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{{DISPLAYTITLE:Inquiry Driven Systems : Part 6}}
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<div align="center">
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems|Contents]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 1|Part 1]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 2|Part 2]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 3|Part 3]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 4|Part 4]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5|Part 5]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8|Part 8]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
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&bull; [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Document History|Document History]]
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&bull;
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</div>
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----
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<div class="nonumtoc">__TOC__</div>
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==6. Reflective Interpretive Frameworks==
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We continue the discussion of formalization in terms of concrete examples and detail the construction of a ''reflective interpretive framework'' (RIF).  This is a special type of sign-theoretic setting, illustrated in the present case by building on the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B}),\!</math> but intended more generally to form a fully-developed environment of objective and interpretive resources, in the likes of which an &ldquo;inquiry into inquiry&rdquo; can reasonably be expected to find its home.  We begin by presenting an outline of the developments ahead, working through the motivation, construction, and application of a RIF that is broad enough to mediate the dialogue of the interpreters <math>\text{A}\!</math> and <math>\text{B}.\!</math>  The first fifteen Sections (&sect;&sect;&nbsp;1&ndash;15) deal with a selection of preliminary topics and techniques that are involved in approaching the construction of a RIF.  The topics of these sections are described in greater detail below.
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The first section (&sect;&nbsp;1) takes up the phenomenology of reflection.  The next three sections (&sect;&sect;&nbsp;2&ndash;4) are allotted to surveying the site of the planned construction, presenting it from three different points of view.  An introductory discussion (&sect;&nbsp;2) presents the main ideas that lead up to the genesis of a RIF.  These ideas are treated at first acquaintance in an informal manner, located within a broader cultural context, and put in relation to the ways that intelligent agents can come to develop characteristic belief systems and communal perspectives on the world.  The next section (&sect;&nbsp;3) points out a specialized mechanism that serves to make inobvious types of observation of a reflective character.  The last section (&sect;&nbsp;4) takes steps to formalize the concepts of a ''point of view'' (POV) and a ''point of development'' (POD).  These ideas characterize the outlooks, perspectives, world views, and other systems of belief, knowledge, or opinion that are employed by agents of inquiry, with especial regard to the ways that these outlooks develop over time.
 +
 
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A further discussion (&sect;&nbsp;5), in preparation for the task of reflection, identifies three styles of linguistic usage that deploy increasing grades of formalization in their approaches to any given subject matter.
 +
 
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In the next three sections (&sect;&sect;&nbsp;6&ndash;8), the features that distinguish each style of usage are taken up individually and elaborated in detail.  This is done by presenting the basic ideas of three theoretical subjects that develop under the corresponding points of view and that exemplify their respective ideals.  The next three sections (&sect;&sect;&nbsp;9&ndash;11) take up the classes of higher order sign relations that play an important role in reflexive inquiries and then apply the battery of concepts arising with higher order sign relations to an example that anticipates many features of a realistic interpreter.  In the light of the experience gained with the foregoing styles and subjects, the next three sections (&sect;&sect;&nbsp;12&ndash;14) are able to take up important issues regarding the status of theoretical entities that are needed in this work.
 +
 
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Finally (&sect;&nbsp;15), the relevance of these styles, subjects, and issues is made concrete by bringing their various considerations to bear on a single example of a formal system that serves to integrate their concerns, namely, ''propositional calculus''.
 +
 
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A point by point outline follows:
 +
 
 +
&sect; 1. &nbsp; An approach to the phenomenology of reflective experience, as it bears on the conduct of reflective activity, is given its first explicit discussion.
 +
 
 +
&sect; 2. &nbsp; The main ideas leading up to the development of a RIF are presented, starting from the bare necessity of applying inquiry to itself.  I introduce the idea of a ''point of view'' (POV) in an informal way, as it arises from natural considerations about the relationship of an immanent ''system of interpretation'' (SOI) to a generated ''text of inquiry'' (TOI).  In this connection, I pursue the idea of a ''point of development'' (POD), that captures a POV at a particular moment of its own proper time.
 +
 
 +
&sect; 3. &nbsp; A Projective POV
 +
 
 +
&sect; 4. &nbsp; The idea of a POV, as manifested from moment to moment in a series of PODs, is taken up in greater detail.
 +
 
 +
A formalization for talking about a diversity of POVs and their development through time is introduced and its consequences explored.  Finally, this formalization is applied to an issue of pressing concern for the present project, namely, the status of the distinction between dynamic and symbolic aspects of intelligent systems.
 +
 
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&sect; 5. &nbsp; The symbolic forms employed in the construction of a RIF are found at the nexus of several different interpretive influences.  This section picks out three distinctive styles of usage that this work needs to draw on throughout its progress, usually without explicit notice, and discusses their relationships to each other in general terms.  These three styles of usage, distinguished according to whether they encourage an ''ordinary language'' (OL), a ''formal language'' (FL), or a ''computational language'' (CL) approach, have their relevant properties illustrated in the next three sections (&sect;&sect;&nbsp;6&ndash;8), each style being exemplified by a theoretical subject that thrives under its guidance.
 +
 
