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# Inquiry Driven Systems • Part 7

Author: Jon Awbrey

## Reflective Expression

### Casual Reflection

Recall that an ostensibly recursive text (ORT), already encountered a bit less formally in discussing the issue of the informal context, is a text that cites itself by title at some site within its body.

Consider a text in progress (TIP) at its growing edge, anywhere that it joins new text to a body of work already established, anywhere that it sends out buds and shoots from a secular truncation of its author's intention. Here is where a growing text advances through its media of language and communication, the potentially nurturing environments and the invariably constraining surroundings that make a definite array of resources available to a text, grant it certain options for continuing its development, and limit the effects of meaning that it can achieve. A text that can form in such a medium is part of what one has in mind whenever one opens a sentence with a phrase like “A text that can ___” and continues by elaborating on a text's abilities, capacities, or intentions as if this text is not a fixed or a static entity but one whose free selection and future development are still open to question.

A text that can cite itself by title is a limiting case of a text that can cite itself by chapter and verse, in other words, a text with a sufficient degree of articulation that it can make appropriate references to its own parts and sections, and can thus invoke the objects, the functions, and the structures that are represented in them. This should go to explain the interest I am taking in ORTs, their kin, and their generalizations. These kinds of texts exhibit an aspect of self reference that is usually taken for granted, to the point that it is hardly recognized as such, but one that is implied in all attempts “to make infinite use of finite means”. A program is generally a text of this sort. A non trivial program, one that wraps an infinite object in a finite sign, whether it numbers its lines and directs its execution by means of instructions that have its interpreter go to this or that place in its own text, or whether its modules call on each other by name, is always recursive in this sense.

The deeper that one looks into a species of text, the further that one's interest tends to shift from the distinctive features of individual texts to the properties of the medium that supports their growth. Although a medium is initially conceived to be a source of texts or a constraint on their production, that is, as a generative facility or a generated space, it is often possible to formalize it as the full grammar of a discursive language, in other words, as a comprehensive theory for that species of texts, accounting for their syntactic, semantic, and pragmatic aspects.

Still, what is the status in reality of these conceptual constructions: a medium, a grammar, or a theory for a species of texts? They have no meaning apart from the texts that they admit to exist. They are only known by means of the texts that they allow to subsist in them, that they enable to live and to grow, and everything that is learned about them ultimately needs to be expressed in a text, or something like it, even if not always a text of the very same order or species.

#### Ostensibly Recursive Texts

 Bein' on the twenty third of June, As I sat weaving all at my loom, Bein' on the twenty third of June, As I sat weaving all at my loom, I heard a thrush, singing on yon bush, And the song she sang was The Jug of Punch.

Is there a true poem, a verse with the echo of divine inspiration, that resounds in the memories of this minor ditty, this song of the pubs and this ballad of the streets? Does ambrosia yet flow in the veins of the one who sings this ode on an amphoric urn? If there is, and if it does, then it is likely to involve a wholly different order of interpretation, one where the reference to a jug of punch, ostensibly denoting a simple demijohn, is sure to denote an object of much greater significance than its literal denotation can convey, and one where the cryptic imports of its invocations are intended to descant a more figurative, metaphorical, and transcendental sense.

For the sake of shortening future references to the epigraph at the top of this subsection, let the acronym “JOP” be taken as equivalent to the phrase “jug of punch”, and let the italicized tag “TJOP” be taken as tantamount to the title “The Jug of Punch”.

There are features of this style of abbreviation that need to be noted. Instead of letting the acronym “JOP” denote the phrase “jug of punch”, and rather than letting the italicized acronym “TJOP” denote the title “The Jug of Punch”, I am merely asking for the reader to take part in forming an augmented scheme of interpretation, one that adds new signs to a formerly established sign relation, but does it in a way that does nothing of serious consequence to its underlying semantic properties. This involves the construction of a semiotic partition (SEP), along with its corresponding semiotic equivalence relation (SER), in which the associated set of semiotic equivalence classes (SECs) serves to stake out a number of parts. In the present illustration there are two sets of synonyms, constellating a pair of mutually exclusive classes of signs that denote their respective objects in parallel, as in Table 17.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Semiotic Equivalence Class}}\!}$ ${\displaystyle {\begin{matrix}{\text{jug of punch}}\\[8pt]{\textit {The~Jug~of~Punch}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }&\}\\[8pt]\{&{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }&\}\end{matrix}}}$

In each case, the abbreviated form and its expansion are set to connote each other all within a single level of signs, while both signs are set to denote their common object in a parallel fashion. This strategy for annexing compressed references to a sign relation can be referred to as an acronymically connotative extension (ACE) of that sign relation.

 What more pleasure can a boy desire, Than sitting down beside the fire? What more pleasure can a boy desire, Than sitting down beside the fire? And in his hand a jug of punch, And on his knee a tidy wench.

Let ${\displaystyle J\!}$ be a hypothetical sign relation that is adequate to interpret the The Jug of Punch. Table 18 gives a part of ${\displaystyle J\!}$ that is called for in order to accomplish this interpretation. Table 19 shows an ACE of this part. Table 20 gives a part of this ACE that suffices to get the gist of it.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{jug of punch}}\\[8pt]{\textit {The~Jug~of~Punch}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\end{matrix}}}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{JOP}}\\{\text{JOP}}\\{\text{JOP}}\\{\text{JOP}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\textit {TJOP}}\\{\textit {TJOP}}\\{\textit {TJOP}}\\{\textit {TJOP}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\end{matrix}}}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{JOP}}\\[8pt]{\textit {TJOP}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\end{matrix}}}$

 When I am dead and left in my mould, At my head and feet place a flowing bowl, When I am dead and left in my mould, At my head and feet place a flowing bowl, And every young man that passes by, He can have a drink and remember I.

Note. Description and discussion of Table 21 needs to be added here.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{JOP}}\\{\textit {TJOP}}\\\ldots \end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{JOP}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {TJOP}}{}^{\prime \prime }\\{\textit {TJOP}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{jug of punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\textit {The~Jug~of~Punch}}{}^{\prime \prime }\\{}^{\backprime \backprime }{\text{Bein' on ... remember I}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle \ldots }$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{Bein' on the twenty-third of June,}}\\~{\text{as I sat weaving all at my loom,}}\\~{\text{I heard a thrush singing on yon bush,}}\\~{\text{and the song she sang was}}~{\textit {The~Jug~of~Punch.}}{}^{\prime \prime }\end{array}}}$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{Bein' on the twenty-third of June,}}\\~{\text{as I sat weaving all at my loom,}}\\~{\text{I heard a thrush singing on yon bush,}}\\~{\text{and the song she sang was just this song.}}{}^{\prime \prime }\end{array}}}$ ${\displaystyle \ldots }$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{What more pleasure can a boy desire,}}\\~{\text{than sitting down beside the fire,}}\\~{\text{and in his hand a jug of punch,}}\\~{\text{and on his knee a tidy wench?}}{}^{\prime \prime }\end{array}}}$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{No more pleasure can a boy desire,}}\\~{\text{than sitting down beside the fire,}}\\~{\text{and in his hand a jug of punch,}}\\~{\text{and on his knee a tidy wench.}}{}^{\prime \prime }\end{array}}}$ ${\displaystyle \ldots }$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{When I am dead and left in my mould,}}\\~{\text{at my head and feet place a flowing bowl,}}\\~{\text{and every young man that passes by,}}\\~{\text{he can have a drink and remember I.}}{}^{\prime \prime }\end{array}}\!}$ ${\displaystyle {\begin{array}{l}{}^{\backprime \backprime }{\text{When I am dead and left in my mould,}}\\~{\text{at my head and feet place a flowing bowl,}}\\~{\text{and every young man that passes by,}}\\~{\text{he can have a drink and remember me.}}{}^{\prime \prime }\end{array}}}$

Needless to say, acute enough hearers of this humble hymn or insightful enough interpreters of its lilting lyrics would no doubt find traces of Arthurian legend and clues to the Grail mythology woven all through its homespun text, but that is not my present task, to guess at its deepest drafts of meaning. Although there are features of this particular text that possess an incidental interest here, the reason for introducing it into the current context is more to illustrate the kinds of issues that are involved in a complex text, one with recursions and multiple levels of interpretation.

#### Analogical Recursion

With these preparations it is possible to return to the problems of analogical recursion, as illustrated by the poem The Lady of Shalott. In the body of the poem, the italicized phrase “The Lady of Shalott” is triply ambiguous, being amenable to any one of the following readings:

1. It can be the title of a person, italicized for emphasis.
2. It can be the name of a vehicle, for instance, a boat or a ship that is named after a person.
3. It can be the title of a text, for instance, a poem named after its principal subject or a story named after its chief character.

The first two readings are available on a literal interpretation and can be distinguished if the difference of emphasis is detected by the reader. The third reading is subtler, requiring both a figurative interpretation and a reason to suspect that some sort of subtext is possibly in force. How is the reader supposed to deal with this three headed equivocation? Is it a deliberate ambiguity on the author's part, one whose design is plotted with the aim of conveying a meaning? Does this question really matter, or does the syntactic structure of text still betray a form of intention, whether or not a conscious one?

If it is frequently necessary to distinguish the equally likely readings of equivocal signs, and if the design of the language in use is a topic open to discussion, then it is possible to bring in a requisite array of typographical conventions and a suitable set of type marking devices to indicate more explicitly the types of objects that are being denoted or the senses of signs that are being intended. But this kind of strategy only puts off the day when a capacity for intelligent interpretation is called on to resolve the ambiguities and the uncertainties that remain to all orders of finite signs. Keeping the inevitability of this outcome in mind, it is probably a good idea to spend a reasonable proportion of the meantime thinking of ways to build a capacity for flexible interpretation into a language from its very conception, or at least to leave room for its growth, and thus to facilitate an aptitude for interpretation under conditions of uncertainty throughout the entire course of development of a sign using capacity.

An intentional ambiguity in the reference of a sign is a primitive way of suggesting that there is an aspect of analogy or equality among the objects denoted, in other words, that there is a respect in which they are similar or a feature they have in common. In short, equivocation is akin to equation, becoming more pertinent the more persistent it is, and ambiguities that are systematic enough can amount to valid abstractions.

In the present case, one can observe the possibility that the author is suggesting the following analogies:

1. One analogy says that authoring a text is like piloting a vehicle. This can be written in either one of two ways.

1. Poet / Poem = Pilot / Boat.

2. Poet / Pilot = Poem / Boat.

3. Pilot / Poet = Boat / Poem.

The arrangements of SECs, SEPs, SEQs, and SERs have to do with the analogies that can be discovered and the equalities that can be created among signs, but a hint of the relevant similarities can be found in the categorical analogies (CANs) or the categorical equations (CEQs) that it is frequently possible to recognize among general terms, namely, the class names that apply to the corresponding categories of objects.

Tables 22 and 23 show two ways of expressing these general kinds of relationship, as they apply to the present example.

