of day that the latest and best descriptions one sees of it are not all that far removed in their basic characters and their degrees of clarity from the very first inklings one can find of it, namely, those intimations of its nature that remain wrapped up in the perennial figures of perceptive allegory and the ancient images of insightful mythology that are passed down from the foundings of every civilized culture. Thus, I find I cannot discuss this issue, even dimly, without first invoking this class of symbols, no matter what difficulties of interpretation they bring in their train. I can only promise to try to clarify their empirical and rational meanings as the discussion continues.

In general, one can treat the dramatic images presented by literature and mythology as not essentially different from scientific images of action, behavior, and conduct. They all attempt to capture something about human aims and human actions in a compact, exact, and memorable image, to catch a glimmer of human behavior in a singular but still moving form, and to cache it in the coin of a common exchange so that it embodies not just a commemorative but a communerative inheritance, one that anyone with access to the store can recurrently cash in as warranted by the occasion and the development of a particular situation, that all can repeatedly bank on to their individual and common profit. No matter what genre it is cast within, a successful image records a moment's insight into an aspect of human nature, preserving it in such a way that it can reveal itself at relevant moments in future experience, and thus avail itself in such a form that it makes this particular insight into this particular aspect available for the use of many other points of view.

An image is useful if it codifies significant insights about character and conduct. To do this it needs to indicate, descriptively or normatively, important aspects of behavior, involving the necessary structures or the contingent potentials of conduct. An image is especially useful if it is indexed to come to mind at the times when it is appropriate, called for, and helpful. An image begins to make itself useful in a more scientific, or a deliberately controlled way, if it can serve flexibly and not just fixedly in the act of reflecting on a present scene or a real situation. This means that it can make itself available as a suggestive hypothesis about a situation in general and can serve as a constructive critique of the ways to proceed from that point forward, but that it does not force itself on any particular situation, does not take the role of an active ingredient in the objective problem to be resolved, and does not elect itself as the primary constituent of that very predicament.

To be useful in critical reflection, an image has to remain transparently suggestive of the potentials that reside in a real and present situation. To continue its utility in a viable process of reflection, an image cannot allow itself to be so cast in stone that it blocks contemplation of all that demands attention in a real situation, and it cannot become so blindingly opaque in its own right that it obscures and occludes any concern that does not fit within its pre-cut scene. In order to preserve its uses in feasible and viable conditions, an image cannot be allowed to coerce the satisfaction of its own application, as in the style of a self-fulfilling prophecy or the spell-binding picture of a prescience that predestines its own end, descriptively and prescriptively determining the form and the fact of its own fate.

In this connection, it is not just in story and fable that one finds the images of self-fulfilling prophecies. The scientific picture of human behavior embodies an equal number of self-satisfying limitations and self-predicting reductions, analogous to the image of a person who is looking under the lamppost for something lost elsewhere simply because the light is better there, or the image of a person with no tool but a hammer who is determined by this utility to view everything as a nail.

These possibilities highlight and point up another source of perils that one risks in trying to craft a serviceable RIF. One of the main reasons for seeking a RIF is to make reflective and critical images of a chosen framework available within the scope of that very same framework itself. But the original aim of the framework, that orients its agent toward an objective reality, should not be lost in the process of adjoining these reflections on its own form. So the next predicament to be solved, once the inclusion of self-images is provisionally made possible and after the license of self-reference is tentatively permitted, is how to prevent the extended framework from being swamped by nothing but images of itself, with nothing on the order of an objective nature and nothing of the other that it originally sought.

The particular problematic I am trying to capture here seems to demand a symbol of a sufficient power, and this forces me to raid the reserves of archetype and mythology. So let me stake out this issue under the rubric of "Cerberus". It deserves this name for at least three reasons. First, there is the way that it blocks one's way to underlying sources of insight, the way it closes off one's access to a potential wealth of deeper understandings of oneself. Second, there is the irresistible challenge presented by external forms of resistance to one's own ideals, the instigation that this very resistance represents to one's own drives against it, and the incitement to collective effort and deliberate trials that it causes to mount, thereby harnessing one's motive instincts and promoting their expression in particular directions. Third, there is the snarling dogmatism that it betrays, of a kind that one encounters most acutely in one's dealings with one's counterparts in the community, but that one can tackle only within oneself, as if all along the doubts and the difficulties that the other comes to represent for oneself are merely the reflections, in the mirror afforded by the external world, of one's own internal opposition.

In practice, the obstructions that an effort of inquiry is bound to meet up with in the world outside its state of intention would not be able to knock it off its target if it were not for the opposing tensions that it maintains within its own intentional bearing. Sometimes, these take the form of intrinsic or inherent oppositions, but more often than not they are “introjected” obstacles, the sort that get themselves internalized at a particular point in time. This brings the mythological portion of this tale around to the figure of “Oedipus”, portraying the predicament of an inquiry that deliberately blinds itself, not just for what it has seen, but for what it might continue to see.

Given the license to temporarily invoke such powerful cultural symbols, and since the issues they try to capture appear already bound together, I can organize the manifestations of this problematic under three heads:

1. The “negative onus” (NO) of inquiry.
2. The “affective mood” (AM) of inquiry.
3. The “existential subjective tone” (EST) of inquiry.

The pragmatic description of inquiry is notorious for the constellation of problematic and negative features that its account the matter points out. In practice, this complex of negative aspects recurrently presents itself as the most difficult to steadily face up to without flinching and the most troublesome to squarely address without blanching, blinking, or otherwise to break off the approach and even to abandon the question. By way of deriving the minimal service that the simplest name affords, I refer to this problematic aspect as the “negative onus” (NO) of inquiry.

The natural instinct of the mind brings it into frequent encounters with this NO, at least, its short term need for adventure and exploration is often brought up short by it. But there are other tendencies at work in the meantime, and independent dispositions can be found at play on each larger scale of the process of inquiry. For instance, there is evidently a concurrent tendency of the mind to run away from this NO, since its desire for security in the intermediate term is threatened by the practical consequences of affronting and so bearing the brunt of it. In any case, this is how the matter typically develops after the initial fascination with a surprising phenomenon or the original compulsion to resolve a problematic situation have faded, and this is usually sometime before a reasonable explanation or a suitable plan of action can appear. And so one finds that successful inquiries often require a second stage, or even more, that their incipient motivations are seldom enough to get them past the first signs of trouble, that it takes renewable resources of persistence to countenance the negative aspects of inquiry, and that it takes a higher order of dedication to keep from running away in the face of a genuine question's more troubling demeanor.

The NO of inquiry arises at a couple of distinct moments in its process. It arises naturally enough at the outset of inquiry, due to the negative, problematic, and troubling aspects of doubt and uncertainty. But again, no sooner does an inquiry get started in some hopeful direction than it runs into a host of distortions, diversions, obstacles, and resistances that act to impede its progress. Some of these obstructions can be seen as derivative expressions of the original uncertainty that occasioned a specific inquiry, but others go deeper than the issues that stem from a particular topic. Other obstacles, harder to address, have to do with a deficient motivation for a specific inquiry, a deficit in competence at inquiry in general, a constitutional incapacity to change beliefs once their status is fixed, or a lack of desire to make the necessary changes in belief and in conduct that are always at risk in an authentic inquiry. Still other obstacles abide at another order entirely, arising from the necessary properties and structures of inquiry itself.

The fact that the pragmatic point of view recognizes uncertainty as the beginning of inquiry means that the dynamic start of its process and the rational foundation of its method are energetically and logically sundered from each other, if not forever split apart, then at least until the inquiry in question is itself resolved.

All attempts to found inquiry on positive intellectual powers and virtues, or to chart its progress through purely rational methods and principles, always come to grief and founder on the fact that one cannot squarely address the obstructions to inquiry without facing up to the negative, troubling, and unruly aspects of truly problematic uncertainties, nor without being willing to look at the affective investments that people have in their own pet notions and their favorite group's fondest ideas. It is neither possible nor necessary to deal with this problem, in its entirety, within the present context. However, it is both necessary and possible to articulate the ways that it impacts on the present concerns. In this regard, a measure of “affective investment” in a customary idea or interpretive conduct is the persistence of the custom or the strength of the habit that associates itself with that particular conduit of ideas. This translates the notion of “affective investment” into a concept with dynamic import, giving it an operational significance and a quantifiable meaning for the current approach to a “dynamic symbolics”.