 +
&sect; 6. &nbsp; For ease of reference, the basic ideas of group theory used in this project are separated out and presented in this section.  Throughout this work as a whole, the subject of group theory serves in both illustrative and instrumental roles, providing, besides a rough stock of exemplary materials to work on, a ready array of precision tools to work with.
 +
 
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Group theory, as a methodological subject, is used to illustrate the ''mathematical language'' (ML) approach, which ordinarily takes it for granted that signs denote something, if not always the objects intended.  It is therefore recognizable as a special case of the OL style of usage.
 +
 
 +
To the basic assumption of the OL approach the ML style adds only the faith that every object one desires to name has a unique proper name to do it with, and thus that all the various expressions for an object can be traded duty free and without much ado for a suitably compact name to denote it.  This means that the otherwise considerable work of practical computation, that is needed to associate arbitrarily obscure expressions with their clearest possible representatives, is not taken seriously as a feature that deserves theoretical attention, and is thus ignored as a factor of theoretical concern.  This is appropriate to the mathematical level, which abstracts away from pragmatic factors and is intended precisely to do so.
 +
 
 +
More instrumentally to the aims of this investigation, and not entirely accidentally, group theory is one of the most adaptable of mathematical tools that can be used to understand the relation between general forms and particular instantiations, in other words, the relationship between abstract commonalities and their concrete diversities.
 +
 
 +
&sect; 7. &nbsp; The basic notions of formal language theory are presented.  Not surprisingly, formal language theory is used to illustrate the FL style of usage.  Instrumentally, it is one of the most powerful tools available to clear away both the understandable confusions and the unjustifiable presuppositions of informal discourse.
 +
 
 +
&sect; 8. &nbsp; The notion of computation that makes sense in this setting is one of a process that replaces an arbitrary sign with a better sign of the same object.  In other words, computation is an interpretive process that improves the indications of intentions.  To deal with computational processes it is necessary to extend the pragmatic theory of signs in a couple of new but coordinated directions.  To the basic conception of a sign relation is added a notion of progress, which implies a notion of process together with a notion of quality.
 +
 
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&sect; 9. &nbsp; This section introduces ''higher order'' sign relations, which are used to formalize the process of reflection on interpretation.  The discussion is approaching a point where multiple levels of signs are becoming necessary, mainly for referring to previous levels of signs as the objects of an extended sign relation, and thereby enabling a process of reflection on interpretive conduct.  To begin dealing with this issue, I take advantage of a second look at <math>\text{A}\!</math> and <math>\text{B}\!</math> to introduce the use of ''raised angle brackets'' <math>({}^{\langle}~{}^{\rangle}),</math> also called ''supercilia'' or ''arches'', as quotation marks.  Ordinary quotation marks <math>({}^{\backprime\backprime}~{}^{\prime\prime})</math> have the disadvantage, for formal purposes, of being used informally for many different tasks.  To get around this obstacle, I use the ''arch'' operator to formalize one specific function of quotation marks in a computational context, namely, to create distinctive names for syntactic expressions, or what amounts to the same thing, to signify the generation of their gödel numbers.
 +
 
 +
&sect; 10. &nbsp; Returning to the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B}),\!</math> various kinds of higher order signs are exemplified by considering a series of higher order sign relations based on these two examples.
 +
 
 +
&sect; 11. &nbsp; In this section the tools that come with the theory of higher order sign relations are applied to an illustrative exercise, roughing out the shape of a complex form of interpreter.
 +
 
 +
The next three sections (&sect;&sect;&nbsp;32&ndash;34) discuss how the identified styles of usage bear on three important issues in the usage of a technical language, namely, the respective theoretical statuses of signs, sets, and variables.
 +
 
 +
&sect; 12. &nbsp; The Status of Signs
 +
 
 +
&sect; 13. &nbsp; The Status of Sets
 +
 
 +
&sect; 14. &nbsp; At this point the discussion touches on an topic, concerning the being of a so called ''variable'', that issues in many unanswered questions.  Although this worry over the nature and use of a variable may seem like a trivial matter, it is not.  It needs to be remembered that the first adequate accounts of formal computation, Schönfinkel's combinator calculus and Church's lambda calculus, both developed out of programmes intended to clarify the concept of a variable, indeed, even to the point of eliminating it altogether as a primitive notion from the basis of mathematical logic (van Heijenoort, 355&ndash;366).
 +
 
 +
The pragmatic theory of sign relations has a part of its purpose in addressing these same questions about the natural utility of variables, and even though its application to computation has not enjoyed the same level of development as these other models, it promises in good time to have a broader scope.  Later, I will illustrate its potential by examining a form of the combinator calculus from a sign relational point of view.
 +
 
 +
&sect; 15. &nbsp; There is an order of logical reasoning that is typically described as ''propositional'' or ''sentential'' and represented in a type of formal system that is commonly known as a ''propositional calculus'' or a ''sentential logic'' (SL).  Any one of these calculi forms an interesting example of a formal language, one that can be used to illustrate all of the preceding issues of style and technique, but one that can also serve this inquiry in a more instrumental fashion.  This section presents the elements of a calculus for propositional logic that I described in earlier work (Awbrey, 1989 and 1994).  The imminent use of this calculus is to construct and analyze logical representations of sign relations, and the treatment here focuses on the concepts and notation that are most relevant to this task.
 +
 