 ${\displaystyle {\begin{matrix}{\text{Pilot}}&:&{\text{Poet}}\\[8pt]&::&\\[8pt]{\text{Boat}}&:&{\text{Poem}}\end{matrix}}}$

 ${\displaystyle {\begin{matrix}{\text{Pilot}}&=&{\text{Poet}}\\[8pt]&\iff &\\[8pt]{\text{Boat}}&=&{\text{Poem}}\end{matrix}}}$

Thus, a rough outline of the ARK that transports The Lady of Shalott from a PORT or a QORT to an ORT is provided by the following example of a "categorical equation" (CEQ).

Pilot = Poet <=> Boat = Poem.

This means that the reader can get a clue as to how the author relates to his text by reading, in a metaphorical way, the statements as to how the pilot or the passenger (the Lady of Shalott) relates to her vehicle (The Lady of Shalott). What one sees illustrated here is a particular form of literary device, one that I refer to as analogical recursion. Given the intricacy of this form, it is probably useful to analyze its workings into several steps.

For the sake of shortening future references to the epitext at the top of the last subsection, the sequence of epigraphs that lace its prose discussion, let the acronym “TLOS” stand for “The Lady of Shalott”, the unofficial title of a legendary person, and let the italicized acronym “TLOS” be taken in token for “The Lady of Shalott”, the title of a poem.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Semiotic Equivalence Class}}\!}$ ${\displaystyle {\begin{matrix}{\text{The Lady of Shalott}}\\[8pt]{\textit {The~Lady~of~Shalott}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime }{\text{The Lady of Shalott}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{TLOS}}{}^{\prime \prime }&\}\\[8pt]\{&{}^{\backprime \backprime }{\textit {The~Lady~of~Shalott}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\textit {TLOS}}{}^{\prime \prime }&\}\end{matrix}}}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle {\begin{matrix}{\text{TLOS}}\\[8pt]{\textit {TLOS}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{The Lady of Shalott}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {The~Lady~of~Shalott}}{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }{\text{TLOS}}{}^{\prime \prime }\\[8pt]{}^{\backprime \backprime }{\textit {TLOS}}{}^{\prime \prime }\end{matrix}}}$

### Conscious Reflection

In this Section I examine how the intellectual process of reflection is expressed in reflective writing. Not so much as materials for analysis, since the power of analysis present in this work remains in a primitive state, but more to provide a constant reminder of what a reflective text is like, I am taking my epitext from the lifelong work of a single author, who made the aim of reflection an integral part of a whole life's work.

The thesis that is developing here is this: Language users have an innate knowledge of the situation of communication (SOC), a knowledge that is built into the language itself and gives its users an inkling of the social setting of communication that the language is meant to serve. Such a knowledge is tantamount to a science of communication that its users develop from its initial state by dint or by virtue of using it. Language users possess an intuitive, if imperfect, appreciation of the forms that are inherent in the social task of communication (TOC), and they exercise an implicit, if incipient, understanding of the practical roles that are constrained by the social hold of communication (HOC). Although every language user actualizes these roles with more or less competence and participates in the requisite forms of relationship with more or less cognizance, it is poets, playwrights, programmers, policy analysts, and other sorts of reflective writers that are especially charged to articulate these forms in a relatively explicit fashion.

The fact that reflective writers are driven to comment on the SOC itself, even if it is not always desirable or feasible to do so straightforwardly, and the fact that perceptive writers are able to find symbols of the SOC in the most inobvious places, reflected in the most refractory settings, and even when its likenesses are cast into the most unlikely images — these are two of the factors that combine to give creative writing its notably recursive and often cryptic character.

A reflective writer converts a situation of communication (SOC), a type of object, into a communication of situation (COS), a type of sign, and links the succession of reflective signs into the ongoing reflective text. But what are the forces that force a text, developing freely in a medium of communication, furnishing the vehicle of an observation, and bearing the impression of an object that occasions it, to double back on its writer and itself, to turn back through the medium of communication, all to form a sign for itself and to make a name for its author?

The relevance of reflective writing to the inquiry into inquiry can be seen in the following way. Let one examine a reflective text, a sample from the work of a suitably reflective writer, and one often discovers, besides the interpretation that bears on the obvious subject and serves to carry the ostensible theme, that there is coded or woven through the covering text a comment on the SOC itself, that is, a reflection on the writer, the reader, and the text itself. This reflexive interpretation reveals the writer's impressions about the process of writing, the very process that led to the text as its end result.

By tracing the analogies that exist between reflective writing and the inquiry into inquiry it is possible to gain a measure of insight into the character of the latter task. It is not a strange circumstance for the life and work of a writer to be represented again in that work, indeed, to be critically reflected there. And there is no question that a text can be used by a writer to talk about itself and its author, in a way that conceivably makes sense of them both — the question is whether what a reflexive text says can be interpreted in the same way as a text about external objects, or has to be taken with a distinct grain of salt.

Reflective writing arises from reflection on life and conduct and issues in a description of what goes on in the scene surrounding the reflective writer's point of view (POV). Of course, among the forms of conduct that are subject to inspection, a piece of reflective writing can also reflect on the process of writing itself, detailing the conditions that affect its intentions and its outcome, and thus taking on a “reflexive” character, though it is customary to express these narrower reflections in any number of less direct manners. With regard to the scene about a POV, a piece of reflective writing can take any stance from admiring, to amused, to bemused, to critical, to simply trying to puzzle out a fraction of what is going on. With respect to the process of writing and the development of a writer, a piece of reflective writing and what it articulates can be a crucial part of changing or preserving a POV. From this description, it ought to be clear that reflective writing is a naturally occurring species of inquiry into inquiry. That is to say, in analyzing the varieties of syntactic, semantic, and pragmatic phenomena that occur in reflective writing, one is performing a task that parallels the inquiry into inquiry.

Notions of recursion, informally taken, arise in this discussion for several reasons. First, there is the appearance of self application that is involved in an inquiry into inquiry, in the idea that an instrumental activity called “inquiry” can have application to an objective argument called “inquiry” and yield a meaningful result. Second, there is the appearance of self reference that is involved in an inquiry into inquiry, in the fact that a textual record of a self described inquiry needs to refer to itself as falling under the general topic of inquiry.

Strictly speaking, the themes of self application and self reference are less properly described as recursive than reflective or reflexive, but it is easy to see how these issues arise in the process of carrying out a genuinely recursive project in an effectively pragmatic context.

In order to do this, I need to give a rough description of these two ideas, that of a recursive project and that of a pragmatic context.

1. In a recursive project, one attempts to clarify a complex concept in terms of simpler concepts. For instance, an important special case occurs when one tries to analyze a complex process in terms of simpler processes. A recursive project recurs upon a type of situation where the same concept is applied to simpler objects, in particular, where the same process, procedure, or function is applied to simpler arguments, proceeding to increasingly simpler arguments until the simplest arguments are reached. A recursive project is sound if there is a bound that can be wound around it, and it redounds to good effect if there is a ground that can be found to found it.
2. In a pragmatic context, the canonical way to clarify any concept is to give it an effective representation or an operational definition, that is, to detail the effects that the object of the concept is conceived to have when it is applied to the objects available in a specifiable variety of practical situations. An interpretive agent that follows this pragmatic prescription for clarifying concepts, persisting at it long enough and pursuing it through an adequate array of applications, can convert each concept analyzed into its corresponding "active formula". This is a form of expression that is logically equivalent, or as nearly as possible, to the intended concept, but suitable for immediate application to the contemplated domain of objects.

Now, consider the concept of inquiry as a candidate for clarification. In the case of a concept like inquiry, the object of the concept in question is an activity that applies to the broadest conceivable variety of objects, one of these arguments being the topic of inquiry itself. As a result, if one approaches a definition of inquiry by way of the pragmatic prescription for clarifying concepts, one quickly discovers that an important ingredient in the active formula for inquiry is a component that characterizes the concept inquiry in terms of its action on itself.

What does the object denoted by “inquiry” have to do with respect to the object denoted by “inquiry”, in the first place, to qualify as a genuine inquiry, in the end, to succeed as an inquiry into inquiry? Evidently, something about the sign, the object, or what transpires between the sign and the object is conducive to attaining a better description of inquiry than that given by the mere name “inquiry”. The word “inquiry” and the symbol ${\displaystyle y\!}$ are like a host of difficult signs, starting with “I” and “you”, where knowing the sign does not mean knowing the object perfectly, although it can lead to a knowledge of it. Simply knowing the word “I” and being able to use it adequately does not mean that I know myself perfectly, or that I can articulate my own nature. At best, these signs can serve to indicate the direction of the object pointed out or help to remind an agent of the action that is called for to be carried out.

Can the senses of a sign be so confused, or the sense of an interpreter be so confounded by it, that between the two it is difficult to know if the sign refers to something inside the self that is in the world or to something in the world that is outside the self?

Given the description of a question as an unclear sign, it might be thought that the sole purpose of an inquiry is to clarify a question until it acquires the status of an answer, and thus to operate wholly within the syntactic realm of signs and ideas. But this would ignore many cases of experimental inquiry and active problem solving, natural to include among inquiries in general, that involve the manipulation of external objects and the alteration of objective states as they occur in the objective world. With these things in mind, it is best to define an inquiry as a sign relation transformation (SRT), in other words, and a bit more pronounceably, as a transformation of sign relations (TOSR). This is conceived to be an operation that acts on whole sign relations, changing one into another, typically by acting in specified ways on the elementary sign relations(ESRs), or on the ordered triples ${\displaystyle (o,s,i).\!}$ An inquiry, regarded as a TOSR, can be treated as a generalized form of sign process. Whereas a sign process is restricted to acting within a single sign relation and can only change signs into their interpretants, a TOSR can subject elements of an object domain to experimental actions and induce objective states to undergo a variety of intentional changes.

From an abstract relational point of view, it is not too far from grasping the concept of a sign relation to seeing that transformations, operations, and other sorts of relations that are possible to define on sign relations are bound to become of significant interest. But the present concern is to decide whether the identification of inquiries with TOSRs constitutes a good definition in practice. A good definition in practice, aside from capturing the necessary and sufficient properties of its subject, is one that facilitates the generation of fruitful, incisive, material, pertinent, and relevant ideas about it. To some extent this depends on the context of practices and the specific purposes that a particular interpreter has in mind. Still, some definitions are more generally useful than others. Accordingly, the task I need to take up next is to examine the abstract concept of a TOSR with regard to its utility in practice, in other words, to determine its practical bearing on a concrete conception of inquiry, as it is topically understood.

If the essence of inquiry, or any aspect of what an inquiry can be, is captured by the concept of a TOSR, then a lot can be learned about the nature of inquiry by studying the manifest varieties and the internal structures of TOSRs.

Expressing this in terms of a prospective calculus, the present inquiry, ${\displaystyle y_{0},\!}$ constituted as an inquiry into inquiry, ${\displaystyle y\cdot y,\!}$ ...

As the clarification of a concept is pursued to the limit, it approaches the status of a definition. And so one finds oneself contemplating a definition of inquiry that defines it at least partially in terms of itself. But an attempt to define a concept in terms of itself is ordinarily considered to be a bad thing, leading to the sort of circular definition that vitiates the utility of the whole effort toward clarity.