Depending on the accidents and the inevitabilities of their historical reception, the trains of consequences that accompany them, the general drift of intervening events, and the finer shade of the mood from which the totality of this sweep is reviewed, a retrospective LOR can take on all the character of any pure choice or any mixture of options from a whole spectrum of characters. Just by way of example, these can range from apology, casuistry, and attempts at exculpation or explanation by way of mitigating circumstances, through elegy, encomium, and eulogy, then all the way to lamentation, melancholy, panegyric, and requiem.

Is the lack of a mirror really lamented? And if it is literally so, then what is the source of remorseful affect that abides in this impression? From whence does the vast but vaporous plague of advisory injunctions, censorious restrictions, circumspect suspicions, consensual admonitions, delinquent proscriptions, imminent suspensions, monitory animadversions, mundane cautions, and tardy but truant afterthoughts arise, along with the vague but vampirous unease of something forgotten, lost, or forlorn? If one arrives at the point of asking in what sort of space does a point of view reside, and what manner of a multitude does it share this manifold with, then the sense of this whole, collective, irksome host begins to appear.

One clue arises from the circumstance that the very purpose of affects, emotions, and motives is to change a point of view, to alter a state of being or a position in space, to get through a fit of pique or a point of impasse, to break out of a fixed opinion in the labyrinth of purely intellectual and speculative convictions. And yet this presents nothing but problems for the effort to see the formal skeleton within the living body of inquiry.

Although emotion remains a pervasive factor in the informal realm, it is difficult to see, at least, at first, how its forces could be transmitted into and through the formal arena, even if, in spite of all appearances, there were found to be forms of good judgment that permitted it to try. The only hint of an answer that I can see at this point is the insight that is stored up in the very etymology of “form” itself, whose often forgotten connotation is literally “beauty”.

The final consequence that I want to derive from these excerpts is their bearing on the differential relationships that exist between a conduct, as it distinguishes itself in action from an action, and the respective ends of this conduct and this action, all in all, which may amount to the very same object in the end. In particular, I want to point out a remarkable implication of this approach that I call the “paradox of conduct” (POC).

Considered as action, the end of life is death, but

considered as conduct, the end of life is life itself.

I am attempting no definition of life here, but merely noting one of its most exemplary and elegant formal properties. In game theoretic terms, if life is a game then its aimed for value is a robustly recursive goal. In generic terms, the pay off, intended target, or desired value of the whole game of life is just the whole game back again. In species terms, the aim of a form of life is to continue its life in the same form, or in what is recognizable to itself as being in its original spirit (“anima”). The content that abides in a form of life is not a satisfaction with the continual repetition of precisely the same state of being or the unending replication of perfectly identical copies of itself, as these by themselves are just different forms of death, but it takes an ability to recognize and regenerate the spirit within the letter, to promote the true content its own essential form, not merely to reproduce the shadow of its shape.

In this sense, and purely with regard to the topographies of their fields and courts of play, life is less like soccer, where the goals fall at the extreme ends of the field, than it is like tennis, where the net measure of its results lies in the midst of the ongoing play. Altogether, this makes life a system of organization that is topologically “open” at both ends, both with regard to its foundations, its “arche”, and also with respect to its goals, its “telos”.

To draw the conclusion: To say that death is the end of life, in the sense of a goal, is obviously going a bit too far. Death is merely the contingent end of life as form of action, not the intentional end of life as a form of conduct, and all the rest of the confusion is merely verbal equivocation around and about these two senses of an end. In the light of the distinction between action and conduct it is easy to see that death is just a bit beyond the true end of life.

In the same way as it is not sufficient, before beginning to rebuild the house in which one lives, only to pull it down and to provide material and architects, or oneself to try one's hand at architecture, and moreover, to have drawn the plan carefully, but one must also provide oneself with some other accommodation in which to be lodged conveniently while the work is going on, so, also, in order that I might not remain irresolute in my actions during the time that my reason would oblige me to be so in my judgements, and so that I would not cease to live from that time forward as happily as I could, I formed a provisional moral code which consisted of only three or four maxims, which I am willing to disclose.

Rene Descartes, Discourse on Method, [Des, 45]

The advisability of justifying one's actions as much as one can is clear, but the problems that arise in trying to do so are not trivial, …

In view of these problems, it is necessary to examine the formation of the JE and to consider its import for the justification of inquiry (JOI). It is useful to begin with a traditional idea or a received sense of what a JOI must be. The default justification, that almost everyone seems to fall back on, even when deliberately trying to be critical and reflective, arises from the common notion of a “foundation” as something that forms a necessary prerequisite to all attempts at reasoning.

After giving a critical account of the standard model in the light of a few additional reflections, I review the question of what a real JOI must be like, at least, if it is to allow for inquiry into inquiry and to account for the other features of inquiry already observed. At last, I renew the quest for those JOIs that befit a pragmatic perspective and that can be found within its survey.

There is a standard sort of proposal to justify inquiry that attempts to place its foundations at the beginning of its process and that insists on making them out as certain. I think it is fitting to describe this as a variety of fundamentalism. If this form of understanding is submitted to reflection, it begins to look inconsistent, or at least hypocritical, since it promises a distinct JOI, but one that it can just as easily tell, by the right reflection at the outset, is not forthcoming by these means. In essence, it claims to have a different sort of justification for itself than every other claim to one's allegiance, but a careful examination of its more finely printed disclaimers begins to turn up the evidence that this, too, is ultimately on a par with every other belief system, with the technical exception that it demands unquestioning faith at the level of a method rather than on the grounds of a doctrine. Even here, it leaves one wondering how to discern these levels in practice, or whether they can be distinguished in principle.

On this fundamental model of inquiry, any appearance of a passage from doubt to certainty has its authenticity placed in doubt, and begins to have its pretensions of creatively discovering new knowledge fall into question, looking more like the illusions of a derivative performance. Indeed, every semblance of a genuine inquiry is parasitic on the host of axioms and methods already taken for granted, and it creates no greater capital of knowledge than the fund of certainty already established in a prior method of inquiry. In effect, this prior method is taken on faith, since it begs to be imitated in a ritual fashion and to have its formulas, while invoked without question, to be invested with blind forms of trust.

In fine, the default manner of approaching the question of foundations makes inquiry into inquiry a moot question, an otiose endeavor that is neither possible to pursue in a bona fide way nor necessary to venture. Given the fundamentalist understanding of inquiry, the application of inquiry to itself can neither accomplish any real purpose nor achieve any goal that is actually at risk. The pretense of establishing the integrity of inquiry under a self-application of its principles always results in something of a put up job, a kangaroo court, or a show trial.

Under these conditions, the proceedings that declaim themselves to be engaged in honest inquiry are nothing more than a hypocritical display. They imitate the exterior form of a due process, but their judgment is fixed in advance and their conclusion but extravagantly reconstructs a previously settled system of belief, one that is never really doubted or put in question. The outer inquiry in the self-application is not a live inquiry but a frame that is prefabricated to isolate the object inquiry. Whether expertly or inertly, it is designed ahead of time to contain and to delimit a picture of inquiry that may or may not already be painted.

Notice that this is not a question of whether the original inquiry is genuine or not. The object inquiry, typically ignited by an external phenomenon, is commonly taken up in good faith, that is, with honest doubts at stake. But when there is never any doubt about what method to use, or about how to use it, or about the chances of its leading to a satisfactory end of the doubts inflamed in the first place, then there is never any need for inquiry into inquiry, and all show of it is vanity.