 +
The next four sections (&sect;&sect;&nbsp;16&ndash;19) treat the theme of self-reference that is invoked in the overture to a RIF.  To inspire confidence in the feasibility and the utility of well chosen reflective constructions and to allay a suspicion of self-reference in general, it is useful to survey the varieties of self-reference that arise in this work and to distinguish the forms of circular referrals that are likely to vitiate consistent reasoning from those that are relatively innocuous and even beneficial.
 +
 
 +
&sect; 16. &nbsp; Recursive Aspects
 +
 
 +
&sect; 17. &nbsp; Patterns of Self-Reference
 +
 
 +
&sect; 18. &nbsp; Practical Intuitions
 +
 
 +
&sect; 19. &nbsp; Examples of Self-Reference
 +
 
 +
The intertwined themes of logic and time will occupy center stage for the next eight sections (&sect;&sect;&nbsp;20&ndash;27).
 +
 
 +
&sect; 20. &nbsp; First, I discuss three distinct ways that the word ''system'' is used in this work, reflecting the variety of approaches, aspects, or perspectives that present themselves in dealing with what are often the same underlying objects in reality.
 +
 
 +
&sect; 21. &nbsp; There is a general set of situations where the task arises to &ldquo;build a bridge&rdquo; between significantly different types of representation.  In these situations, the problem is to translate between the signs and expressions of two formal systems that have radically different levels of interpretation, and to do it in a way that makes appropriate connections between diverse descriptions of the same objects.  More to the point of the present project, formal systems for mediating inquiry, if they are intended to remain viable in both empirical and theoretical uses, need the capacity to negotiate between an ''extensional representation'' (ER) and an ''intensional representation'' (IR) of the same domain of objects.  It turns out that a cardinal or pivotal issue in this connection is how to convert between ERs and IRs of the same objective domain, working all the while within the practical constraints of a computational medium and preserving the equivalence of information.  To illustrate the kinds of technical issues that are involved in these considerations, I bring them to bear on the topic of representing sign relations and their dyadic projections in various forms.
 +
 
 +
The next four sections (&sect;&sect;&nbsp;22&ndash;25) give examples of ERs and IRs, indicate the importance of forming a computational bridge between them, and discuss the conceptual and technical obstacles that will have to be faced in doing so.
 +
 
 +
&sect; 22. &nbsp; For ease of reference, this section collects previous materials that are relevant to discussing the ERs of the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B}),\!</math> and explicitly details their dyadic projections.
 +
 
 +
&sect; 23. &nbsp; This section discusses a number of general issues that are associated with the IRs of sign relations.  Because of the great degree of freedom there is in selecting among the potentially relevant properties of any real object, especially when the context of relevance to the selection is not known in advance, there are many different ways, perhaps an indefinite multitude of ways, to represent the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B})\!</math> in terms of salient properties of their elementary constituents.  In this connection, the next two sections explore a representative sample of these possibilities, and illustrate several different styles of approach that can be used in their presentation.
 +
 
 +
&sect; 24. &nbsp; A transitional case between ERs and IRs of sign relations is found in the concept of a ''literal intensional representation'' (LIR).
 +
 
 +
&sect; 25. &nbsp; A fully fledged IR is one that accomplishes some measure of analytic work, bringing to the point of salient notice a selected array of implicit and otherwise hidden features of its object.  This section presents a variety of these ''analytic intensional representations'' (AIRs) for the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B}).\!</math>
 +
 
 +
'''Note for future reference.'''  The problem so naturally encountered here, due to the embarrassment of riches that presents itself in choosing a suitable IR, and tracing its origin to the wealth of properties that any real object typically has, is a precursor to one of the deepest issues in the pragmatic theory of inquiry:  ''the problem of abductive reasoning''.  This topic will be discussed at several later stages of this investigation, where it typically involves the problem of choosing, among the manifold aspects of an objective phenomenon or a problematic objective, only the features that are:  (1) relevant to explaining a present fact, or (2) pertinent to achieving a current purpose.
 +
 
 +
&sect; 26. &nbsp; Differential Logic and Directed Graphs
 +
 
 +
&sect; 27. &nbsp; Differential Logic and Group Operations
 +
 
 +
&sect; 28. &nbsp; The Bridge : From Obstruction to Opportunity
 +
 
 +
&sect; 29. &nbsp; Projects of Representation
 +
 
 +
&sect; 30. &nbsp; Connected, Integrated, Reflective Symbols
 +
 
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The next seven sections (&sect;&sect;&nbsp;31&ndash;37) are designed to motivate the idea that a language as simple as propositional calculus can be used to articulate significant properties of <math>n\!</math>-place relations.  The course of the discussion will proceed as follows:
 +
 
 +
&sect; 31. &nbsp; First, I introduce concepts and notation designed to expand and generalize the orders of relations that are available to be discussed in an adequate fashion.
 +
 
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&sect; 32. &nbsp; Second, I elaborate a particular mode of abstraction, that is, a systematic strategy for generalizing the collections of formal objects that are initially given to discussion.  This dimension of abstraction or direction of generalization will be described under the thematic heading of ''partiality''.
 +
 