In summary, because the subject of inquiry is something that one can reasonably be in question about, and because the topic of inquiry is something that one can sensibly inquire into, the chances that one can make sense of an inquiry into inquiry is not merely an interesting and diverting possibility but a necessary part of the meaning of inquiry.

Definitions are limiting cases of clarifications, since a process of clarification pursued far enough approaches a formulation of a concept that is tantamount to its definition.

Before an inquiry can proceed very far, it needs to develop a map or a plan of the territory that the agent of inquiry intends to investigate. This task involves the drawing of distinctions, the finding of natural differences and the making of useful separations, among the objects of inquiry.

Let me call attention to a compound form of existence, the kind that is composed of a sign and the interpreter that authors it, and describe it more briefly as a sign and issuer (SAI) or a text and writer (TAW). As long as one moves through a casual context it is convenient to carry along these portmanteau words, precisely because their two components are confounded so consistently in informal speech, where it is hardly polite to keep on objecting to their ambiguities and anthropomorphisms. When I say that a SAI does this or that, it is up to the good sense of a charitable interpreter to decide whether this or that is something that a sign or rather its issuer is supposed to be able to do. In these terms, a SAI that speaks of and to itself and addresses its own composition or a TAW that talks about itself in either sense are not likely to have the same interest for others as they do in themselves.

It is ordinarily thought to be a good thing for a SAI or a TAW to be able to reflect on itself, but one whose subject is solely oneself is not ordinarily thought to be of interest to others.

In this work, I am interested in SAIs and TAWs that survive the onset of recursion while avoiding the snares of sheer self reference, that pose patterns of self reference but only in the service of a greater subject, and that slip the snarly bonds of narcissism frequently enough to say something significant about something else.

It is a form of narcissism to think that others are necessarily as interested in every detail of one's existence as one is oneself. But narcissism is an unnatural condition that has to be distinguished from one's more commonly understandable interest in oneself. In its extreme forms, a full blown narcissism is not the natural flourishing of a healthy self interest but the outgrowth of deep and typically early disturbances in the systematic structure of the self.

In order to understand how a sign functions as a sign it is necessary to understand the interpreter for whom it actually functions as a sign. The ways that a sign denotes its objects and connotes its interpretants say a lot about the interpreter for whom it denotes its objects and for whom it connotes its interpretants, where the antecedents of all these occurrences of “its” can be either the sign or its interpreter. To the extent that all knowledge is expressed in signs, to know anything at all is to know an aspect of oneself, however unwittingly. In this way, one can arrive at the epigrammatic formulas that “all knowledge is self knowledge” and that “every inquiry is an inquiry into inquiry”.

A symbol is a type of sign whose relation to its object is constituted solely by the fact that an interpreter employs it to denote that object, in other words, that an interpretant connects it with that object in an elementary sign relation, or an ordered triple of the form ${\displaystyle o,s,i.\!}$ This means that the nature and the character of an interpreter can be studied especially well as reflected in the symbols that it employs.

Unlike icons and indices, which have rationales for their denotations in the properties and instances, respectively, which are common to objects and their signs, ...

term/premiss/argument: symbols with internal or instructive hints?

An argument is a type of symbol that incorporates among its syntactic provisions an independent indication of the method that is intended for its interpretation, that is, it embodies a series of hints about the ways and the means that its issuer intends its prospective interpreter to use in order to achieve its interpretant, in short, to reach its conclusion.

#### The Signal Moment

 One night as I did wander, When corn begins to shoot, I sat me down to ponder Upon on auld tree root. Auld Ayr ran by before me, And bicker'd to the seas; A cushat crooded o'er me, That echoed through the trees. — Robert Burns, One Night As I Did Wander, [CPW, 48]

There is a thought that forms the theme of the present inquiry, indeed, as a chorus to a lyric are its evocations to the text that records this inquiry, and I find myself returning to its expressions on a constantly recurring basis, however much I strive to introduce variations for the sake of developing its implications and reflecting on its meanings from a fresh angle. So let me give the current rendition:

The present inquiry, ${\displaystyle y_{0},\!}$ portraying itself as an inquiry into inquiry, ${\displaystyle y\cdot y,\!}$ proceeds on the premiss that a generic inquiry, ${\displaystyle y,\!}$ can generally inquire into a generic inquiry, ${\displaystyle y,\!}$ thereby achieving a settled result, one that awaits a mere determination to be signified by the name ${\displaystyle {}^{\backprime \backprime }y\cdot y{}^{\prime \prime }.\!}$ Thus the present inquiry, acting on the pretext of a formal posability, that is, a poetic license, a verbal permission, or a written suggestion, being motivated and justified by no more authority than these connote, is led to define itself in terms that appose its own term to its own term, and so it is led to take on a recursive, a reflective, or a reflexive cast.

The terms of this description need to be inquired into, and their implications pursued in greater detail.

The present inquiry, ${\displaystyle y_{0},\!}$ portraying itself as an inquiry into inquiry, ${\displaystyle y\cdot y,\!}$ proceeds on the premiss that a generic inquiry, ${\displaystyle y,\!}$ can generally inquire into a generic inquiry, ${\displaystyle y,\!}$ and thereby achieve a settled result, and that this result awaits nothing other than its determination by the present inquirer to confer an objective significance on the name ${\displaystyle {}^{\backprime \backprime }y\cdot y{}^{\prime \prime }.\!}$ All of this is summed up in the formula: ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }.\!}$

Thus the present inquiry, acting on the pretext of a formal posability, namely, the circumstance that the rules of a prospective formal grammar allow one to write the expression ${\displaystyle {}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\!}$ and to inquire after its meaning, is led to define itself in terms that apply to its own case as argument, since the present inquiry, ${\displaystyle y_{0},\!}$ must be an example of whatever genus, ${\displaystyle Y,\!}$, that a generic inquiry, ${\displaystyle y,\!}$ is selected to represent. As a consequence, the present inquiry is forced to pursue the development of its own case in terms that appose its own actions to its own motives, and so is led to take on a recursive, a reflective, or a reflexive cast.

#### The Symbolic Object

 I dream'd I lay where flowers were springing Gaily in the sunny beam, List'ning to the wild birds singing, By a falling crystal stream; Straight the sky grew black and daring, Thro the woods the whirlwinds rave, Trees with aged arms were warring O'er the swelling, drumlie wave. — Robert Burns, I Dream'd I Lay, [CPW, 45]

To paraphrase, the present inquiry acts on the pretense that an inquiry can inquire into other inquiries, perhaps even those that are presently ongoing, and even inquire into itself, in sum, being entitled to inquire into the full genus of inquiry, ${\displaystyle Y,\!}$ a class that includes ${\displaystyle y_{0}\!}$ as a member. But these representations, under cross examination, lead to a number of unanswered questions, like: Just what is a “generic inquiry”, anyway? Even more critically, their close and repeated examination leads to a host of “unquestioned answers”, answers already accepted as adequate, but whose appearances as answers need to be questioned again.

The formal posability of a self application, for example, as expressed by the term ${\displaystyle {}^{\backprime \backprime }y\cdot y{}^{\prime \prime },\!}$ especially when the formal calculus that is called on to make sense of these applications is still merely prospective and still highly speculative, ought to arouse a lot of suspicion from the purely formal point of view. Indeed, I cannot justify this way of proceeding, beginning in the middle of things and without stopping to establish a well defined formal system ahead of time, except to say that something very like it is unavoidable in a large number of natural circumstances, and so one ought to find a way of getting used to it. A way of getting used to the natural situation of inquiry is one of the things that the present inquiry hopes to find.

If it appears that this allows the present inquiry an unlimited scope or an excessive freedom, it has to be remembered that a formal posability is barely enough of a formal subsistence to begin an inquiry, but rarely enough to finish it. It can be invaluable as the provisional grubstake for a prospecting expedition, supplying the initial overhead it takes to prime the pump of subsequent exploration, but it is not sufficient to continue very far with an investigation. In essence, it is nothing more substantial than a grammatical allowance or a syntactic hypothesis, in effect, a poetic license, a verbal permission, or a written suggestion. Taking all of these cautions into account, it leaves the present inquiry motivated and justified by no more authority than their titles connote, and it obliges the precocity of what is written to be atoned for with all the critical benevolence of afterthought that can be mustered after the fact, to wit, through the diligent application of that turn of mind that allows one to write first and only later to think on the meaning.

 Such was my life's deceitful morning, Such the pleasures I enjoy'd! But lang or noon, loud tempests storming, A' my flowery bliss destroy'd. Tho fickle Fortune has deceiv'd me (She promis'd fair, and perform'd but ill), Of monie a joy and hope bereav'd me, I bear a heart shall support me still. — Robert Burns, I Dream'd I Lay, [CPW, 45]

The present inquiry acts on the purely formal suggestion that a generic inquiry can inquire into other inquiries, perhaps even those that remain ongoing, moreover, that a particular inquiry can even inquire into itself. Interpolating the appropriate symbols, the present inquiry, referring to itself as ${\displaystyle {}^{\backprime \backprime }y_{0}{}^{\prime \prime },\!}$ acts on the instance of a purely formal possibility, one that it expresses as a premiss in the formula ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime },\!}$ intending this to be interpreted to the effect that an inquiry can inquire into a class of inquiries that includes itself as a member, and this is a hypothesis that is based on little more authority than the fact of its expression a prospective formal language, in other words, one whose interpretation is still a largely prospective matter.

Stepping back and reflecting on the situation, one needs to ask how in general and how in particular does one fall so blithely into these forms and into these manners of representation. Once that process is better understood then it becomes possible to evaluate in a fairer way whether this direction of fall is tantamount to a happy accident of the natural intuition or whether it constellates a disastrous catastrophe that needs to be remedied through the application of a severer style of reasoning. Generally speaking, the point at which intellectual developments like these begin to take on an automatic character is when the intention is formed of devising a formal calculus, in the present case, a prospective calculus of applications or appositions of the form ${\displaystyle f\cdot g,\!}$ the terms of which are intended to be capable of referring to processes potentially as complex as inquiries. The project of an appositional calculus (AC) is what formalizes the intuitive possibility of an inquiry into inquiry and continues to suggest the formal possibility that any inquiry can be applied to itself, at least, any inquiry that can be symbolized in this calculus.

But not every form of words that can be formed within the permissions of a formal language does in fact point to a form of objective reality. Whether an inquiry into inquiry is a real possibility, how its possibility is to be actualized if it is indeed real in fact, and why it is necessary for an individual species of agents to bother with the actualization of this possibility — these are just some of the questions that demand to be addressed at this point, no matter how gingerly and how tentatively it is presently conceivable to respond to them, and they are just a few of the issues the distribution of whose partial solutions are found to occupy the greater body of this work.