As a result, the fundamental JOI renders the hallowed method of inquiry just another doctrine among others, equal in its manner of justification, its final appeal, and its ultimate justice to every other belief system. But this is not the criticism that finally condemns it. Being just the same as other systems of belief is not the fatal flaw. That only makes all systems of belief equal under the law, if no longer a law of inquiry but a law of compromising positions and convenient resolutions. Still, there would not necessarily have been anything wrong with this, if it were not for the self-imposed burden that inquiry brings down on itself via the dishonesty or the self-deception of promising something else.

Could great men thunder
As Jove himself does, Jove would never be quiet,
For every pelting petty officer
Would use his heaven for thunder, nothing but thunder.
Merciful heaven,
Thou rather with thy sharp and sulphurous bolt
Split'st the unwedgeable and gnarlèd oak
Than the soft myrtle. But man, proud man,
Dressed in a little brief authority,
Most ignorant of what he's most assured,
His glassy essence, like an angry ape
Plays such fantastic tricks before high heaven
As makes the angels weep, who, with our spleens,
Would all themselves laugh mortal.
	Measure for Measure, 2.2.113–126

It is probably wise to stress this point. It is not being claimed that an authority based system of belief, simply by building itself on traditional foundations, is necessarily hypocritical or inconsistent in its own right. It can be as accurate, authentic, and honest in what it says and tries to say as any other belief system or knowledge base. In fact, a modicum of reliance on one source of authority or another is not only prudent but most likely to be found inescapable. Authority based systems, in form so analogous to axiom systems, if not in the context of their use, simply have the specific properties and the generic limitations that they can be observed to have.

At this point, let authority based systems and axiom systems be lumped together into the same class, at least temporarily, on the basis of the forms of derivation that they allow, and without regard for the different ways that they are initially brought to light or subsequently put to use. Further, let this whole class be described as founded systems, for the moment ignoring the distinction between informal and formal systems, or regarding all prospectively, in anticipation of their formalizations.

Every project of a founded system voluntarily risks certain limitations. But there is one limitation that appears to be a genuine defect from the standpoint of this inquiry, amounting to the chief source of worry that this inquiry has about the whole class of founded systems. This is the fact that whatever acuteness of reverence or accuracy of reference to their objects they do in fact achieve is a matter of grace or luck, and not something that can be subjected to change, criticism, or correction. This puts it outside the sphere of inquiry, as I understand it, even if its formulations are suggested by data within the sphere of experience.

In effect, there is no amplification of intelligence, no leverage of reason, in short, no instrumental gain or “mechanical advantage” to be acquired from the use of a founded system. It can transmit the force of reason, in a conservative way at best, from premisses to conclusions, but the effective output of the system achieves no greater level of certainty as it bears on any question than the level of authority it can grant itself on input or justly claim for itself at the outset. If I can continue to use the image of a lever, while delaying the examination of its exactness until a later point of this work, it is as if the lack of leverage in a founded system can be traced back to one of several defects:

1. The fulcrum of a founded system, the fixed point of its critique, is the examen of its critical powers, the tongue of its balance, and this has to be placed so evenly between the objective domain, whereof its ignorance is writ so large, and the fund of applied information, wherein its share of accumulated knowledge resides, that no gain in the effective intelligence of the actions thus founded can be derived.
2. A founded system is forced to be a grounded system, that is, one that requires a moderately strong emplacement on grounds already settled and a preponderance of certainty on the side of the applied intelligence.
3. In effect, a founded or grounded (FOG) system requires absolute certainty with respect to some of its points, the points on which it is said to rest. It is as if these fixed points put it in contact with an infinite source of knowledge or connect it to an infinite sink for uncertainties. Of course, a FOG system that casts itself as a beacon of enlightenment and sells itself under the label of “science” can never admit to seeing itself in this image, since the very act of making the claim explicit already puts its grant in jeopardy. But that is what it amounts to, nevertheless.

Another way to see the over-constrained nature of these FOG conditions, for the certainty of foundations, is by expressing them in terms of the boundary conditions that a given system of belief is assumed to have. In this regard, it helps to make the following definition. An open system of belief is one that has each of its points mediated by the system itself, in other words, surrounded by, apprehended within, and evidentially or argumentatively justified by a neighborhood of similar points that falls entirely within the system in question.

When it is considered in the light of this definition of openness, a FOG system is clearly seen to constitute a non-open system of belief. In short, not all of its axioms, points, or tenets are mediated within the system itself, but have their motives, reasons, and supports lying in points ulterior to it. In hopes of serving both the understanding and the memory, let me try to express this situation in a couple of striking, if slightly ludicrous, metaphors, a pair of judicial, if not entirely judicious, figures of speech:

1. The corpus delicti, the body of material evidence and substantial fact that is necessary to justify the institution of the system and the initiation of its every process, is always found to lie in such a disposition that it rests partially beyond the system in question.
2. The habeas corpus, the body of probable causes and sufficient reasons that is tendered to justify the holding of certain points, is always deposed in such a demeanor that its true warrant either stays unwrit or is writ largely outside the system in question.

Whether it is verifiably jurisprudent or merely a fantastic simile, whether it is really a conspiracy of their natural bents or purely a coincidence of their accustomed distortions, the parody of a judicial process that one constantly sees being carried on in the name of this or that FOG system, and always apparently up to the limits of their several FOG boundaries, makes a mockery of the spirit of inquiry, and of all its pretensions to a critical reflection, since it places not only the first apprehension but the final justice of such a system beyond all question of executive examination, judicial review, and constitutional amendment. The whole matter is even more deceptive that it appears at first sight, precisely because a FOG system, as lit within, or according to its own lights, often takes on all the appearance of being open. But this is only because the boundaries of its viability and the outlines of the external obstacles that represent a threat to the illusions of its omni pervasiveness are actively being obscured by the limitations inherent in its unreflective nature.

This is just the kind of situation that one would expect in the purely deductive or demonstrative sections of science, for instance, in logics and mathematics of the “purer” and less “applied” sorts. In these more abstract traces and more refined extracts of a fully scientific method, the authority of the conclusions, or the level of certainty achieved on output, is no greater than the authority of the premisses, or the level of certainty possessed on input. Thus, the work of reasoning in such a case is purely expliative, that is, wholly expository or explicational.

But a truly synthetic or ampliative analysis should be able to reduce a complex induction to simple inductions, meanwhile gaining a measure of certainty in the process, and all without losing the power to reconstruct the complex from the simple. The perceived gain of practical certainty that develops in this analysis can be explained in the following manner. A complex induction, prior to analysis, is likely to be a very uncertain induction, but is likely to have its certainty shored up if the analysis to simple inductions is successful.

This is a pretty sorry picture, especially in view of all the bright promises of enlightenment through inquiry that inquiry makes, to be a veritable system of belief for constituting systems of veritable belief. But the promise of inquiry to be better than all that, to be an advance over other systems of belief, not just another dogma in the management of uncertainty but a unique way of life, holds out hopes that are still tempting and that deserve to be pursued further. So it is time to ask: If not by means of these foundations, then what form of constitution can provide the sought for JOI?

Fortunately, there is another JOI, arising from the pragmatic critique of even the most enlightened fundamentalism. If the fundamental approach is viewed as a project to conjoin three positive features — founding, beginning, and certain — in a single point of conceptual architecture, then the pragmatic critique of this plan can be understood as objecting that this point is overloaded. There are ways to preserve this triarchic association, but not without protracting other angles of approach to the juncture and not without compassing other senses of the terms than the meanings originally intended. It is perhaps easier just to abrogate one of the terms, either rescinding its constraint or trading it in for its logical negation.

The pragmatic approach to the foundations of inquiry, more precisely, its approach to the hoped for JOI, whether or not this leaves room in the end for a notion of secure foundations, suggests that reason does begin with unreason, but only in the sense that inquiry starts from a state of uncertainty. If one objects that this doubt is not radical, because many things in the meantime are never in fact doubted at all, then this is correct, but only in the sense that these things are not doubted because they are never even consciously questioned. If that sort of lack of doubt is the type one plans to found their reason on, then I think it is a very fond notion indeed.