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&sect; 33. &nbsp; Third, I present an alternative approach to the issue of ''defective'', ''degenerate'', or ''fragmentary'' <math>n\!</math>-place relations, proceeding by way of generalized objects known as ''<math>n\!</math>-place relational complexes''.  Illustrating these ideas with respect to their bearing on sign relations the discussion arrives at a notion of ''sign-relational complexes'', or ''sign complexes''.
 +
 
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In the next three sections (&sect;&sect;&nbsp;34&ndash;36) I consider a collection of ''identification tasks'' for <math>n\!</math>-place relations.  Of particular interest is the extent to which the determination of an <math>n\!</math>-place relation is constrained by a particular type of data, namely, by the specification of lower arity relations that occur as its projections.  This topic is often treated as a question about a relation's ''reducibility'' or ''irreduciblity'' with respect to its projections.  For instance, if the identity of an <math>n\!</math>-place relation <math>L\!</math> is completely determined by the data of its <math>k\!</math>-place projections, then <math>L\!</math> is said to be ''identifiable by'', ''reducible to'', or ''reconstructible from'' its <math>k\!</math>-place components, otherwise <math>L\!</math> is said to be ''irreducible'' with respect to its <math>k\!</math>-place projections.
 +
 
 +
&sect; 34. &nbsp; First, I consider a number of set-theoretic operations that can be utilized in discussing these ''identification'', ''reducibility'', or ''reconstruction'' questions.  Once a level of general discussion has been surveyed enough to make a start, these tools can be specialized and applied to concrete examples in the realm of sign relations and also applied in the neighborhood of closely associated triadic relations.
 +
 
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&sect; 35. &nbsp; This section considers the positive case of reducibility, presenting examples of triadic relations that can be reconstructed from their dyadic projections.  In fact, it happens that the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B})\!</math> fall into this category of dyadically reducible triadic relations.
 +
 
 +
&sect; 36. &nbsp; This section considers the negative case of reducibility, presenting examples of ''irreducibly triadic relations'', or triadic relations that cannot be reconstructed from their lower dimensional projections or ''faces''.
 +
 
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&sect; 37. &nbsp; Finally, the discussion culminates in an exposition of the so called ''propositions as types'' (PAT) analogy, outlining a formal system of ''type expressions'' or ''type formulas'' that bears a strong resemblance to propositional calculus.  Properly interpreted, the resulting ''calculus of propositional types'' (COPT) can be used as a language for talking about well-formed types of <math>k\!</math>-place relations.
 +
 
 +
&sect; 38. &nbsp; Considering the Source
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&sect; 39. &nbsp; Prospective Indices : Pointers to Future Work
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&sect; 40. &nbsp; Interlaced with the structural and reflective developments that go into the OF and the IF is a conceptual arrangement called the ''dynamic evaluative framework'' (DEF).  This utility works to isolate the aspects of process and purpose that are observable on either side of the objective interpretive divide and helps to organize the graded notions of directed change that can be actualized in the RIF.
 +
 
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&sect; 41. &nbsp; Elective and Motive Forces
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&sect; 42. &nbsp; Sign Processes : A Start
 +
 
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&sect; 43. &nbsp; Reflective Extensions
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&sect; 44. &nbsp; Reflections on Closure
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&sect; 45. &nbsp; Intelligence <math>\Rightarrow</math> Critical Reflection
 +
 
 +
&sect; 46. &nbsp; Looking Ahead : The &ldquo;Meta&rdquo; Issue
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&sect; 47. &nbsp; Mutually Intelligible Codes
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&sect; 48. &nbsp; Discourse Analysis : Ways and Means
 +
 