#### The Endeavor to Communicate

 When o'er the hill the eastern star Tells bughtin time is near, my jo, And owsen frae the furrow'd field Return sae dowf and weary, O, Down by the burn, where scented birks Wi dew are hangin clear, my jo, I'll meet thee on the lea-rig, My ain kind dearie, O! — Robert Burns, The Lea-Rig, [CPW, 474]

An agent involved in an effort to communicate, no matter how various the signs and the media that make its conveyance conceivable, and no matter how articulately the character of its endeavor is styled, whether it is pointed and straightforward, or allusive and recursive, whether it is elliptic, hyperbolic, parabolic, or otherwise conically sectioned, or whether it is much less smoothly sliced into its initial approximations and final truncations, there are only so many ways that a finitely informed creature can find to figure out what meaning the world has and to formulate what sense a life's work can add to it.

The present situation, as far as it goes, is a suitable subject for being investigated along the lines of the pragmatic theory of sign relations.

Since ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ is a sign, it has the potential to denote an object ${\displaystyle x,\!}$ if and when there is determined to be a signified object, and one with a power to impress itself on the mind of the operative interpreter of that sign. Likewise, since ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ is a sign, it has the potential to denote an object, one that syntactic compunctions stop me from saying is ${\displaystyle y_{0}=y\cdot y,\!}$ that is, if I want to avoid a definite risk of failing to be understood. But what is this object, if it exists? At any rate, what sort of object is the receiver of the sign thereby entitled to expect it to be, whether or not the object that it foreshadows ever does come to be actualized?

In order to have a variety of more convenient names for referring to the object potentially denoted by the sign ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime },\!}$ I refer to the expression ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ as “The Initial Equation”, or as “TIE”, for short. Although it is not strictly necessary for such a small piece of text as ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime },\!}$ I here obey the rule that the titles of texts are italicized. Furthermore, the object, situation, or state that satisfies TIE, to the effect that ${\displaystyle y_{0}=y\cdot y,\!}$ and is therefore potentially denoted by TIE, can also be referred to as “the intended state”, or as “TIS”, for short.

 At midnight hour in mirkest glen, I'd rove, and ne'er be eerie, O, If thro that glen I gaed to thee, My ain kind dearie, O! Altho, the night were ne'er sae wild, And I were ne'er sae weary, O, I'll meet thee on the lea-rig, My ain kind dearie, O! — Robert Burns, The Lea-Rig, [CPW, 474]

For the sake of shortening future references to the chief object of the present inquiry and the initial sign of its potential existence, let the acronym “TIS” be equiferent to the phrase “the intended state”, and let the italic tag “TIE” be equiferent to the title “The Initial Equation”. Further, let the connotations be so arranged that “TIS” is semiotically equivalent to “the intended state” and “TIE” is semiotically equivalent to “The Initial Equation”. It is important to note that a set of signs can be equiferent among themselves in the wholly vacuous sense that all of them have no objective reference, and, strictly speaking of what they denote, that all of them refer to nothing at all, whereas a set of signs that are equivalent in the properly semiotic sense still have each other as their connotations.

There is a feature of this style of abbreviation to which it is useful to call attention. Rather than letting the acronym “TIS” strictly denote the phrase “the intended state” and instead of letting the tag “TIE” strictly denote the title “The Initial Equation”, I am merely asking the reader to arrange in behalf of the interpretation a semiotic partition (SEP), along with its corresponding semiotic equivalence relation (SER), in which a particular pair of semiotic equivalence classes (SECs) serve to stake out a couple of parts, that is, to represent mutually exclusive classes of signs that denote their respective objects in parallel. This situation is depicted in Table 26.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Semiotic Equivalence Class}}\!}$ ${\displaystyle {\begin{matrix}{\text{the intended state}}\\[8pt]{\textit {The~Initial~Equation}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime }{\text{the intended state}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\text{TIS}}{}^{\prime \prime }&\}\\[8pt]\{&{}^{\backprime \backprime }{\textit {The~Initial~Equation}}{}^{\prime \prime }&,&{}^{\backprime \backprime }{\textit {TIE}}{}^{\prime \prime }&\}\end{matrix}}}$

In each case, the abbreviated form and its expansion are set to connote each other all within a single level of signs, while both signs are set to denote their common object in a parallel fashion. This strategy for annexing compressed references to a sign relation can be referred to as an acronymically connotative extension (ACE) of that sign relation.

 The hunter lo'es the morning sun, To rouse the mountain deer, my jo, At noon the fisher takes the glen Adown the burn to steer, my jo: Gie me the hour o gloamin grey It maks my heart sae cheery, O, To meet thee on the lea-rig, My ain kind dearie, O! — Robert Burns, The Lea-Rig, [CPW, 474]

#### The Medium of Communication

 The gloomy night is gath'ring fast, Loud roars the wild inconstant blast; Yon murky cloud is filled with rain, I see it driving o'er the plain; The hunter now has left the moor, The scatt'red coveys meet secure; While here I wander, prest with care, Along the lonely banks of Ayr. — Robert Burns, The Gloomy Night is Gath'ring Fast, [CPW, 250]

Before I can advance this discussion to a higher level of reflection on my own and other texts, in other words, to augment its participation in syntactic and textual processes beyond the level of rote recitation and routine replication of whatever text comes to mind, I need to introduce a minimal set of syntactic devices and textual mechanisms for adverting to and reflecting on syntactic entities and textual objects, in other words, for generating and interpreting, or else recognizing and elaborating, a level of references to objects that are themselves composed of signs and that therefore have the characters of complex signs in their own rights.

In general, signs that denote signs are called higher order (HO) signs, leaving the signs denoted to be referred to as lower order (LO) signs. These form the subject of detailed discussions later on in this work, but the critical need for now is merely to make available an informal set of plausible devices for availing the discussion of names for pieces of text. Thus, the tools that are required can be sufficiently well illustrated in their immediate applications to the present materials.

 The Autumn mourns her rip'ning corn By early Winter's ravage torn; Across her placid, azure sky, She sees the scowling tempest fly; Chill runs my blood to hear it rave; I think upon the stormy wave, Where many a danger I must dare, Far from the bonie banks of Ayr. — Robert Burns, The Gloomy Night is Gath'ring Fast, [CPW, 250]

Depending on whether it is possible to adapt, appropriate, and otherwise make use of what HO signs are already extant in a field of discussion or whether it is necessary to create, invent, or otherwise make up further HO signs to denote the signs and the texts that one notices in an area, one finds that the sorts of syntactic devices, textual mechanisms, and reflective operators that one needs are divided into two broad camps:

1. There are the anaclitic, ancillary, or auxiliary devices that an agent uses to imp out each HO connotative plane by extrapolating its indirections in novel directions, to allude in a connotative fashion to the current signs of signs and the established titles of texts, to sharpen up the reflective references already extant, and to take full advantage of the ancient orders of associations and the antecedent layers of citations that are already in place.
2. There are the creative, generative, or productive devices that an agent uses to eke out each HO denotative plane in the first place, to adduce the initial signs in that order, to create new HO signs, to refer in a denotative fashion to what thereby becomes an order of comparatively LO signs, and to issue HO citations of LO texts.

The connotative mechanism, relying on prior quotations and established titles, ...

Acronyms.

 'Tis not the surging billows' roar, 'Tis not that fatal, deadly shore; Tho death in ev'ry shape appear, The wretched have no more to fear; But round my heart the ties are bound, That heart transpierc'd with many a wound; These bleed afresh, those ties I tear, To leave the bonie banks of Ayr. — Robert Burns, The Gloomy Night is Gath'ring Fast, [CPW, 250]

The denotative mechanism, ...

These are devices whose function it is to operate on signs, including all sorts of characters, expressions, phrases, and texts, and whose result it is to generate signs that refer to their respective arguments as objects.

Quotation marks. Ordinary quotation marks (“ ”) can be used in the customary ways to create names for signs, concatenated signs, or pieces of text that they enclose. Unfortunately, for formal purposes, ordinary quotation marks have the disadvantage of being used for several other functions besides that of creating names for enclosed signs and texts. In particular, the same marks are frequently used for a motley crew of emphatic functions or monitory purposes, that is, simply to call an extra measure of attention to the sign or the text enclosed, but without necessarily intending to interrupt its significance or to interfere with the corresponding process of denotation.

Arch quotations. An alternative form of quotation is provided through the employment of raised angle brackets (< >), also called arches or supercilia. These marks are reserved to the sole purpose of creating signs for signs and generating names for pieces of text, in keeping with the nominal intention and the normal use of quotation marks.

Titles and headings. An arbitrary title for a syntactic object or a textual segment is created simply by designating anything whatsoever to a service in that role. Whatever it is before being dubbed as the title of the material in question, it becomes a pointer to its appointed object simply by virtue of being so dubbed, if nothing else, at least as regarded by a single interpreter that is duly appointed to appoint things so, if only for the sake of a purely personal recognizance.

 Farewell, old Coila's hills and dales, Her heathy moors and winding vales; The scenes where wretched Fancy roves, Pursuing past unhappy loves! Farewell my friends! farewell my foes! My peace with these, my love with those — The bursting tears my heart declare, Farewell, my bonie banks of Ayr! — Robert Burns, The Gloomy Night is Gath'ring Fast,, [CPW, 251]

The highest order of generality among titles is not absolutely necessary in the present context. More commonly, a title is a pre-arranged sign, a pre-established mark, a prefixed epithet, or a pre-ordained piece of text that gets re used, perhaps subject to a conventional modification or a special inflection, to serve as a sign or a name for what is customarily a disjoint sign or a distinct piece of text. Under typical circumstances, although not universal, the syntactic entity or the textual object to which a title refers is a much longer text, and thus one that occasions the practical need among its interpreters of having a briefer alias or a compressed designation for it. In short, a title is intended to serve a purpose that is similar to one of the roles of ordinary quotation, but subject to orders of pragmatic constraints that quotation marks, when literally taken and expressly used, are clearly not able to satisfy. Putting aside for the time being the issues that are raised by this general discussion, I revert to the ordinary use of quoted expressions and italicized phrases as the titles of texts.

#### The Ark of Types : The Order of Things to Come

 Now westlin winds and slaught'ring guns Bring Autumn's pleasant weather; The moorcock springs on whirring wings Amang the blooming heather: Now waving grain, wide o'er the plain, Delights the weary farmer; And the moon shines bright, as I rove by night, To muse upon my charmer. — Robert Burns, Now Westlin Winds, [CPW, 44]

The present situation, as far as it goes, is a suitable subject for investigation along the lines of the pragmatic theory of sign relations. The state of the resulting examination, as it stands at the current stage of analysis, is summarized in Table 27, indicating little more than this hypothetical circumstance: That a couple of terms of a formal language, a prospective calculus of applications or appositions of the form ${\displaystyle f\cdot g,\!}$ are intended to be identified in all of their current objective references. Thus, the terms ${\displaystyle y_{0}\!}$ and ${\displaystyle y\cdot y,\!}$ formed in accord with the still inchoate and yet developing grammar of the intended appositional calculus, are set to denote the very same object or objects, all the while that the precise nature of what these signs actually denote is still up for grabs, and in spite of the circumstance that the bare consistency of its logical possibility remains unknown, for all the plausibility of its “posability”.