There's a double meaning in that.
	Much Ado About Nothing, 2.3.246

(Yes, there is a subtext. (There is always a subtext.) A reader who has access to the subtext, who can read it in the face of the pretext, and who remains both sensitive to and sensible about its connotations, is already beginning to suspect that what I intend to argue in the end is exactly that the chief justification of inquiry is nothing less and nothing more than the pure joy of it. But the moment that I depend on this subtext to carry the logical argument, to go beyond supporting the intuition and encouraging the effort of reasoning, is the moment that I utterly fail in my intention. This bears on the matter of a harmonious balance between rhetoric and logic, where the former appreciates and is bound to consider the affective and the impressionable nature of the interpreter, and takes into account the need for reason's ponderous beacon to be buoyed over the deep by incidental glosses and light exhortations.)

Self-awareness is our capacity to stand apart from ourselves and examine our thinking, our motives, our history, our scripts, our actions, and our habits and tendencies. It enables us to take off our “glasses” and look at them as well as through them. It makes it possible for us to become aware of the social and psychic history of the programs that are in us and to enlarge the separation between stimulus and response.

Covey, Merrill, and Merrill, First Things First, [CMM, 59]

How is it possible for one to use an organization of thought in order to think about that same organization of thought, or indeed, about others? How is it possible to draw distinctions, even the most basic distinctions necessary to thought, in such a way that they can be redrawn and even withdrawn when necessary? In other words, what are the conditions for having a critical reflection of inquiry (CROI), a system of assumptions and methods that acts continuously and self-correctively to constitute a critically reflective belief system? This would be tantamount to a POV where no assumption is forced to be taken for granted, even if at any given moment many assumptions are contingently being acted on just as if they were true. For instance, if a distinction between dynamic and symbolic systems, or aspects of systems, is a part of one's present POV, to what extent can one reflect on that fact, and thus be able to think about alternative POVs or to think about changing one's current POV?

This ends my preview of the kinds of issues that the pragmatic theory of sign relations and their reflective extensions is intended to comprehend.

In the sequel I propose a particular way of approaching these problems. I introduce a simplified model of the general situation to be addressed, but one with sufficient structure to embody analogous versions of many of the problems and phenomena of ultimate interest. By exploring the issues that develop in this miniature model, and by looking for ways of resolving them that work on this scale, I hope to gain insight into ways of dealing with the corresponding issues in the larger study of inquiry.

To be specific, I restrict my discussion at first to propositional or sentential models of POVs, and I examine a particular type of logical strategy that allows agents operating within this framework to describe the constitutions of a broad class of POVs. If this strategy turns out to be flexible enough, it can permit agents to reflect on the bases and the biases of their POVs and those of others, at least, to some degree.

This circumscription of expressions with a double meaning properly constitutes the hermeneutic field.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 13]

Even with its meaning duly circumscribed, “reflection” retains the dual senses of an “-ionized” word, referring to both a process and a result. As such, it is already on its way to becoming a highly charged term in this investigation. Even though a complete analysis of inquiry, from the top to the bottom of its putative hierarchy, is yet to be made available, the tendency to invoke “reflection” at every step and stage of inquiry is already apparent. This is clear from the fragmentary and scattered, but steadily mounting evidence of the word's textual circumstances that is currently piling up at the level of inquiry's most primitive details.

In other words, the constant invocation of “reflection” as an auxiliary to inquiry is apparent from the elementary syntactic fact that the charge of “reflection” is found in the mission statements of so many processes that are already noted to be involved in inquiry. In this connection, any time one senses the need to add the adjective “reflective” to the title of an agent, process, or faculty, then it speaks to the suspicion that the simple carrying out of actions and the perfunctory execution of procedures is not enough for the sake of composing intelligent conduct, but that there is an obligation to adjoin a component of reflection to whatever else is going on.

The elliptic nature of the discussion in this subsection, touching on topics that must be left in the forms of questions, raising issues that cannot be answered or even fully addressed until later sections of this project, lighting on a range of promontories in a field of problematic icebergs, and glancing up against problems that stay largely submerged and keep barely connected only through a medium of chance associations constantly in flux — all of this makes it advisable for the writer to come up with a device for continually warning the reader of the text's approaching discontinuities.

In view of these requirements, the text proceeds by highlighting a number of thematic points that find themselves to be reinforced in prior stages of its own construction, not all of which stages survive erasure enough to be explicitly marked in the text, and all in all continuing to develop as if by a pattern of constructive and destructive interference. It is hoped that this can reveal significant aspects, however partial and confounded, of its subject, its medium, and the forms that shape them.

A few words need to be spent in advance on the status of these points. Most of them are no longer controversial from my current POV, indeed, they partially constitute that POV. However, I recognize that some of them are likely to be controversial from the perspective of other POVs. Thus, these points are not intended to be taken as self-evident axioms, the kinds of logistical supports on the basis of which one customarily and confidently marches forward to the conquest of ever more powerful theorems. It is true that one of the best ways of testing these points is to take them up as premisses and to reason forward from them as far as one can. But the main reason for pointing them out in an explicit form of expression is so that their meanings, their logical implications, and their practical consequences can be examined in a circumspect light.

In short, none of the points to be staked out here is taken as evident or proven, and nothing of final certainty can be proved from them, but a demonstration can be made from them in the sense of an illustration, showing and testing their strength, trustworthiness, and utility for organizing an otherwise overwhelming complexity and depth of material. This process of examination and clarification, just as often as it has to reason forward, in the direction of the contingent theorems, also has to reason backward, to interrogate the mediately obvious principals and to ask whether more basic points can be discerned, as if lurking within the points already noted and secretly required to shore them up.

Out of this material I need to develop a method of inquiry, one that is extensible to its self-application. As an adjunct, or in adjutant fashion, I need to develop a justification of this method that can lend support to the justification of inquiry in general, and in its turn help to justify the application of inquiry to itself. Accordingly, the prospective aim to be sighted through the series of points ahead, and the line of survey to be projected through the elliptic text that charts it, are directed toward an effective theory of sign relations, one that is capable of resolving some of the subtleties it discerns in discourse, on occasions when a resolution is what is called for.

Points Forward

If exegesis raised a hermeneutic problem, that is, a problem of interpretation, it is because every reading of a text always takes place within a community, a tradition, or a living current of thought, all of which display presuppositions and exigencies — regardless of how closely a reading may be tied to the quid, to “that in view of which” the text was written.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 3]

Point 1. Thought takes place in signs

This makes a sign relation the setting of thought, where thought occurs.  In particular, the connotative plane of a sign relation is the medium of thought proper, and the denotative plane of a sign relation embodies the lines of thought's orientation toward its objects.

This point is one that may be thought controversial, until it is realized that the meaning of the term “sign” is being extended to cover anything that might conceivably occur in thought.  Far from intending to restrict thought to a circumscribed domain of signs, it expands the definition of “sign” to encompass anything that might enter into thought, so long as this entrance into thought is understood not in the sense of being its object but as something that lends a place to it.  Properly taken, this point is tantamount to an empirical definition of the term “sign”, more like an indication of where in experience a ready supply of examples can be found.  It says that if you seek signs then look to your thoughts.

Point 2. Thinking is a form of conduct

Conduct is action with a purpose. Synonymous with the term “purpose”, as used in this statement, are “aim”, “end”, “goal”, or “object”. The object domain of a sign relation is the place where these objects are envisioned to be, and thinking is the action that is carried out with a view to these ends.

Rightly taken, this point, too, is purely definitional. It classifies thinking as a species of action that has, or is meant to have, a purpose. In particular, thinking is the kind of action that passes from sign to interpretant sign in relation to an object. If one wishes to object that not all that passes for thinking has any assignable purpose, and if one desires to maintain an alternative POV that recognizes forms of aimless thinking, then it is nothing more than a technical problem to translate between the two ways of thinking, reclassifying unconducive thinking as a “degenerate form” from the standpoint of the pragmatic POV.

Point 3. Reflection on thinking is reflection on conduct

Even though it can appear too evident, too immediate, and too obvious to bear pointing out, there are several good reasons to make a point of noticing this simple corollary of the previous point, namely, that if thinking is a special case of conduct then reflection on thinking is a special case of reflection on conduct.