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&sect; 49. &nbsp; Combinations of Sign Relations
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&sect; 50. &nbsp; Revisiting the Source
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===6.1. The Phenomenology of Reflection===
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This part of the discussion is fair to cast as the phenomenology of reflection.  It aims to amass the kinds of observations that extremely simple reflective agents, as a matter of principal and with a minimal of preparation, can make on the ebb and flow of their own reflective acts.  But this is not the kind of phenomenology that pretends it can bracket every assumption of a sophisticated or a theoretical nature off to one side of the observational picture, or thinks it can frame the description of reflection without the use of formal concepts, such as depend on the bracing and support of a technical language.
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On the contrary, the brand of phenomenology being wielded here makes the explicit assumption that there are likely to be an untold number of implicit assumptions that contribute to and conspire in the framing of the picture to be observed, while it is precisely the job of reflective observation to detect the influence of these covertly acting assumptions.  Further, this style of phenomenology is deliberately set free of prior constraints on the choice of descriptive devices, since it can appeal to any formal means or any technical language that serves to articulate the description of its subject.
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Certain things need to be understood about the aims, the scope, and the self-imposed limits of this phenomenology, especially when it comes to the question of what it hopes to explain.  It is not the task of this phenomenology to explain consciousness but only to describe its course.  This it does by making an inventory of the &ldquo;contents&rdquo; that appear in consciousness and by delineating the relationships that appear among these contents.  Along the way, it must take into account, of course, that each moment of taking stock and each moment of charting relations needs to have its resulting list or map, respectively, realized as the content of a particular moment of consciousness.
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Already, this lone requirement of the descriptive task raises a host of questions about what it means for something to be counted as a content of consciousness, and it leads, according to my present lights and aims, to a closer examination of a critical relationship, the logical relation &ldquo;content of&rdquo;, taken abstractly and in general.  Since it does not appear that very extensive lists or very detailed maps can be &ldquo;wholly realized&rdquo; as contents within a limited field of consciousness, it is necessary to recognize an extended sense of &ldquo;realization&rdquo;, where a list or a map can be &ldquo;partially&rdquo; or &ldquo;effectively&rdquo; realized in a content of consciousness if and when an indication, pointer, or sign of it is present in awareness.
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In particular, this tack suggests that some things, that otherwise loom too large to fit within the frame of immediate awareness, can be treated as contents of consciousness, in the extended sense, if only an effective indication of them is present in awareness.  For instance, an effective indication of a larger text is a sign that can be followed to the next, and this to the next, and so on, in a way that incrementally leads to a traversal of the whole.  By extension, a list of contents of consciousness or a map of relations among these contents is &ldquo;effectively realized&rdquo; in a single content of consciousness if that content effectively points to it, and if the object to which it points has the structure of an object that pointedly reveals itself in time.  Given the evidence of the sign and the effective analysis of its object, a manifest of contents can be prized for the sake of the items it enumerates or the estates it maps, with each in due proportion to their values.  Both parts of this condition are needed, though, since knowing the name alone of a thing, even if it lends itself to knowing the thing, does not itself amount to knowing the thing itself.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>The concepts with which a theory operates are not all objectivized in the field which that theory thematizes.</p>
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<p>In short, my philosophical working hypothesis is concrete reflection, i.e., the ''cogito'' as mediated by the whole universe of signs.</p>
 +
|-
 +
| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 166, 170]
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|}
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 +
This understanding of the task of phenomenology bears on three features of the approach to consciousness that I am charting here.
 +
 
 +
# It is under the heading of ''description'', especially as qualified by the adjective ''effective'', that the rationale of using mathematical models and the strategy of seeking computational implementations of these models can be found to successively fall.
 +
# As a rule, I find it helps to avoid hypostatizing consciousness or self-awareness as statically constituted entities, but to use the systematic notions of dynamic agency and developing organization.  However, in order to make connections with other approaches to phenomenology I need occasionally to mention concepts and even to make use of language that I would otherwise prefer to avoid.
 +
# Finally, it is under the cumulative aims of effective description and systematic dynamics that the utility of sign relations is key.  Sign relations are the minimal forms of models that are capable of compassing all that goes on in thinking along with whatever it is that thinking relates to in all the domains that it orients toward.  The use of sign relations as models, as mathematical descriptions, and as computational simulations of what appears in reflecting on conduct is especially well suited to including in these models a description of what transpires in the conduct of reflection itself.
 +
 
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The type of phenomenology that is being envisioned here depends on no assured power of introspection but only on a modest power to reflect on conduct and thereby to give it a description.  These descriptions, all the better if they are inscribed in external media, can be examined with increasing degrees of detachment and have their consequences projected by deductive means.  In time, the mass of descriptions that accumulates with continuing experience and persistent reflection on conduct begins to constitute a de facto ''model of behavior'' (MOB).  In common regard this ''prescribed code'' or ''catalog of procedure'' (COP) can range from an empirical standard of comparison, through a provisional regulation, to a tentative ideal for future conduct.  However, the status that a MOB or a COP has when it starts out is not as important as its ability to test its prescriptions, along with their deductive and pragmatic implications, against the corpus of continuing observation, reflection, and description.
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{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>Reflection and consciousness no longer coincide.  &hellip;</p>
 +
 
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<p>What emerges from this reflection is a wounded ''cogito'', which posits but does not possess itself, which understands its originary truth only in and by the confession of the inadequation, the illusion, and the lie of existing consciousness.</p>
 +
|-
 +
| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 172, 173]
 +
|}
 +
 
 +
It is pertinent at this point to draw a distinction between the power of reflection, that is claimed as a capacity crucial to inquiry, and what is likely to be confused with it, the presumptive power of introspection.  &ldquo;Introspection&rdquo;, in the sole part of its technical meaning that leads to its being excluded from empirical inquiry, refers to an infallible, and thus incorrigible, power of observation that one is supposed to possess with respect to one's private experiences, matters over which there is imagined to be no higher court of appeal than one's own particular and immediate awareness.  But the horizon of experience that is plotted with regard to this static standpoint fails to reckon with the dynamic nature of an ongoing circumstance, that subsequent experience continually rides a circuit around its antecedents and ever constitutes a higher court for every proceeding and every precedent that falls within its jurisdiction.
 +
 
 +
The distinction that marks reflection and sets it apart from introspection is its own acknowledged fallibility, which involves its ability to be seen as false in subsequent reflections.  Naturally, this has an import for the status of reflection in empirical inquiry.  Paradoxically, its admission of fallibility is actually a virtue from the standpoint of making reflection useful in science.  If reflection on conduct leads to a description that cannot be falsified by any contingency of conduct, then that description is insufficient to specify any particular conduct at all.  This means one of several things about the description, either (1) it remains a condition of conduct in general, or (2) it resides as a part of a necessary logic at the bounds of all experience, or (3) it rests in a realm of metaphysics that abides, if anywhere, beyond the bounds of purely human experience and thus abscounds altogether from the sphere of empirical inquiry.
 +
 