Recalling that a part of a sign relation is any subset of its extension, that is, an arbitrary selection of its ordered triples, Table 27 presents a part of a sign relation that is needed to interpret The Initial Equation, also known as TIE.

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle {\text{Interpretant}}\!}$ ${\displaystyle Y\!}$ ${\displaystyle {}^{\backprime \backprime }Y{}^{\prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime }Y{}^{\prime \prime }\!}$ ${\displaystyle y\!}$ ${\displaystyle {}^{\backprime \backprime }y{}^{\prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime }y{}^{\prime \prime }\!}$ ${\displaystyle {\begin{matrix}y_{0}\\y_{0}\\y_{0}\\y_{0}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }y_{0}{}^{\prime \prime }\\{}^{\backprime \backprime }y_{0}{}^{\prime \prime }\\{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\\{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\end{matrix}}}$ ${\displaystyle {\begin{matrix}{}^{\backprime \backprime }y_{0}{}^{\prime \prime }\\{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\\{}^{\backprime \backprime }y_{0}{}^{\prime \prime }\\{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\end{matrix}}}$

 The paitrick lo'es the fruitfu fells, The plover lo'es the mountains; The woodcock haunts the lonely dells, The soaring hern the fountains: Thro lofty groves the cushat roves, The path o man to shun it; The hazel bush o'erhangs the thrush, The spreading thorn the linnet. — Robert Burns, Now Westlin Winds, [CPW, 44]
In order to refer to an object x, it is necessary to use a sign "x", or something equally good, an equiferent sign, to do so.  In a similar vein, in order to refer to a sign "x", it is necessary to use a HO sign <"x">, or something equally good, an equiferent HO sign, to do so.

In referring to the signs "x" and "y0 = y.y", I am of course using a definite style of HO signs to do so, while the corresponding LO signs, the ones that are being denoted by these mechanisms, are homologous to the portions of text that appear within the bounds of these quotations.  The chief exception to this rule, attaching a note of practical caution to its exercise that precludes its overly automatic use, is due to the problem already noted, that not every LO sign extracted from quotation is safe to use, semantically speaking, in every discursive context, grammatical environment, syntactic frame, or textual niche.

As long as I am referring to the signs "x" and "y0 = y.y", I can keep on using the HO signs that refer to them, all without having to employ the next layer of encapsulation in arch quotes.  I am obligated to use the new order of arches only when I want to awake to, become aware of, and directly mention the order of signs that I find myself employing, in the present case, when I get a notion to critically reflect on and thus to make explicit reference to the HO signs <"x"> and <"y0 = y.y">.  It is almost as if, in using an order of signs, that one takes off the wraps that one uses in order to mention them.  This is generally true, but subject to exceptions at the boundary conditions, where there are no more lamina to strip away.


[Table 28 description]

The part of a sign relation that is shown in Table 28 is an example of this type of sector.

${\displaystyle {\text{Table 28-a.}}~~{\text{Sector of a Sign Relation for}}~{\textit {TIE}}\!}$
 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {\text{Interpretant}}\!}$
 ${\displaystyle y_{0}\!}$ ${\displaystyle {}^{\backprime \backprime }y_{0}{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\backprime \backprime }y\cdot y{}^{\prime \prime }\!}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Semiotic Equivalence Class}}\!}$ ${\displaystyle y_{0}\!}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime }y_{0}{}^{\prime \prime }&,&{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }&\}\end{matrix}}}$

 Thus ev'ry kind their pleasure find, The savage and the tender; Some social join, and leagues combine, Some solitary wander: Avaunt, away, the cruel sway! Tyrannic man's dominion! The sportsman's joy, the murd'ring cry, The flutt'ring, gory pinion! — Robert Burns, Now Westlin Winds, [CPW, 44]

Table 29 shows a variety of notations that are available for the first two orders of signs above "x".

${\displaystyle {\text{Table 29-a.}}~~{\text{Simple Signs and Their Higher Order Signs}}\!}$
 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {\text{Interpretant}}\!}$
 ${\displaystyle x\!}$ ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle }x{}^{\rangle }\!}$
 ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime \,\backprime \backprime }x{}^{\prime \prime \,\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \backprime \backprime }x{}^{\prime \prime \rangle }\!}$ ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ ${\displaystyle {}^{\langle \backprime \backprime }x{}^{\prime \prime \rangle }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\backprime \backprime \langle }x{}^{\rangle \prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime \langle }x{}^{\rangle \prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \langle }x{}^{\rangle \rangle }\!}$

 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Semiotic Equivalence Class}}\!}$ ${\displaystyle x\!}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime }x{}^{\prime \prime }&,&{}^{\langle }x{}^{\rangle }&\}\end{matrix}}}$ ${\displaystyle {}^{\backprime \backprime }x{}^{\prime \prime }\!}$ ${\displaystyle {\begin{matrix}\{&{}^{\backprime \backprime \,\backprime \backprime }x{}^{\prime \prime \,\prime \prime }&,&{}^{\langle \backprime \backprime }x{}^{\prime \prime \rangle }&,&{}^{\backprime \backprime \langle }x{}^{\rangle \prime \prime }&,&{}^{\langle \langle }x{}^{\rangle \rangle }&\}\end{matrix}}}$

 But, Peggy dear, the ev'ning's clear, Thick flies the skimming swallow; The sky is blue, the fields in view, All fading green and yellow: Come let us stray our gladsome way, And view the charms of Nature; The rustling corn, the fruited thorn, And ilka happy creature. — Robert Burns, Now Westlin Winds, [CPW, 44]

[Table 30 description]

${\displaystyle {\text{Table 30.}}~~{\text{Complex Signs and Their Higher Order Signs}}\!}$
 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {\text{Interpretant}}\!}$
 ${\displaystyle {\text{TIS}}\!}$ ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle }y_{0}=y\cdot y{}^{\rangle }\!}$ ${\displaystyle {\text{TIS}}\!}$ ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle }{}^{\backprime \backprime }y_{0}{}^{\prime \prime }=_{E}{}^{\backprime \backprime }y\cdot y{}^{\prime \prime }{}^{\rangle }\!}$
 ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ ${\displaystyle {}^{\langle \backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime \rangle }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \langle }y_{0}=y\cdot y{}^{\rangle \rangle }\!}$ ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$ ${\displaystyle {}^{\backprime \backprime }{\textit {TIE}}~{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle }{\textit {TIE}}~{}^{\rangle }\!}$

 We'll gently walk, and sweetly talk, While the silent moon shines clearly; I'll clasp thy waist, and, fondly prest, Swear how I lo'e thee dearly: Not vernal show'rs to budding flow'rs, Not Autumn to the farmer, So dear can be as thou to me, My fair, my lovely charmer! — Robert Burns, Now Westlin Winds, [CPW, 44]

[Table 31 description]

${\displaystyle {\text{Table 31.}}~~{\text{More Complex Signs and Their Higher Order Signs}}\!}$
 ${\displaystyle {\text{Object}}\!}$ ${\displaystyle {\text{Sign}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {\text{Interpretant}}\!}$
 ${\displaystyle {\text{TIS}}\!}$ ${\displaystyle {}^{\backprime \backprime }{\text{TIS}}{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\backprime \backprime }{\text{The Intended State}}{}^{\prime \prime }\!}$ ${\displaystyle {\text{TIS}}\!}$ ${\displaystyle {\textit {TIE}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {\textit {The~Initial~Equation}}\!}$ ${\displaystyle {\text{TIS}}\!}$ ${\displaystyle {\textit {TIE}}\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime }\!}$
 ${\displaystyle {}^{\backprime \backprime }{\text{TIS}}{}^{\prime \prime }\!}$ ${\displaystyle {}^{\langle \backprime \backprime }{\text{TIS}}{}^{\prime \prime \rangle }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \langle }{\text{TIS}}{}^{\rangle \rangle }\!}$
 ${\displaystyle {\textit {TIE}}\!}$ ${\displaystyle {}^{\backprime \backprime }{\textit {TIE}}~{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\backprime \backprime }{\textit {The~Initial~Equation}}{}^{\prime \prime }\!}$ ${\displaystyle {\textit {TIE}}\!}$ ${\displaystyle {}^{\backprime \backprime }{\textit {TIE}}~{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \backprime \backprime }y_{0}=y\cdot y{}^{\prime \prime \rangle }\!}$ ${\displaystyle {\textit {TIE}}\!}$ ${\displaystyle {}^{\backprime \backprime }{\textit {TIE}}~{}^{\prime \prime }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle }{\textit {TIE}}~{}^{\rangle }\!}$
 ${\displaystyle {}^{\backprime \backprime }{\textit {TIE}}~{}^{\prime \prime }\!}$ ${\displaystyle {}^{\langle \backprime \backprime }{\textit {TIE}}~{}^{\prime \prime \rangle }\!}$ ${\displaystyle =\!}$ ${\displaystyle {}^{\langle \langle }{\textit {TIE}}~{}^{\rangle \rangle }\!}$

#### The Epitext

 Green grow the rashes, O; Green grow the rashes, O; The sweetest hours that e'er I spend, Are spent among the lasses, O. — Robert Burns, Green Grow the Rashes, O, [CPW, 81]

It is time to make explicit mention of a certain wrinkle in this text, even at the risk of warping the record that records this reconnaissance and rendering all the rest of its traces an unceasing problem to itself.

Throughout the course of this ongoing discussion is threaded what I refer to as an “epitext”, a linked succession of epigraphs, that, aside from the incidental interest that their contents may hold, are designed to keep before the mind what a real text is like, with all the potential for meaning and all the problems of interpretation that genuine symbols, complex imagery, and transcendental allusions can present. I cannot be expected to comment on, much less to clarify, all of the relevant aspects and all of the problematic features that are likely to be obvious to even the most casual reader of this epitext, but I think it is important to keep in mind a sense of the distance that is yet to be covered before any theory can claim a true comprehension of real language use.

Why are poetic texts and lyrical materials relevant to the aims of the present project? It is because they “face the music” as soon as they can speak and continue to address it for the rest of their developments. In other words, they speak from the very beginning of their invocations to the most pressing issues of communication and they attempt to tackle in their informal ways the most difficult problems of interpretation, those that formal languages and formal logics often put off till the end of their days, if they ever face up to them at all. Of course, if a set of troubles can be avoided then perhaps it is best to do so. Therefore, if I want to convince anybody that it is worth their bother to engage a given array of issues and problems, then I ought to supply an argument to make it plausible why the types of phenomena in question are likely to be inevitable.

One of the reasons for drawing this epitext from poetic sources is that a genuine poem, aside from its commentary on the passing show, what it seems to say about this ostensibly concrete subject or that divertingly pastoral scene, usually has something extra to say, a surplus meaning or an ulterior motive that sets its aim above and beyond the call of beauty, and this is usually something that it ventures to say about the reasons for its own existence, about the endeavor to communicate that goes into its making, and thus about its total context of interpretation (COI). In sum, a poem is often meant, at least partly, to address the implicit questions: Why am I writing this? And why am I writing this way?