First of all, it means that reflection on thinking and reflection on conduct have a reciprocal bearing on each other, the way that special cases and general types always do. Reflection on thinking can tell us something about reflection on conduct in general. This is because the special case informs the general type and can be used inductively to discover its possible properties. Reflection on conduct in general can tell us something about reflection on thinking. This is because the general type constrains the special case and can be used deductively to derive its necessary properties.

(Bearing on the order of the normative sciences : logic < ethics < aesthetics?)

There is more to this point than first meets the eye, especially when it is considered in the light of its abstract form. Aside from its present application to the matters of reflection, thinking, and conduct, one can see in this instance the form of a distributive law, that distributes an operation (“reflection”) across a relation (“implication” or “inclusion”), and where this order of dyadic relation is the very one that constitutes the ordering of special cases under general forms. The point of this is that the general intention of this dyadic relation, in its full extension, must be to capture the relation of a special application of any principle (say, a distributive law) to its own general formulation. For instance, therefore, reflection on a special kind of distribution is a special kind of reflection on distribution in general.

In light of these relations between the specialization of thinking and the general capacity for conduct, I can now turn to a logical analysis of the concept of conduct for the light it reflects on the nature of thought.

Point 4. Conduct = (Act, End) = (State₁, State₂, State₃)

One can say that a conduct is a pair comprised of an act and an end. In this formula, the act can be anything from a complex activity to an extended action and the end can be anywhere among a vast diversity of destinations that are found to be encompassed by a general description. If it is recognized that the data needed to specify a minimum of action, a mere transition, is an ordered pair of states, and if it is remembered that the data appropriate to specifying a singular end is a single state, then an element of conduct, at its minimum, can be conceived to consist of an ordered triple of states.

Point 5. Reflection, joined to conduct, generates an image of it

Reflection on conduct produces an image of that conduct. In relation to the active nature of the conduct the image is just what its etymology says it is, an inactive sign or an inert icon of the action. The image of a conduct presents itself as a hypothesis about it, a tentative description that may or may not be accurate out of the starting blocks and may or may not continue to be useful in the long run.

Point 6. There is a type of reflection which merely reproduces the images produced by previous reflections

The images produced by this kind of reflection, affected by an imitative or nearly identical character, can be referred to as “reproductions”, “stereotypes”, or “simple copies”. A reproductive reflection has the option of attaching additional marks to distinguish the reproduced copy from the original image. If it does add a distinguishing mark or a distinctive notation to identify the source, then one has the type of reproduction that can safely be regarded as a reflective “quotation”.

Point 7. There is a type of reflection which captures an extended sequence of events in a single image

The images produced by this kind of reflection, affected by a creative, critical, reductive, selective, or truly imaginative character, using types of plastic representation with a capacity to condense, edit, summarize, and transform, all at the risk of serious distortions going beyond simple errors of transmission, may be referred to as “adaptations”, “redactions”, “renditions”, “versions”, or “transformed interpretations”.

These effect reflection, when it is efficient, to do just this, to produce a single image which captures a poignant, salient, or relevant aspect of an entire dramatic sequence.

Point 8. Inquiry, if deliberate and critical, involves reflection

The capacity for reflection is necessary to carry out the deliberately conducted and critically controlled varieties of inquiry that make up the principal interest of this work, and especially to entertain any form of inquiry into inquiry.

The pragmatic theory of signs sets the stage for a broad definition of inquiry. It includes under “inquiry” all the fortuitous and instinctive processes that agents exploit to escape from states of uncertainty, to soothe the “irritation of doubt”, in Peirce's phrase, along with all the deliberate and intelligent procedures that enable communities of agents to deal in systematic ways with the surprises and the problems that they encounter in their several and common experiences. At one end of this spectrum, the more incidental, instinctive, and casually intuitive forms of inquiry can be carried on without the interruptions of critical reflection. But an intelligent inquiry is necessarily a reflective inquiry.

Point 9. The need for a capacity of reflection is the reflection of a certain incapacity to see certain things without it

This point has a bearing on the capacity that one has to recognize one's own character as an objective form of being and to realize it within an active pattern of conduct.

Point 10. At this point, the circumstances bearing on the previous few points interact in such a way as to produce a series of further points

Expressed in abstract fashion, the injunction of a “reflective capacity” and the injunction of a “capacity limitation” impinge on each other in a way that brings a number of additional issues to light.

Expressed in more concrete detail, the experiential instances leading to the formation of those two injunctions, as organizing poles of topics explicitly noted, continue to surround their particular arrangements.

Point 11. Computational models of intelligent agents are limited to the consideration of “finitely informed constructions and computations”, or as I more affectionately call them, finitely informed creatures (FICs)

This point arises as a specialization of the point about capacity limits, where the discussion is restricted to the kinds of interpretive agents and the models of interpretive faculties that are available in a computational framework.

Something is a FIC to the extent that it falls into any of the following sorts:

1. Anything that exists in the form of a finite number of bits,
2. Anything whose objective being can be described in terms of a finite number of bits,
3. Anything whose moment to moment activity can be specified by means of a finite number of bits.

Notice that this depiction makes being a FIC a term of description, and thus of possible approximation, not of necessity an exact definition of the thing's essential substance. An objective being or a real activity, even one that escapes all bounds of finite description, can be usefully represented “as” or “by means of” a FIC precisely to the extent that a particular description of it in this form succeeds in helping the agent concerned to orient toward its underlying reality and to deal with its ultimate consequences.

Point 12. Reflection involves higher orders of sign relations

As a minimum requirement, a capacity for reflection implies an ability to generate names for the elements, processes, and principles of thought. Assuming the tenet of pragmatism that all thought takes place in signs, this is tantamount to having signs for signs, signs for sign processes, and signs for sign relations. Further, each higher order sign that is generated in a process of reflection is required to take its place and to find its meaning within a correspondingly higher order sign relation.

In this connection, the designation higher order (HO) can be used as a generic adjective to describe a sign of any object whose nature it is to involve signs as a part of its being. The use of this adjective is subject to extension in natural ways to describe not only entire classes of signs but also the kinds of sign relations that involve them.

In order to reflect on signs themselves, it is necessary to have signs for signs, a necessary supply of which can be generated by quotation. But reflection on sign processes requires a much larger supply of signs. Initially, it requires a HO sign for each sign transition that actually occurs, that is, a name for each ordered pair of signs that is observed. Eventually, it requires a HO sign for each sign sequence that actually appears in experience, that is, a name for each $k$-tuple of signs seen. And reflection on sign relations requires an even larger stock of signs. It requires, initially, a HO sign for each sign transaction of the form $(o,s,i)$ that is observed in experience and, ultimately, a HO sign for each sign relation that is encountered in experience or contemplated in a hypothetical situation.

If reflection is to constitute more than a transient form of observation, then provision needs to be made for permanently recording its HO signs. Under these conditions the capacity for instituting and maintaining an order of reflection is just a capacity for creating and storing HO signs.

This gives a brief glimpse of the issues involved in the effort toward reflection and the roughest possible estimate of the kinds of growth rates in the population of HO signs that are engendered by the need to provide a durable and stable medium for reflection. Further discussion of these topics can be put off to a later point. At this point it only needs to be clear that the injunction of a reflective capacity and the injunction of capacity limitations have an acute bearing on each other.

The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of “naive empiricism” or “naive intuitionism” can continue to support viable forms of inquiry.

This is what makes the mediation of a higher order hypothesis (HOH), a hypothesis about the qualifications of a hypothesis, or a hypothesis about what can count as a hypothesis, so essential to the life of a FIC.

The process of generating signs that refer to things already signs is incited by a syntactic operation that is commonly called a “quotation”. Strictly speaking, the descriptive term “quotation” refers to generic class of syntactic functions, each of which maps one order of signs into the next higher order of signs. A proper form of quotation function is required to map signs in a one to one or “injective” fashion, and thus associates each element of its source domain with a HO sign that denotes it and it alone. In short, a quotation produces a unique “name” or a distinctive “number” to index each piece its source material.

