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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.
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.
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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, is "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, reclassifing 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 relection 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.
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 decription that may or may 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 that only 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 that 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 manners of plastic representation that can condense, edit, summarize, and transform, all at the risk of serious distortions that go beyond simple errors in the transmission, can be referred to as "adaptations", "redactions", "renditions", "versions", or "transformed interpretations".
These effect of reflection, when it is efficient, is to do just this, to produce a single image that 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 an abstract fashion, the injunction of a reflective capacity and the injunction of a capacity limitation are recognized to impinge on each other in a way that brings to light a number of additional issues. Expressed in more concrete detail, the experiential instances that lead to the formation of these two points in the first place, as organizing poles of topics explicitly noticed, and that 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" (FIC's).
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, or (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 13. A "finitely informed creature" (FIC), if it is reflective up to the point that it reflects on its own nature as such, crosses a singular threshold of reflection, whereupon it not only obeys its own capacity limitations, as it instinctively and necessarily must, but also observes and reflects on their character.
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, ..., 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 "y.y" 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 only act 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 or 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: (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.
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.
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 dispell 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, I use either one of the phrases "X collects Y" or "X encases Y" to mean that Y C 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 SOI's, 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 OF's and IF's 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 "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 OF's and IF's 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 OF's and IF's 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 OF's and IF's. 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" (RO's) 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 28. Adequate reasoning about the propositional constitution or the sentential representatation of POV's and POD's requires a logical system that can work with "higher order propositions" (HOP's).
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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