 There's nought but care on ev'ry han', In every hour that passes, O: What signifies the life o man, An 'twere na for the lasses, O. — Robert Burns, Green Grow the Rashes, O, [CPW, 81]

Aside from its apparent subject, its basic theme, and its commentary on diverse idyllic scenes, a genuine poem often has something to say about the reasons for its existence, the very idea that an author can form an intention, and the form of reception that it is aimed or averse to find. Thus its bits of reflective imagery, properly reconstituted and happily interpreted, make it tantamount to an implicitly recursive text (IRT).

What is it that forces a text to bear an immense variety of meanings, a few of them obvious, the bulk of them less so, if not the desire of its author to capture an image of a huge reality in an utterly tiny space, and to convey a fragment of a thicker truth along invisibly thin lines? A task like this can only be achieved through the use of multifaceted symbols and mirrored expressions, the results of multiple and repeated reflections. And a text like this can only be understood by means of an imaginative interpretation. Altogether, this mode of communication is comprehended by establishing a relation between writer and reader, one that is imprisioned at either end by the capacity at that terminus for imagination and reflection.

What is it that makes a text able to hold a wealth of meanings within it, if not the complementary desires of a writer and a reader to capture a huge reality between them?

The living creature, in its drive to write itself irreplacwably into the text of the universe and in its essay to render itself indispensable to the task of reading this text with any measure of understanding, ...

 The war'ly race may riches chase, An riches still may fly them, O; An tho at last they catch them fast, Their hearts can ne'er enjoy them, O. — Robert Burns, Green Grow the Rashes, O, [CPW, 81]

The more one steps back from the objects and the phenomena that first struck one's fancy to know, the ones one really desires to understand, in order to get what one imagines will be a better, more analytic, and more conceptual view of them, the more one sees the envisioned ends of understanding receding into the distance of one's altered perspective, leaving one with respect to them barely at the beginnings of analysis. Over time, the visionary ends of inquiry appear to disappear into the mists of one's lately imposed starts, to skip over the marks of one's recently interposed stations, perhaps to await one's tardy arrival at the alpha and omega of one's upstart inquiry.

These effects, that are due to a developing perspective, especially the appearance of an expanding universe that grows out of one's increasing ability to see detail, can turn from being awe inspiring at one moment, increasing one's desire to know an object, and encouraging the work of understanding, to being disheartening at the next moment, overwhelming one's mind and senses with the power of a phenomenon, and dashing all hopes of comprehending it. As a consequence, short of renouncing the quest altogether, one is likely to restrain oneself to any fragment of the original question that seems easy enough to address in due order, and then to settle for any semblance of an answer that happens to present itself in due time.

The intervention of an epitext is designed precisely for this reason, to compensate, counteract, and remediate the more deleterious effects of an otherwise heathily growing perspective. The epitext is meant to keep the end in view, to remind the participants in a communication of the type of text that is ultimately desirable to understand, but without demanding its complete unraveling within the immediate frame of time, nor taunting each other so severely with the distances that remain to their goals that all are daunted from continuing with the ongoing task.

 But gie me a cannie hour at e'en, My arms about my dearie, O, An war'ly cares an war'ly men, May a' gae tapsalteerie, O! — Robert Burns, Green Grow the Rashes, O, [CPW, 81]

In this way, an epitext can serve a couple of functions within a text:

1. The epitext maintains an internal model of the informal context, the actual, intended, or likely "context of interpretation" (COI), or the typical "situation of communication" (SOC) that prevails in a given society of interpretive agents. It does this by preserving a constant but gentle reminder of the type of text that ultimately demands to be understood within this social context. In other words, it represents its social context in terms of its ideals, [??? the expectation that contains it dialogue between the epitext helps to provides an image of the dialogue that ???]

2. The epitext and the text are in a relation, analogous to a dialogue, that mirrors the relation of the text itself to its casual, informal, or social context. In general, the analogy can be set up in either one of two ways, and can shift its sense from moment to moment:

1. Epitext : Text :: Context : Text. Here, the epitext plays the part of common expectations, generic ideals, or social norms that are invoked in the process of communication.

2. Epitext : Text :: Text : Context. Here, the epitext gives vent to the individual conceits, idiosyncratic caprices, or whims of the moment that are stirred up by the process of communication.

What type of text is best to use in an epitext, if it is going to achieve these stated objectives? A "paragon of writing is an apt title to give to the type of text at issue, since it marks the type of text that is originally desired to be understood and the type of text that ultimately demands to be understood.

 For you sae douce, ye sneer at this; Ye're nought but senseless asses, O: The wisest man the warl' e'er saw, He dearly lov'd the lasses, O. — Robert Burns, Green Grow the Rashes, O,, [CPW, 81]

The epitext acts as a kind of tether that helps to keep the end in view. It maintains an internal model of the informal context and preserves a reminder of the kinds of texts that ultimately demand to be understood. In this way, the epitext supplies a canon, a guideline, or a standard within the text, and secrets within the main text not only an image of the object to be analyzed but also an icon of the object to be achieved. Naturally reflective texts, the kinds that occur in poems, in plays, and in other sorts of creative writing, are the best sources of stock for an epitext. These kinds of text have a double relevance to the aims of AI. As materials for analysis, they exemplify the character of real language use in natural settings. As models for methods of analysis, they are capable of addressing complex issues in a casual fashion. Because they are freely chosen from natural sources of exemplary language use, they can serve as examples for analysis that are realistic enough to exemplify the types of phenomena that one desires to understand and difficult enough to test the methods of analysis that one proposes to use. Because it is their nature in part to reflect on their own nature as texts, they often contain insightful commentaries on this very nature.

 Auld Nature swears, the lovely dears Her noblest work she classes, O: Her prentice han' she try'd on man, An then she made the lasses, O. — Robert Burns, Green Grow the Rashes, O, [CPW, 81]

Let me then try to summarize the bearings that these poems and songs, these innocently reflective and innocuously self reverent types of texts, can be contemplated as having on the present inquiry, and again on the encompassing viability of AIR. Their relevance is twofold, bearing on the matter in question from complementary directions:

First, there is their negative or limitative bearing. As materials for analysis, poetic and lyrical texts contribute some of the hardest, most resilient, and most resistant cases that are known to confront the work of natural language understanding, and so they serve to puncture many of the rashest pretenses that this task is anywhere near to being done. Of course, if poetic and lyrical modes of production and comprehension are justly relegated to the status of mere diversions, then the task of unraveling their mysteries can be deemed a much less critical problem. However, if the resources that are elaborated and exploited in these manners of impression and expression are somehow essential to the very ideas of significant communication and meaningful interpretation, then it becomes a more crucial requirement to understand how they operate.

Second, there is their positive or productive bearing. As hints of models and heralds of methods, these types of texts hold out some hope that a text can sensibly comment on the task of achieving its own style of communication, the writing of it, the sending of it, the reading of it. More than that, their stock in variety of canonical styles helps to offer a cornucopia of constructive suggestions for ways of actually doing so. The chance of a text being able to express a perceptive reflection comes near the heart of the present matter, and the likelihood of a text having the power to embody an insightful self commentary brings the immediate discussion within a heartbeat of the inquiry into inquiry, for if a writing can teach about writing then perhaps an inquiry can learn about inquiry.

#### The Context of Interpretation

 To the weaver's gin ye go, fair maids, To the weaver's gin ye go, I rede you right, gang ne'er at night, To the weaver's gin ye go. — Robert Burns, To the Weaver's Gin You Go, [CPW, 306]

As this discussion proceeds, it is designed to expand the scope of what it can analyze successfully from simple signs to complex expressions to extended texts. In this progression, the pragmatic theory of signs is used as a unifying thread to connect the different levels of complexity. Accordingly, it needs to be kept in mind throughout the discussion that references to signs, unless specified otherwise, can generally be taken in a maximally inclusive sense, referring also to expressions and texts.

The more complex and more extended a sign, expression, or text becomes the more occasion it has for referring to many other objects on its way to achieving its ultimate denotation. Some of these implicit, incidental, and intermediate objects can be components, properties, and relations of the sign, expression, or text itself, perhaps amounting to its accidental connotations and its intended interpretants. When it comes to a highly involved sign, expression, or text, some of its subsidiary effects and ulterior objects can even be aspects or elements of those very agents and those very media that are actually, imagined, or intended to be involved in its production, transmission, or reception.

In many respects, these side effects are actually more important from a practical standpoint than the token objects of denotation, that is, the nominal results and the ostensible values that merely serve to mark the successful outcome of the interpretation process. Anything that an agent strives toward achieving or that a system moves toward attaining can be called its object, and so there arises the possibility that a global object or a derivative object, a thing constructed or reconstructed from various bits and pieces of extraneous references, is that which primarily or effectively calls or drives the greater action. If it strikes one as strange that an object construed from epiphenomenal marks and tangential signs should be the main motive and real object of the process of interpretation, it ought to be remembered that a special case of this already appears in the form of the semantic partitions that reconstruct the forms of their object domains. Accordingly, the types of global objects and derivative objects that emerge from the present considerations are just the ultimate generalizations of SECs.

 My heart was ance as blythe and free As simmer days were lang; But a bonie, westlin weaver lad Has gart me change my sang. — Robert Burns, To the Weaver's Gin You Go, [CPW, 306]

Signs are typical of the contents of consciousness. Indeed, from the standpoint of the pragmatic theory of signs, where a maximally general definition of signs holds sway, signs are considered to be all inclusive, generically identical, or simply co extensive with the class of phenomena that are commonly known as the contents of consciousness. In this view of the matter, a complex expression is analogous to a complex concept, of an order that is typically but not exclusively constructed in deliberate and purposeful thinking processes, while an extended text is analogous to an ongoing stream of consciousness or a long drawn out process of reasoning, whatever its character may be.

This analogy or identity between signs and contents of consciousness can help to explain the pains I am taking in the present discussion to elucidate the structures of self referent signs, expressions, and texts. With this key to its interpretation, a sign that denotes itself attracts interest because it presents an icon of self awareness. In other words, a sign relation that is called on to make sense of a self denoting sign affords a particular type of formal model, one that captures a relevant aspect of the structure that is involved in a content of consciousness referring to itself. In a corresponding fashion, a text that refers to itself, in whole or in part, is analogous to a conscious process that makes reference to itself, its aspects, or its instants.

It needs to be noted what I am not saying here. I do not say that signs and texts are themselves aware, or that consciousness needs to emerge from them, however much they can serve to attract the attention of already conscious agents. Indeed, I am taking no position yet on the questions of whether or how consciousness can emerge from conceivably non conscious materials. At present, I am only interested in describing the formal relations or the structural relationships that can be noted to exist among contents of consciousness, as noted, and not to explain the bare facts of these contents, much less to explain the circumstance of consciousness itself. With regard to this purely descriptive purpose, the main task for the near future is to develop an array of conceptual frameworks that can be put to work in organizing formal descriptions and in converting suitable portions of them into effective descriptions. As long as one works under the aegis of these methodological limitations, the following maxim needs to be kept in mind: The only thing that a formal model can capture is the form of something. Whether form is of the essence in the case of the human psyche is in fact an ancient and a still important question, but not one that I hope to answer just yet. The patent answer that presents itself is to keep the question open, and to continue exploring all of the available options.