Some sort of quotation operation has to be made available as a standard mechanism to support almost any level of theoretical discussion about syntax. In computational settings, various types of quotation operation need to be implemented as computable functions and provided among the basic resources for almost any adequate system of symbolic computation. Conceived as a stock device of computation, and supplied with domains of arguments already well established as signs, quotation is relatively easy to implement.

Given a well defined domain of signs as the initial material, it is not difficult to contemplate the generation of successively higher orders of signs that stem from the examples of the founding domain.

But a level of genuine reflection on sign processes and sign relations exceeds the generative capacity of mere quotation.

Point 14. Higher order sign relations tax the pragmatic resources of an interpretive agent to such a severe extent that they impinge on the practical limits of its representational capacity and computational ability

When it is necessary to be precise, I use the term “matriculation” to refer to the first permanent recording of a sign by an agent, the one that marks in a relatively indelible fashion the initial recognition, original declaration, or principal registration of a sign by an agent, on which every subsequent use of that sign by that agent depends, and to which every later usage of that sign by that agent implicitly or explicitly refers.

The feature of matriculation that is important to the present argument is that it uses up memory capacity in a monotonic way. It is an economical strategy of memory usage to matriculate only the first token of each sign type observed and to let the observation of each subsequent token generate only a derivative reference to the primary registration. However, the present argument does not depend on the hypothesis of such a model actually being used, since this standard is only proposed to establish a lower bound on memory usage.

If quotation were the only mechanism for introducing HO signs, then each new round of HO signs would require for its primary registration only the same constant amount of memory capacity. The laying down of each new order of signs over the original foundation would take up an increment of memory equal to that used by the initial domain of signs.

But tagging sign processes and sign relations with signs that actually stick to them requires an agent to catch them first. In other words, the generation of signs for sign processes and signs for sign relations demands that an agent be able to perceive them or conceive them amidst the flow of an ongoing sign process that is itself governed by the law of a prevailing sign relation. This involves a contribution from the higher faculties of reasoning, in particular, taking steps of synthetic inference to introduce or invent the necessary signs. Since it resorts to the processes of inductive and abductive reasoning, this is naturally much more difficult to achieve.

In order to reflect on sign processes it is necessary to have signs for sign processes. One needs to start with signs for sign transitions, that is, signs for ordered pairs of signs, and work up to signs for arbitrary sequences of signs. As an empirical matter, every transition between signs that actually appears in experience is worth noting. By extension, it is useful to note as many sequences of transitions from sign to sign as actually occur, so long as one can spare the capacity to record them. If one also attends to the objects with regard to which these transitions occur, then one has the material of an empirical sign relation.

But this is a tricky matter, much less obvious than it seems at first. Pragmatic objects are more than just the physically compacted objects that happen to be present in a given situation, at, during, or in causal relation to a particular transition. In general, a pragmatic object is a hypothetical object, one whose presence in a situation, relevance to a transition, or association with a system of interpretation has to be hypothesized. But a hypothesis incurs a risk of error that goes beyond the elementary faults of observation and recording. The hypothesis has to be tested in subsequent experience and corrected by future inquiry. What this all comes down to is the circumstance that not even the raw empirical matter of a theory of signs can be panned from the pure stream of consciousness without a good admixture of speculation.

To amplify this point, in many cases the objects of a sign relation cannot be pointed out with any sense of clarity or resolve until the semantic equivalence classes are fairly and adequately sampled and the semantic partition that mirrors the structure of the object domain is at least partially reconstructed in the experience of an interpretive agent.

In order to reflect on sign relations, it is necessary to have signs for sign relations. Failing this, the laws or principles that sign processes follow, even if fleetingly half intuited, remain forever semi conscious, and thus they continue to rule in a subcritical state of representation.

At this point it becomes clear that the ideals of a naive empiricism must be left behind. The combinatorial explosion set off by the need to contemplate HO sign relations …

If it becomes necessary to entertain hypotheses about sign transitions, then the space of HO signs that has to be matriculated is potentially as large as the space of all ordered pairs of signs from the initial domain. If it becomes necessary to hypothesize about sign processes in general, then the space of HO signs that has to be matriculated grows like the union of the spaces of $k$-tuples of signs from the initial domain, where $k=1,2,3,\ldots ,$ and possibly increases with no limit in principal.

The acuteness of this point, if taken in its full generality, brings the discussion to an appreciation of the next point.

Point 15. Pragmatic incapacities have practical consequences

A limitation of an agent's capacity along a pragmatic dimension …

Point 16. Reflection involves a sense of context, and this involves a notion of community

The capacity for reflection involves an ability to view one's own conduct in a context of other conceivable actions, and this implies viewing one's choices not just in a context of other possible actions for oneself, but also in a context of other conceivable actors, ones that are comparable to but characteristically distinct from oneself.

Remarkably, the capacities for criticism and creativity that are needed for reflection spring from a common source, namely, from the sense of possibility that can regard every process as occurring within a context of alternative actions. An inquiry, to be intelligent and innovative, critical and creative, has to be reflective, with the capacity to regard itself as one inquiry among others. In this “regard” is implied the ability of an interpretive agent to reference and to evaluate its own progress in inquiry, to observe it more dispassionately in subsequent reflections as the conduct of one inquirer among a host of many others, choosing one way of doing inquiry from the array of others conceivable. Accordingly, solely out of these reflections is developed the notion of a virtual or a potential community, quite independently of the empirical matter of how any actual or present community is constituted or realized at the moment.

Point 17. Recalling the proposed application ${}^{\backprime \backprime }y\cdot y{}^{\prime \prime }$ once again, it needs to be pointed out that an action cannot really act on an action, but only on its signs

In technical terms, an action can act only on certain signs that exist in association with another or the same action, signs that are often called the “images” of the action to be affected.

Point 18. The images, depictions, or descriptions of conduct generated by reflection, as records of experience, can be accumulated into theories and compiled into models of the corresponding conduct

The collected images of conduct serve as “codes”, in both the senses of a descriptive datum and a prescriptive emblem. Both types of code fall subject to being tested in future experience, for their trustworthiness as bodies of observation or recommendation, respectively, with regard to their objects or intentions, as the case may be. Reviving an old term with just this spectrum of meanings, an encyclopedic corpus of received code can be called a “pandect”.

Point 19. The power of reflection involves a risk of distortion

The quality that separates reflection from introspection is its admission of fallibility. Although it is often troublesome to undo its distortions, the very fact that it can be in error, can miss its mark, or is by nature defeasible and falsifiable is exactly what makes a reflective image useful as a hypothesis, as an approximation to an infinitely subtler reality and as a simplification of an infinitely more complex and detailed truth, and yet one that retains a sufficient measure of realistic truth to be useful in the meaner times of a mortal existence.

The capacity of reflection to create an image in description of an action incurs a liability toward corruption in the image, both before and after its initial form is cast. The way that an image produced by reflection is designed to act as a sign of the action or permitted to behave as a code of the conduct is bound to be an imperfect device, due in large part to limitations of the media and affected in unaccounted measures by flaws in the mechanisms of reflection. How these distortions can be undone with repeated reflections, and how this clarification can be achieved without waylaying the conduct that reflection is meant to describe and control, is one of the main technical problems for empirical inquiry.

The power of reflection involves a capacity to project false images and thereby to generate distorting perspectives. The possibilities include the following:

1. Views in which small things seem large and large things seem small,
2. Value systems in which the apparent imports of things are reversed in relation to their actual imports,
3. Forms of representation in which the places of contents interior and exterior to the surfaces of reflection are exchanged, reversed, or transposed.

There is a positive spin on the fallibility of the reflective imagination. In terms of its practical bearings on continued experience, the fallibility of reflection involves an ability, not only to make its errors over again in the form of their consequences for experience, but eventually to find its faults recognized as such in a finite order of subsequent reflections.

The way that reflection, in adjunction to conduct, leads conduct to yield a description of itself, thus creating a relation between action and sign, behavior and code, that is open to be traced in either direction, is the principal mystery of its operation. How reflection can be led to do this in a way that positively reinforces the intention of the conduct and that constructively criticizes its ongoing performance, controlling its desire to control the action so that it does not destructively interfere with the completion of the task, is the critical practical question of the work.