 +
{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>In this way the psyche is itself a technique practiced on itself, a technique of disguise and misunderstanding.  The soul of this technique is the pursuit of the lost archaic object which is constantly displaced and replaced by substitute, fantastic, illusory, delirious, and idealized objects.</p>
 +
|-
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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 185]
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One of the most difficult problems that arises for the phenomenology of reflection, and one that falls under the heading of &ldquo;fallibility&rdquo; in a markedly strong way, is the issue of systematic distortion.  Aside from the false idols that are deliberately constructed, there is another host of false images whose generation is so thoroughly systematic that only their lack of consciousness prevents them from being called &ldquo;deliberate&rdquo;.  All the more naive projects of enlightenment, capitalized or not, are brought down by a failure to recognize this category of human frailty.
 +
 
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If the phenomenology of reflection that is developed and justified from this point on is not to be naive about this brand of fallibility, then it needs to constitute safeguards, a system of checks and balances, if you will, against it.  If no method of remediation can permanently arrest the perpetrator of these schemes from generating distractions in perpetuity, then at least one can hope for ways to arraign the forms of fallibility under various recognizable themes, so that their dangers can be avoided in the future.  In this vein, it is necessary to institute the study of those more opaque obstructions that limit the medium of investigation and to facilitate the analysis of those more refractory resistances to clear reflection, whose names are legion, but whose characters can be diversely noted under the themes of ''obstruction'', ''resistance'', the ''shadow'', the ''unconscious'', the &ldquo;dark side of the enlightenment&rdquo;, or even better yet, the &ldquo;underbrush of the clearing&rdquo;.
 +
 
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In the general scheme of things, the forms of distortion that remain peculiar to particular agents of reflection need garner to themselves nothing outside the incidental degrees of interest.  The best check to counter this species of distortion, to which the isolated individual is likely to fall prey, is the balance of cultural wisdom that is commonly stored up and invested in the living praxis of a reflective community.
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It is only when the incidence of singular distortions is not damped out by the collective incitement of countermeasures, when the aggregation of local distortions is overlooked by the powers of a general reflection, when the flaws in the individual lights and mirrors of the scientific organon are not taken into account and duly compensated in the shape of the social &ldquo;panopticon&rdquo;, or when the grinding accumulation and the precipitous mounting up of infinitesimal but significant deviations from accurate reflection are not met with an adequate power of oversight, one that can maintain solely the interests of community integrity at heart, that a truly false ideal begins to hold sway over the very perceptions of every specialized agent of reflection.
 +
 
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When these aberrations and astigmatisms develop unchecked, and when the strain to see things clearly reaches the point of breaking all the instruments thereof, then the most circumscribed faults, the distorted reflections of individual hypocrisy, the strange lack of insight and the missing sense of mutual reciprocity that manifest themselves in the most parochial forms of self interest, then all of these defects, and ills, and shocks begin to &ldquo;pass through&rdquo; to the collective strata, to be inherited and propagated by the highest levels of social organization, and then a systematic and widespread falsification of the whole conduct of society begins to pervade its view of itself.
 +
 
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On macroscopic scales of organization, with medium sized bodies and bodies of media that extend over considerable distances, with masses of activity that successfully propagate their own forms through vastening expanses of time, the general condition of thoughtfulness cancels out and compensates for all but the most singular of disturbances, namely, those that are peculiar to the microscopic realm of observation.  If the matter is regarded on this grander scale, then it is not hard to find a sufficient reason for the stubborn persistence of the cosmic order, and thus the desirable necessity of doing just this is never far from mind.  In the case of whole societies, a like reason is often enough to explain their inertia, their resistance, and their overall slowness to change.
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If there is felt a need to devise an object explanation, a presumptive sources of troubles that is already compact, concrete, and thus confined enough to accuse, apprehend, and hopefully imprison on account of the mass's retarded potential, then resorting to a hypostasis posed in the form of an &ldquo;archaic object&rdquo; is a prototypical way of controlling anxiety, and it frequently, if not infallibly, can serve just as well as any other device on which to pin the common blame.  This highlights the question:  What sort of archaic object would account for the general malaise in a community whose dedication to inquiry has become root-bound?
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<p>I wish to apply a determinate philosophical method to a determinate problem, that of the constitution of the symbol, which I described as an expression with a double meaning.  I had already applied this method to the symbols of art and the ethics of religion.  But the reason behind it is neither in the domains considered nor in the objects which are proper to them.  It resides in the overdetermination of the symbol, which cannot be understood outside the dialecticity of the reflection which I propose.</p>
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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 175]
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The archaic object of this global aimlessness, that informs the course of the general drift, that the total condition and the specific culture of inquiry revolve about in their orbits, as if they aim to be constantly accelerated toward it, but never quite manage to resolve their situation toward it, as if they fear to dissolve into it, is very likely nothing more than the whole community of interpretation itself, effectively realized as an object of its own devising.
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The community of interpretation, whose currency funds the community of inquiry as a going enterprise within its fold, has sufficient reason to preserve itself in its present form as a valuable object, commodity, or resource.  But the dialectical nature of the process that is currently conducted between them, due in part to the dialectrical charges of the &ldquo;-ionized&rdquo; terms that pass for information between them.  A term of this charge splits the action from the end and shares it between the parties to an ambiguity, the active and passive objects that together comprise its full denomination.  This division of denotation forces interpretation to vacillate between the two extremes of meaning in a vain and eternal effort to rejoin their senses of value to the realm of the rendered and misspent coin, in hopes of regaining the meaning what was mint in their original condition.  The stowing away of one portion or the other drives the potential that drives both themselves and all the actions that they are meant to convey toward their designate and their destinate ends, but the unstable equilibrium that is their due, especially when it is permitted to be waged by uncontrolled forms of oppositional attraction, does not permit the dialogue to rest.  It continues to remain in doubt and does not fail to renew its ambivalence regarding the maintenance of any fixed form it happens to take, always wondering whether its present form is literally necessary, precisely sufficient, or whether it is but transiently and contingently convenient.  Accordingly and otherwise the whirl of dialogue, for all its own reasons, is always in imminent danger of wasting away into the echo of its own narcissism.
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The problem arises of how to bring these systematic distortions under systematic control.  It helps to stand back a bit from the problem and to cast a somewhat wider net.  Accordingly, let the whole category of phenomena that are gathered around this issue be thematized under the family name of an ''obstruction to inquiry'' (OTI).  This includes as a subordinate genus the panoply of systematic distortions, generated by disingenuous reflections, that can be hypothesized to have their source in protecting the favored assumptions and defending the implicit claims of a particular status quo, no matter whether the implicated propositions are held to be the prerogatives of a privileged POV or whether they are delivered up to indictment as the prejudices of a more widely sanctioned world view.  The archetype of this behavior is appropriately addressed under the mythological or the psychological category of ''narcissism''.
 +
 