One benefit of this openness is that it permits the exploration of the thinking mind's connection with information.

 My mither sent me to the town, To warp a plaiden wab; But the weary, weary warpin o't Has gart me sigh and sab. — Robert Burns, To the Weaver's Gin You Go, [CPW, 307]

The reason for my interest in signs, a reason that accounts for their part in inquiry and helps to explain their role in AIR, is that I take signs to be identical with all that is able to appear in awareness, or all that can be a content of consciousness. This amounts to saying that the ostensible analogy between signs and contents of consciousness, and thus between texts and streams of consciousness, is a potential identity. Speaking with respect to their potentiality, I would like to suggest that signs are identical with the possible contents of consciousness, and that the contents of consciousness all have the characters of potential signs. The broadest conceivable definition of what constitutes a "sign" leads to the broadest conceivable definition of what constitutes a "text", and so one is led to the idea that the whole stream of consciousness belonging to a person or a community, not just the miniscule fraction of it that happens to get written down in the conventional arrays of characters, can literally be regarded as a text.

What appears in awareness is a case of what one calls "phenomena", and a study that considers what can be a content of consciousness is called a "phenomenology". This means that

This is not the place to argue for the full strength of the proposed identity:

Phenomena	=	Appearances in Awareness
=	Contents of Consciousness
=	Signs.


Indeed, if one conceives consciousness to be a continuum, more exactly, if one considers every connected field (and stream) of consciousness to be a continuous manifold, as it very likely is, then this argument would depart from the realm of discrete signs and finite texts that is proper to computational models.

No matter how carefully the terms are qualified, allowing the equations to apply in purely formal and wholly potential senses, the argument for the soundness of this joint identification is by no means easy, presents the danger of leading this discussion far afield, if not astray, and is, in any case, not really needed to achieve the aims of the present work. Fortunately, while the full strength of the identity is not required for the present application, it can continue to serve as a useful analogy.

 A bonie, westlin weaver lad Sat working at his loom; He took my heart, as wi a net, In every knot and thrum. — Robert Burns, To the Weaver's Gin You Go, [CPW, 307]

This is not the place to argue for my particular way of seeing things, whose rationale ultimately depends on the integral relationship between the pragmatic style of phenomenology and the pragmatic theory of signs. There is still too much potential for misunderstanding between the writer that is due merely to possible differences in the uses of words, and not to any matters of substance. Until these ideas can be fully developed, the relation between signs and contents of consciousness, or the relation between texts and streams of consciousness, can still be treated as a useful analogy.

The array of what appears in awareness and the condition of what can be a content of consciousness is the range and quality of "phenomena". To study what is able to appear in awareness and to contemplate what could be a content of consciousness is to consider "phenomena" in general. A study that treats of phenomena, whether in their widest generality or restricted in a particular way, is appropriate to call a "phenomenology". There are many different styles of phenomenology, in spite of the factious pretenses of universality that are likely to be part and parcel of any style that is particular enough to find favor with a party of individual agents.

From the pragmatic point of view, there is a close relation between phenomena and signs.

The style of phenomenology that is needed for this work is the subject of a later discussion. Here, I make only the remarks that are needed for orientation.

 I sat beside my warpin wheel, And ay I ca'd it roun. But every shot and every knock, My heart it gae a stoun. — Robert Burns, To the Weaver's Gin You Go, [CPW, 307]

The pragmatic idea about phenomena is that all phenomena are signs of significant objects, except for the ones that are not. In effect, all phenomena are meant to appear before the court of significance and are deemed by their very nature to be judged as signs of potential objects. Depending on how one chooses to say it, the results of this evaluation can be rendered in one of the following ways:

1. Some phenomena are in fact signs of significant objects. That is, they turn out to exist in a certain relation, one that is formally identical to a sign relation, wherein they denote objects that are important to the agent in question, an agent that thereby becomes the interpreter of these signs.

2. Some phenomena fail to be signs of significant objects, however much they initially appear to be. In this event, the failure can be accounted for in either one of two ways:

1. Some phenomena can fail to be signs of any objects at all. This amounts to saying that what appears is not really a sign at all, not really a sign of any object at all.

2. All phenomena are signs in some sense, even if only granted a default, nominal, or token designation as signs, but some signs still fail to qualify as signs of significant objects, because the objects they signify are not important to the agents in question.

 The moon was sinking in the west, Wi visage pale and wan, As my bonie, westlin weaver lad Convoy'd me thro the glen. — Robert Burns, To the Weaver's Gin You Go, [CPW, 307]
 But what was said, or what was done, Shame fa' me gin I tell; But Oh! I fear the kintra soon Will ken as weel's myself! — Robert Burns, To the Weaver's Gin You Go, [CPW, 307]

#### The Formative Tension

 A lassie all alone, was making her moan Lamenting our lads beyond the sea: — “In the bluidy wars they fa', and our honor's gane an a', And broken hearted we maun die.” — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]

An incidental purpose of this reconnaissance is to point out the more problematic features of interpretation, and especially the properties of sign comprehension that are observed to be salient in natural settings. It is these more problematic aspects of interpretation that ultimately place the greatest demands on artificial intelligence research, at any rate, if it is going to support an understanding of the ways that human beings use real languages in real practice, or if it is ever going to supply a medium for modeling the ways that human beings develop an ability to produce and to understand real texts.

I am sensitive to the possibility that there are many features in the situation of the present inquiry, perhaps due solely to my description, that make it appear like an artificial, an implausible, or a specialized set of circumstances. I begin by discussing a number of these features, after which I argue that they are really quite typical of any situation where one has to interpret a problematic text in a problematic language. A text or a language is problematic, of course, only in relation to a prospective interpreter. To clarify this sense of the word problematic it helps to introduce the following definitions.

1. A "fully interpretive language" (FIL) is one whose attributes are fully filled out in all three directions of natural language use, to wit, along syntactic, semantic, and pragmatic dimensions.
2. A "fully interpretive grammar" (FIG), more commonly referred to as the "full grammar" of a language, is a body of knowledge that generates or specifies a FIL, incorporating the full details of its syntax, semantics, and pragmatics.
3. A "problematic text" is one that seems to make some sort of sense, but whose meaning, if any, is not entirely clear on first reading.
4. A "problematic language" is one whose "full grammar" is not yet available for articulation by the user in question, no matter how well the user is able to employ the language itself. It ought to be obvious that all "natural languages" are problematic for their customary users.
 As I stood by yon roofless tower, Where the wa'flow'r scents the dewy air, Where the houlet mourns in her ivy bower, And tells the midnight moon her care: — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]

One of the functions of the epitext that I am weaving through the main text of this discussion is to keep constantly before the mind the more problematic features of natural languages, to illustrate the diversity of their utilities, and to notice a few of the elaborative, figurative, and imaginative devices that are not so easily formalized.

It is true that poems and programs share a conscious definition, coming to their collective senses under the head of effective description. At least, it ought to be clear to the impartial observer that there is a close kinship between the words that do to engender action, that start it toward the hope of eventual success, and the words that fit a finite ambition, that point it toward the realms of eternal truth, and that this relation amounts to an accord that unites their intentions or a resonance that serves to bind their performance into a concerted whole, so I leave the reader to rede which is which and to judge on a case by case basis what the individual occasion demands.

It is also true that abstract category theory, in the ways that it affords a view of formal analogies, is largely a study of mathematical metaphors. But aside from all that, there is much else that mathematicians, poets, and programmers are bound to see alike and ought to share in common.

Under many natural circumstances, the only way to unravel the meaning of a problematic text is to place it in the field of influence of a FIL, typically as embodied in a variety of different interpreters, and to see how it is led to develop along the prevailing lines of interpretive force. In corresponding circumstances, approached in a complementary fashion, the only way to uncover the structure of a problematic language is to scatter a sample of signs and texts throughout its field of influence, and then to observe how these literal test particles are led to develop along interpretive lines, and if there is a coherent sensibility in force.

 The winds were laid, the air was still, The stars they shot along the sky, The tod was howling on the hill, And the distant-echoing glens reply. — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]

One of the abiding tasks of artificial intelligence research is to figure out how natural languages do what they do for the human mind. This task amounts to articulating the FILs that humans actually use, and thus to arrive at the fully interpretive grammars (FIGs) that generate these FILs, shaping their syntax, semantics, and pragmatics. The main tool that one has in this task is formalization, the process that devises formal models for the ongoing processes of interpretation.

Until one develops a battery of formal methods for exploring fields of interpretive influence and for tracing lines of interpretive force, one tends to be impelled by signs without understanding how or why one is moved by them, to wallow around in interpretive phenomena with little control over what develops, and to wander aimlessly through domains of apparent significance and evident meaning with no insight into their underlying structures and generative forms. Consequently, an attempt to avoid all formalization, though it appears at first sufficient to the gaining of experience, is not sufficient to the gaining of understanding, and therefore ultimately leads to the impoverishment of experience itself.

Unfortunately, there are equally pernicious tendencies that arise in the attempt to formalize experience and thus to arrive at formalized models. There is the tendency, in pursuing formalizations of a difficult subject, to settle on a premature formalization, that is, a narrowly circumscribed set of models, or an overly simplistic typology for addressing the topic, and then, in a vain attempt to avoid further difficulties by dictating to the subject how it ought to behave, to think that a partially successful formalization gives one the right to bar the subject from leaving the charmed circle swept out by its survey, or else to think that one can afford to ignore all aspects of the subject that do not fit within it. This temptation seems to arise on a recurring basis in the history of every formal science, being so well known from the dawn of awareness that its pattern is emblazoned in myth under the name of Procrustes.

 The burn, adown its hazelly path, Was rushing by the ruin'd wa', Hasting to join the sweeping Nith, Whase roaring seemed to rise and fa'. — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]

Generally speaking, formalizations constitute an indispensable utility in adapting the intellect to its environment and in helping it to build up relatively stable systems of organized knowledge. But it takes a force to make things fit, since the formal picture is partial to its own bias, and the intellectual image distorts the world as much as it adapts to it.

The violence that is involved in a formalization, that is, the degree of its departure from nature, is observed to become especially acute each time that a specialized community of inquirers succeeds in developing a fresh array of formal methods and formal models, and thereby acquires a standardized resource that appears to equip them with an expanded range of formal powers. For those inquirers, these are competencies whose winning is not easy and whose salve they do not wish to give up, as they think they might by thinking too much about the lineaments of its ligaments and the limitations of its liniments. Consequently, one finds that the following sort of situation typifies the state of formal inquiry: Against every conscious caution that the formalization is only partial and in spite of every conscientious concession that the object domain is vastly more complex that any representation can contain, the tendency persists, once a formalization is fixed, to treat it just as if it were already and always would be perfectly adequate to the object.