In sum, the feature of reflection that seems to render it most defective, its fallibility, which involves its ability to be recognized as false in the future of reflection, is the main trait that allows it to play a part in the staging of empirical inquiry.

Point 20. The capacity for reflection involves an ability to question one's working assumptions, especially when there is occasion to suspect that they are no longer working as well as they once did

Whenever one operates on a particular assumption, whether knowingly or otherwise, one tends to see certain patterns of features in perception and to miss others, but until one reflects on the operative assumption, makes it explicit, considers its alternatives, and thereby is empowered to put it in question, then one lacks a fundamental insight into how these figures are generated in perception, failing to see how one's own sensitivities and dispositions are biased toward allowing them to arise.

To act on the basis of a certain assumption, as though the assumption were already certain, is to act in abstraction of the total situation. When a feature or a pattern of features is abstracted from a situation, there is always something left behind, the grounds from which a feature or pattern originally rises and against which it subsequently becomes a figure of importance to the moment. There needs to be a name for this actively recessed background, suggesting the potential complement of alternative features and elliptic patterns that it contains within its share of the total configuration. But it is important to remember that this is not just the ground that comes to complement a figure in the present situation but the ground that is dynamically pushed into the past so that the current configuration can come to be formed as it is.

Exactly what it is that abstraction leaves out is something that seems currently to escape description, failing to be pinned down by any name I can think of in common or in technical use. The abstraction itself, as the process whose result is signaled by its “-ionized” designation, acts toward the end of constellating a figure that is relevant to the moment. But the concurrent and complementary process that results in a residual plurality is one that lacks a common denomination. For the sake of a harmonious balance between the syntactic expressions of these actions, it would be good if the process that recesses the background were also to be assigned an “-ionized” term.

Point 21. There appears to be a large variety of ways that the process of reflection can go wrong

One of the jobs of an inquiry into inquiry is to classify this variety, compassing the diversity of incidental errors and systematic distortions that are likely to occur in reflection.

One dimension of variation that runs through this variety of pathologies characterizes the degree of fixity or persistence that is invested in the images of conduct. The range of variation conceivable can be suggested by marking the prototypical figures that fall at its two extremes.

1. At one extreme there is the character of a stolid fixity that can be adumbrated in terms of a mythological or a psychological archetype, appearing to be ruled by the image of Narcissus. This identifies the kind of regressive and fixed ideation that leads one to seize on a single image of one's characteristic conduct, to fix it in mind as a static ideal, and to resist at all costs letting go of its hold on the imagination.
2. At the other extreme there is the character of an insipid volatility that corresponds to the complementary archetype, answering a bit dully to the name of Echo. This identifies the kind of digressive and fluid skepticism that leaves one in a permanently fugitive state. Paradoxically enough, it is typically pursuant to a precocious but transient condition of dedication, one that marks its earliest forms of conscious recognition. If it follows the usual course, it can start from being too soon fixed on the initial object of attention or the original ideal of conduct, but it eventually falls into a compensatory, defensive, and reactionary pattern. Soon it withers away into little more than the afterimage of a reflexive reaction, an account due to the ensuing trauma of disappointment, and a record commemorating a final disillusionment with its distant illusions. Whatever the initial case, the issue is such that it makes one reluctant to commit to any future image of behavior or ideal of conduct, at least, readily enough to try its utility in action or steadily enough to test it out in practice. Instead, it disposes one merely to keep repeating in an automatic, derivative, imitative, involuntary, reflexive, stereotypical, and tautologous manner any impression of the outside world that seems to inform the moment.

Point 22. Intelligent inquiry involves inquiry into inquiry

In view of the previous points, it appears that intelligent inquiry is necessarily reflective inquiry, seeing itself as one inquiry among others and evaluating its own progress in a setting of comparable alternatives. This means that intelligent inquiry into any subject whatever is forced to embody a component of self-study, of inquiry into inquiry. Thus, the general capacity for successfully conducting inquiry both relies on and bears on a specialized kernel of talent for doing inquiry into inquiry.

Point 23. Inquiry into inquiry involves integrating independent inquiries

One way of gathering data that is relevant to the task of self-study is to conduct a multiplicity of independent studies, each of which tries to track what the others are most likely to miss. This requires a monitor, a moderator, or a non-parallel but mutually concurred upon medium of comparison for overseeing and reconciling the mosaic of disparate and scattered results that can derive from a multitude of isolated studies.

Finally, this project of self study demands a comprehensive method for integrating the divergent and fragmentary imports of individual studies into a unified form, constituting the resultant bearing that they are meant to have on the main inquiry. Toward this end, it is a frequent stratagem of intelligent inquiry to maintain a form of “outrigger”, an attached but esthetically distant study that serves to steady the main course of study by embodying a full program of peripheral perspectives and exploratory investigations. In this way, the global aims of even a specialized inquiry can be achieved more robustly by keeping a studied eye out for its own systematic alternatives, often involving precisely those “outliers” that are ignored by the more focal styles of inquiry.

In times of shifting paradigms the outrigger of an established inquiry can take on a signal purpose as the forerunner of a new investigation, and can with added reinforcements even take over the role of the main. With nothing more than a few spare kernels of aptitude for reflective inquiry, that is, with a minimal but germinal talent for inquiry into inquiry to serve as a catalyst, the outriding projections and their deponent objections, testifying all along in what seems like a purely negative fashion to the mounting accumulations of anomalous evidence, can find themselves converted, refitted, and positively reconditioned. Transformed in this way, the original outrigger, with its outrageous hypotheses and its crew of motley anomalies, are ready to become the new hull, the mainstays, and the supporting constituency of a renewed constitution for inquiry, one that can sustain its overall course but more significantly its overriding cause through another day.

Point 24. Reflective projects being partial, their refractory parts are likely to remain partial to their outward projections

An unreflective framework (UF), if it does not devolve into a condition of total confusion, and thus deserves to be called a framework at all, ordinarily maintains a clear separation between the objective and the interpretive parts of its organization. This pragmatic division of labor coincides with a substantive distinction that is ordained to exist between the object system that is subject to observation or interpretation and the agent system that observes or interprets it.

But the goal of reflection is to make one's own conduct an object among other objects, something that can be critically evaluated as one choice among many and subsequently amended if found wanting. In this aim a realistic project of reflection never sees more than partial success. There is always a refractory residue of ongoing conduct that resists analysis and remains unreflected in any clear form of representation. Thus, the actual effect of a reflective project is to represent only a part of one's interpretive conduct as a part of one's objective regard, in other words, to reconfigure a part of one's IF as a part of one's OF.

Point 25

The purpose of constructing a RIF is to demonstrate how it might be possible for interpretive agents to reflect on their own processes of interpretation, to critically evaluate the interpretive choices they make, and to choose from alternate interpretations based on the results of this reflection and evaluation. These are the abilities that interpreters need to carry out inquiry, and especially to pursue an inquiry into inquiry.

It seems that human beings do have the ability to reflect on their own interpretive processes, at least, to the extent that they can observe the obvious aspects of the interpretive experience and control the overt features of the interpretive activity, and insofar as these aspects and features of the experimental activity are manifested at the phenomenal surfaces of its underlying processes. Moreover, it seems that people do know how to interrogate their own judgments, turning again and again to investigate the traces of their past reflections and pausing in anticipation to examine the balance of their next evaluation.

Consequently, it must be possible to explain these apparent abilities in just one of two ways: either to account for the faculties of reflection and selection by presenting a logical model of the processes involved, or else to dispel the illusion of each performance by showing what goes on in its place. In either case, an inquiry into the virtues of critically reflective phenomena is called on to provide a plausible model for what is happening beneath the semblances of reflective and critical thought. Whether the resulting resolution of a particular phenomenon preserves or dissolves its appearances is a matter that depends on the details of the case, and perhaps to a degree on personal taste.