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It is important to note that the family OTI and the genus ''narcissus'' differ in the levels of hypothesis that are involved in their concepts, both in their speculative formation and in their provisional attribution.  The presence of an OTI is fairly easy to surmise from its distinguishing traits:  the dissipative conduct and the rambling course that affect the inquiry in question.  To the degree that the suspicion of its effect and the verification of its force can be assembled from superficial traces, this makes its maintenance supportable on circumstantial evidence alone.  In a phrase, one says that the wider hypothesis lies &ldquo;nearer to nature&rdquo; than the narrower construction, or that it makes its appearance closer to the purely phenomenal sphere.  In contrast, unraveling the precise nature of the obstruction requires a deeper investigation.  There is an additional hypothesis involved in guessing the source of the resistance, no matter how prevalent a particular genus of distortion is found and no matter how likely an individual species of explanation is in fact.
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Within this wider setting it may be possible to focus more clearly on the species of threats to accurate reflection that need to be clarified here.  Already, besides the stigma of stubborn error that hangs over the whole refractory horde, there is a germ of paradox that hides within the very folds of this classification.  Namely, it is that the first obstacle one finds to reflection, and hence to every form of reflective inquiry, is a kind of narcissism or self love.  It begins naturally enough, ensconced in the not unnatural desire of every form of life to preserve itself in its present form.  But the simple desire to remain as is can be diverted into a blinded esteem of the self, one that admires its present condition only as reflected in the array of disingenuous reflections and contrived presentations that make up a fixed, idealized, and very selective image.  Finally and strangely enough, this unreflective form of narcissism even comes to prefer the simplistic and beautiful lies to the realistic forms that a veritable mirror would show.
 +
 
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The danger of narcissism, with respect to the prospects of a reflective inquiry, is not in the dynamic attractions and the realistic affections that a person or a society bears toward its truer self, and that in turn inform their respective bearings toward the selves they are meant to be, but in the static character of its attachment to a fixed, idealized, and partial image of that self.
 +
 
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Once again, the quality that distinguishes reflection from introspection, its fallibility, is a trait that sufficiently reflective agents can find reflected in their own conduct of reflection, and needless to say, their conduct in general.  This quality of fallibility, thus cognized and thus converted, that is, once its application to oneself is acknowledged and its consequences for one's experience are recognized, becomes a type of self-recognizant character, an internalized trait that leads reflective agents to become more corrigible, more docile, and thus more educatable.  This makes it possible for reflective agents to build up their images of reality from scratch materials, to proceed through steps that are always revisable and edifiable, and to leave the finishing of their forms to the work of future editions.  In the final analysis, while this mannerism of aesthetic distance and tempered discretion prevents any affection or any impression from becoming too &ldquo;immediate&rdquo;, in the strictest sense of that word, it is just this mode of detachment that assures the sensible image of its eventual remediation.
 +
 
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The nature and use of reflection in inquiry, as it currently appears, can be described as follows.  Reflection on conduct leads to a description of that conduct, posed in terms of a reflective image.  Over an interval of time or an extended period of investigation, these descriptive images are accumulated into exhaustive theories and compiled into compact models of the conduct in question.  To be useful in science, or empirical inquiry, these theories and models must be capable of being false with respect to their intentions, amenable to being tested in further experience, and subject to being amended on subsequent reflection.
 +
 
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In sum, the very feature of reflection that seems to be its chief defect, the fact that it can generate false images, casting reflections that are false to the actions they intend to represent and even leading to wholly distorted perspectives on the objectified scene of activity, is the very characteristic that saves its appearance in experience and the very trait that permits it to show its face at the court of inquiry, which all along admits that distortions acknowledged to be imperfect images can still be disclosed to subsequent experience and remedied in future reflections.