Point 26. This marks a branch point. I tentatively assume that the apparent power of reflection is really more or less as it appears to be, at least, in the same spirit as it appears to be, and not some radically insidious self-deception arising on the part of its apparent agents

Setting out initially on the positive track, I begin with the assumption that a RIF is a real possibility. In order to conceive of a RIF being possible it is necessary to set aside a host of set theoretic difficulties that might be imagined to afflict any invocation of self referent themes. No matter whether interpretation is presented in terms of a framework, a faculty, a process, a trajectory, or a hypostatic agent that is assumed to carry out its procedures, there is a problem about how anything so fleeting and so sweeping as an ongoing interpretation can refer to itself as a situated form of activity, in other words, as an objective system of interpretation that rests within a context of alternative interpretations.

There is a piece of terminology that is often useful in this connection. In set-theoretic contexts, either one of the phrases X collects Y or X encases Y can be used to mean the same thing as Y ∈ X. These formulations can be taken as abbreviated ways of saying that X enumerates Y among its cases. Thus, they express the converse of the membership relation but manage to avoid the ambiguity of the phrase X contains Y, a form that would otherwise have to be qualified on each occasion of its use by specifying whether one means contains as an element or contains as a subset, as the case may be.

To wrap up the development of this reflective project in a single line: When the mind's original effort to catch itself at work seizes on the inventions of set theory to encapsulate its speculations, the ensuing breed of self reification that comes from mingling an unbridled capacity for self referent expressions with an unchecked propensity for creating abstract objects gives rise to the generation of set theoretic paradoxes. As a result, it is incumbent on me to show how the concretely limited kinds of constructions that I have in mind can avoid a similar excess and steer clear of the corresponding difficulties.

If formalized, a RIF would be an IF that can properly, if only partially, refer to itself as an OF. Thus, as formalized, a RIF amounts to both a reflexive and a recursive SOI, one that can refer to itself as an object, to the extent that any formal system can. As a reflexive SOI, a RIF has a sign that refers to itself. As a recursive SOI, a RIF has a character that can be determined by invoking the record of signs that it uses to refer to simpler versions and earlier developments of itself.

But more than all this, in order to be genuinely reflective a RIF's consideration of itself as a situated form of activity must extend to the consideration of alternative selves. This means that a RIF must have references to other SOIs, not only those that are continuous with the space of its own potential conduct and correlated to the course of its own form of activity, but also those that are discontinuous from and independent of its own way of being.

In keeping with the spirit of a discussion based on concrete examples, the RIF to be improvised here is restrained to the scale of a minimal IF that can reflect on the scene of A and B, in this case, synthesizing a portion of the OFs and IFs suggested by the sign relations $A$ and $B$ into an integrated SOI. While I do not plan to specify the additional constraints that would be needed to determine this RIF uniquely, even to say whether it is finite or infinite, it forms a convenient reference point for the rest of this section to designate the purported ideal as the RIF generated by $A$ and $B$ and to notate it as $\mathrm {RIF} (A,B).$

In accord with the customary figure of speech, a RIF can be personified in the agency of a “reflective interpreter” that possesses the faculties to carry out its actions, and this agent is in turn characterized as the localized representative of a suitably reflective and situated process of interpretation.

A reflective interpreter needs a capacity for referring to its own role in the process of interpretation, for conceptualizing each transition from sign to interpretant sign as occurring within a context of alternatives, and for noticing that each option has a potentially distinctive value with respect to a prevailing object or objective. Capacity, as used in this connection, is a word with both structural and functional connotations. It implies the structural capacity that is required to articulate, record, and maintain data about observable forms of interpretive conduct, and it involves the functional capacity that is demanded to create and exploit this data, in effect, constituting a higher order of interpretive activity.

If one tries to understand the conduct of a reflective interpreter as a process of interpretation there are a number of questions that arise. How can anything so ongoing as a process of interpretation refer to an object, and how can anything so fleeting as a process of interpretation be referred to as an object?

A process that refers to itself is not like a set that collects itself, or a collection that would enroll itself among its own elements, even if some attempts to process the reference and to lay it out in a literal account do try to dissect and explain it as such. A sign that is elemental to a universe, perhaps by means of which one seeks to explain the universe, does not in fact collect, dominate, or encase the entire universe simply by referring to it, even if some interpretive interloper, at the risk of vitiating the whole account, is tempted to explain the elementary part in terms of the complex totality.

One reason for introducing the distinction between OFs and IFs into the present discussion is to keep track of the complex relationships between object domains and sign domains, between the constitutions of objects and the constitutions of signs. It is a frequent practice in mathematics to blur this distinction, often saying that an object is constituted as a set of further objects when one really means that the sign or information one has about the object is constituted as a set of further signs or further informations about the object, all of which can refer to further objects, but not always the sorts of objects that are literally intended as elementary constituents of the original object. Furthermore, each use of the directive further in this description marks a place where a suitably reflective interpreter ought to ask whether further implies simpler or merely other, and in turn whether other means essentially other or only otherwise appearing.

But the distinction between object and sign, however important, is still a pragmatic distinction, involving a thing's use in a particular role, and not an essential distinction, fixing a thing's prior and eternal nature. Of course, it can turn out that some objects will never serve as signs and that some signs will never be observed as objects, but these types of eventuality involve empirical questions and contingent facts, and their actualization depends on the kinds of circumstances that have to be discovered after the fact rather than dictated a priori.

The construction of a RIF forces the discussion to a point where the OFs and IFs and the relationships between them suddenly become much more complex, and where confusion can arise precisely from the fact that the purpose of a RIF is to convert an IF into the sort of thing that can be referred to and reflected on as an object. Developments like these make it all the more necessary to understand the exact character of the distinction between OFs and IFs. In a complex IF signs do participate in constitutional relationships, with complex signs being constructed out of simpler signs. But the relations involved in denotation and connotation are not limited to constitutional linkages of this sort, and thus they cannot be expected to generate by themselves the necessary sorts of analytic and synthetic hierarchies.

All in all, a RIF involves the close coordination of an OF and an IF, plus mechanisms for carrying out the so called reflective operations (ROs) that go to negotiate between the objective and the interpretive realms. The work of ROing permits processes of interpretation, initially taking place largely in the IF and impinging on the OF only at isolated points, to be formalized and objectified, thereby becoming segments of the OF. Taken over time the cumulative effect of this ROing motion gradually turns more and more of the IF into new sectors and layers of the OF.

Point 27

There is a portion of reasoning that consists in drawing distinctions, signifying the features thereby distinguished by means of logical terms, recognizing constraints on the conjoint occurrences of these features, expressing these constraints in the form of logical premisses, and then drawing the implications of these premisses as the occasion warrants. This part of logic, in its formalizable aspects, is generally referred to as propositional calculus (PropC), sentential logic (SL), or sometimes as zeroth order logic (ZOL).

With any system of logic, at least, that does not propose a purely syntactic rationale for itself, it is necessary to draw a distinction between the logical object that is denoted, expressed, or represented in thinking and the logical sign that denotes, expresses, or represents it. Often one uses the contrast between proposition and expression or the shade of difference between statement and sentence to convey the distinction between the logical object signified and the syntactic assemblage that signifies it. Another option is to let the division lie between a position and a proposition, with the suggestion being that the function of a symbolic proposition is to indicate indifferently a plurality of logical positions. In accord with my personal preference, I use the term proposition ambiguously, expecting context to resolve the question, and resorting to the term expression when it does not.

Point 29

Finally, interlaced with the structures of the OF and the IF, there is a need for a structure that I call a dynamic evaluative framework (DEF). This is intended to isolate the twin aspects of process and purpose that are observable on either side of the objective interpretive divide and to assist in formalizing the graded notions of directed change that are able to be actualized in the medium of a RIF.

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• Overview • Part 1 • Part 2 • Part 3 • Part 4 • Part 5 • Part 6 • Part 7 • Part 8 • Part 9 • Part 10 • Part 11 • Part 12 • Part 13 • Part 14 • Part 15 • Part 16 • Appendix A1 • Appendix A2 • References • Document History •

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