Revision as of 04:00, 28 August 2014


ContentsPart 1Part 2Part 3Part 4Part 5Part 6Part 7Part 8AppendicesReferencesDocument History


6. Reflective Interpretive Frameworks

We continue the discussion of formalization in terms of concrete examples and detail the construction of a reflective interpretive framework (RIF). This is a special type of sign-theoretic setting, illustrated in the present case by building on the sign relations \(L(\text{A})\!\) and \(L(\text{B}),\!\) but intended more generally to form a fully-developed environment of objective and interpretive resources, in the likes of which an “inquiry into inquiry” can reasonably be expected to find its home. We begin by presenting an outline of the developments ahead, working through the motivation, construction, and application of a RIF that is broad enough to mediate the dialogue of the interpreters \(\text{A}\!\) and \(\text{B}.\!\) The first fifteen Sections (§§ 1–15) deal with a selection of preliminary topics and techniques that are involved in approaching the construction of a RIF. The topics of these sections are described in greater detail below.

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

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

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

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

A point by point outline follows:

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

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

§ 3.   A Projective POV

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

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

§ 5.   The symbolic forms employed in the construction of a RIF are found at the nexus of several different interpretive influences. This section picks out three distinctive styles of usage that this work needs to draw on throughout its progress, usually without explicit notice, and discusses their relationships to each other in general terms. These three styles of usage, distinguished according to whether they encourage an ordinary language (OL), a formal language (FL), or a computational language (CL) approach, have their relevant properties illustrated in the next three sections (§§ 6–8), each style being exemplified by a theoretical subject that thrives under its guidance.

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

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

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

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

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

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

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

§ 10.   Returning to the sign relations \(L(\text{A})\!\) and \(L(\text{B}),\!\) various kinds of higher order signs are exemplified by considering a series of higher order sign relations based on these two examples.

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

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

§ 12.   The Status of Signs

§ 13.   The Status of Sets

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

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

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

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

§ 16.   Recursive Aspects

§ 17.   Patterns of Self-Reference

§ 18.   Practical Intuitions

§ 19.   Examples of Self-Reference

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

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

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

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

§ 22.   For ease of reference, this section collects previous materials that are relevant to discussing the ERs of the sign relations \(L(\text{A})\!\) and \(L(\text{B}),\!\) and explicitly details their dyadic projections.

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

§ 24.   A transitional case between ERs and IRs of sign relations is found in the concept of a literal intensional representation (LIR).

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

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

§ 26.   Differential Logic and Directed Graphs

§ 27.   Differential Logic and Group Operations

§ 28.   The Bridge : From Obstruction to Opportunity

§ 29.   Projects of Representation

§ 30.   Connected, Integrated, Reflective Symbols

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

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

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

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

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

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

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

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

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

§ 38.   Considering the Source

§ 39.   Prospective Indices : Pointers to Future Work

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

§ 41.   Elective and Motive Forces

§ 42.   Sign Processes : A Start

§ 43.   Reflective Extensions

§ 44.   Reflections on Closure

§ 45.   Intelligence \(\Rightarrow\) Critical Reflection

§ 46.   Looking Ahead : The “Meta” Issue

§ 47.   Mutually Intelligible Codes

§ 48.   Discourse Analysis : Ways and Means

§ 49.   Combinations of Sign Relations

§ 50.   Revisiting the Source

6.1. The Phenomenology of Reflection

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

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

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

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

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

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

In short, my philosophical working hypothesis is concrete reflection, i.e., the cogito as mediated by the whole universe of signs.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 166, 170]

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

  1. It is under the heading of description, especially as qualified by the adjective effective, that the rationale of using mathematical models and the strategy of seeking computational implementations of these models can be found to successively fall.
  2. As a rule, I find it helps to avoid hypostatizing consciousness or self-awareness as statically constituted entities, but to use the systematic notions of dynamic agency and developing organization. However, in order to make connections with other approaches to phenomenology I need occasionally to mention concepts and even to make use of language that I would otherwise prefer to avoid.
  3. Finally, it is under the cumulative aims of effective description and systematic dynamics that the utility of sign relations is key. Sign relations are the minimal forms of models that are capable of compassing all that goes on in thinking along with whatever it is that thinking relates to in all the domains that it orients toward. The use of sign relations as models, as mathematical descriptions, and as computational simulations of what appears in reflecting on conduct is especially well suited to including in these models a description of what transpires in the conduct of reflection itself.

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

Reflection and consciousness no longer coincide. …

What emerges from this reflection is a wounded cogito, which posits but does not possess itself, which understands its originary truth only in and by the confession of the inadequation, the illusion, and the lie of existing consciousness.

Paul Ricoeur, The Conflict of Interpretations, [Ric, 172, 173]

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

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

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

Paul Ricoeur, The Conflict of Interpretations, [Ric, 185]

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

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

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

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

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

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

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

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

Paul Ricoeur, The Conflict of Interpretations, [Ric, 175]

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

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

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

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

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

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

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

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

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