 The cauld blae North was streaming forth Her lights, wi hissing, eerie din: Athort the lift they start and shift, Like Fortune's favors, tint as win. — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]
 Now, looking over firth and fauld, Her horn the pale faced Cynthia rear'd, When lo! in form of minstrel auld A stern and stalwart ghaist appear'd. — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]
 And frae his harp sic strains did flow, Might rous'd the slumbering Dead to hear, But O, it was a tale of woe As ever met a Briton's ear! — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]
 He sang wi joy his former day, He, weeping, wail'd his latter times: But what he said — it was nae play! I winna ventur't in my rhymes. — Robert Burns, As I Stood by Yon Roofless Tower, [CPW, 570]

#### Recursions : Possible, Actual, Necessary

 Is there a whim-inspired fool, Owre fast for thought, owre hot for rule, Owre blate to seek, owre proud to snool? Let him draw near; And owre this grassy heap sing dool, And drap a tear. — Robert Burns, A Bard's Epitaph, [CPW, 220]

The purpose of a sign, for instance, a name, expression, program, or text, is to denote and possibly to describe an object, for instance, a thing, situation, mode of being, or activity in the world. In cases of practical interest, the object is usually very complex and the sign is usually very simple. Indeed, the intention of the whole descriptive enterprise is take objects as complex and as subtle as possible and to arrive at signs as simple and as concrete as the agent can conceive of fashioning to describe that object. Not surprisingly, the value of this exercise to the agent that carries it out is measured by the degree of difference in the apparent complexities of the object and the sign, or the proportion of success in this project is the measure of its value to the agent involved in it. In the cases of ultimate interest, the sorts of objects that the agent is charged to describe begin with something like the natural and social world itself, moves on to the natural and social language that avails itself to describe this world, and ends up with the natural and social mind that evolves in association with this language and with this world. In effect, a trialogue, a three way dialogue or a threefold dialectic.

When the reality to be described is infinitely more complex than the typically finite resources that an agent has to describe it, then any number of elliptic, multiple, and repeated uses of these resources are bound to occur, leading to the strategies of approximation, abstraction, and recursion, respectively. All of these techniques have in common the fact that a systematic ambiguity in the use of signs is introduced and tolerated, necessitating a new order of context sensitivity, discernment, intelligence, or just plain good sense in the conduct of interpretations. A systematic ambiguity or a controlled equivocation occurs when the same sign is used for many different things or when the same sign is used at many different stages of a process.

Although the elliptic strategy of approximation is tantamount to simply leaving off from the effort to describe a difficult object, in effect, throwing up one's hands in exasperation, exhaustion, supplication, or surrender, by this means hoping to escape from the self imposed part of the requirement to describe it more closely, and finally giving up the attempted description with the significance of the data already recorded, no matter how much the broken off approach falls short of its goal, the closely related strategies of abstraction and recursion are rather more persistent in their tries at describing the object.

 Is there a Bard of rustic song, Who, noteless, steals the crowds among, That weekly this area throng? O, pass not by! But, with a frater-feeling strong, Here, heave a sigh. — Robert Burns, A Bard's Epitaph, [CPW, 220]

In effect, so long as an agent sticks to the object and persists in the purpose of describing it / this kind of object, ... In other words, an agent is forced to resort to the stratagems of abstraction and recursion, where the same sign is used for many different objects and when the same sign is used to mark the progress of an activity at many different stages of its process, respectively. The underlying principle involved here is a kind of pragmatic pigeonhole principle.

 Is there a man, whose judgment clear Can others teach the course to steer, Yet runs, himself, life's mad career, Wild as the wave? — Here pause — and, thro the starting tear, Survey this grave. — Robert Burns, A Bard's Epitaph, [CPW, 220]

A resilient enough system of interpretation (RESOI), if driven to the point of distraction by the task of describing an inexhaustibly complex reality, makes several strategies available to its interpretive agent, either for preventing its being driven over the edge or for recovering from the inevitable lapses of attention that nevertheless happen to occur. The most salient of these strategies can be organized for discussion in the following manner:

Approximation. In resorting to approximation, one accepts the variety of natural bounds that apply to one's capacities for significant denotation, acknowledges the practical constraints that affect one's abilities for attending to detail and retaining exact records, and acts accordingly. This means recognizing the limitations of one's capacity for attention, recording the amounts that one can at the levels of accuracy that are feasible, and restricting one's intentions appropriately to capturing an aspect of one's object or representing a fraction of its reality.

Abstraction. In resorting to abstraction, one is trying to escape the limitations of a strict democracy in one's representations, otherwise known as the "one object, one sign" rule. Abstraction occurs when the same sign is used to refer to many different things, often conceived to form a class or a set of objects. In effect, abstraction introduces a common name or a general concept that denotes each individual object in a multitude of particular objects. Typically and most effectively, this comes about in recognition of a common attribute, a general feature, or a universal property that all of these objects share, giving the process of abstraction the beneficial side effect that the abstract sign can be newly re interpreted as referring to the abstract property in question.

Depending on the kinds of entities that are covered by an abstraction and the orders of logical complexity that are involved in this coverage, abstractions can be classified according to their domains of application and qualified according to their manners of construction and derivation. The next topics for discussion are two varieties of abstraction, called recursion and polymorphism, that are especially important for the purpose of building computational models of interpretation and that deserve special mention in the present inquiry.

 The poor inhabitant below Was quick to learn and wise to know, And keenly felt the friendly glow, And softer flame; But thoughtless follies laid him low, And stain'd his name! — Robert Burns, A Bard's Epitaph, [CPW, 220]

Recursion occurs when the same sign is used at different stages of a designated process, referring to different amounts of work to be done, marking the different amounts of work already done that establish the different settings of work going on, and often appearing at different levels of the agenda, charge, or mission that plots out this process. When a process is described by a text, that is, by a recorded agenda, outline, program, recipe, or script, then the recursion is typically reflected in the recursive sign's appearance at different structural levels of the text that serves to recapitulate or specify the process. For instance, a recursive sign can show up initially in the heading and then turn up at least one more time in the body of a text that codes a specification of a procedure, a text that formulates a definition of a function, or a text that constitutes a program, routine, or subprogram.

Polymorphism is a type of higher order abstraction that occurs when the same sign is used to denote elements of many different conceptual classes or objects of many distinct logical types. Comprehending the possible options calls for many alternative "conventions of intention", many heterogeneous "directions of connotation", and many splintered if still overlapping "moments of interpretation" to sort out the profusion of senses that is engendered. In the intermediate time frame, this type of diversity can appear to require a panoply of intellectual conceptions to organize the resulting multitude of meanings and to demand a variety of connotative planes to arrange their separate senses across, but it ultimately leads to a richer idea of the original aim or the intended object, as the potential for interpretation can be attributed to it.

 Reader, attend! whether thy soul Soars Fancy's flights beyond the pole, Or darkling grubs in this earthly hole, In low pursuit; Know, prudent, cautious, self control Is wisdom's root. — Robert Burns, A Bard's Epitaph, [CPW, 220]

One of the aims of this work as a whole is to explain the use of sign relations in the interpretation of complex texts, for instance, this sentence, this paragraph, this entire work, just to name a few of the most obvious examples among the many that are conceivable. As the text I produce to explain the pragmatic theory of sign relations is itself just a sign in a sign relation to which the theory is intended to apply, the encounter with self reference, in both the senses of a self referent text and a self referent writer, cannot be avoided. Among the questions that this encounter brings in its train are the issues of self indicating signs, texts, and interpreters, bringing the following topics to a head:

1. Indexical signs are signs that indicate their own interpretive context.
2. Reflexive signs are signs that indicate themselves or their issuer.
3. Recursive signs are signs that embody, enclose, or invoke themselves, that count themselves among their own parts or that include references to these parts within their own compositions, for instance, texts that incorporate references to their own headings, subtitles, or titles.

#### Reflectively Indexical Texts

 Now Robin lies in his last lair, He'll gabble rhyme, nor sing nae mair; Cauld poverty wi hungry stare, Nae mair shall fear him; Nor anxious fear, nor cankert care, E'er mair come near him. — Robert Burns, Elegy on the Death of Robert Ruisseaux, [CPW, 268]

A reflectively indexical text (RIT) is a text that refers to any aspect of its actual or intended context of interpretation (COI). With respect to a text, a COI is everything that is conceived to embody its prospects for communication, incorporating the dynamics to actuate the text along with the media to situate the text. For instance, a RIT can refer to any of the formal roles that play a part in actualizing the meaning of a text, in particular, it can refer to the roles of the agents that collaborate to bring its sense to life, in effect, the agents that work to animate it. A special case of a RIT, distinguished as a reflexively indexical text, is one that adverts to its issuer. Depending on whether its references to a COI are explicit or implicit, a RIT is called an ERIT or an IRIT, respectively. Because the same RIT can make many different references, explicit and implicit, to many different aspects of a contemplated COI, the associated attributions do not lead to mutually exclusive categories but merely to overlapping qualifications, any number of which a RIT can possess in parallel, inclusively and independently.

Aside from the usual arrays of messages that a text is meant to convey, a RIT has something to say about the communication situation where it finds itself engaged, where it happens to fall whether the possibility of such an occasion falls within its original intention or not, and where it summons agents to fall in line with its images of things and its patterns of action even if they fail to suit the occasions of their invocations. But more than that, a RIT can indicate the pragmatic setting where it has a call to be understood, where it is designed to evolve one or more clear meanings, and where it presses agents to render these meanings ever more effective in practice.

 To tell the truth, they seldom fash'd him, Except the moment that they crush'd him; For sune as chance or fate had hush'd 'em, Tho e'er sae short, Then wi a rhyme or sang he lash'd 'em, And thought it sport. — Robert Burns, Elegy on the Death of Robert Ruisseaux, [CPW, 268]
 Tho he was bred to kintra-wark, And counted was baith wight and stark Yet that was never Robin's mark To mak a man; But tell him, he was learn'd and clark, Ye roos'd him then! — Robert Burns, Elegy on the Death of Robert Ruisseaux, [CPW, 268]

#### The Discursive Universe

 Wee sleekit, cow'rin, tim'rous beastie, O, what a panic's in thy breastie! Thou need na start awa sae hasty, Wi bickering brattle! I wad be laith to rin an chase thee, Wi murdering pattle! — Robert Burns, To a Mouse, On Turning Her Up in Her Nest with the Plough, [CPW, 131]

This project began with the aim of articulating an aspect of intelligent activity, namely, the inquiry into inquiry that appears to be implied in the very ability to do inquiry, to learn from the impressions of passing experience, and to reason about their indications for future experience. Inspired by the enunciation of these high aims the work proceeds in a top down fashion, though of course the rubble of previous experience is always there to suggest the orders of material to expect at the bottom. This mode of investigation, when it works, amounts to a recursive form of conceptual analysis, starting from the barest conception of its aim, seeking the conditions necessary for the possibility of its actualization, trying to determine the functional components that allow it to operate in principle, undertaking to shore up the practical supports that permit it to prosper in reality, and working to alleviate the practical obstacles that impact on its implementation in adverse ways.

A particular agent does what appears to be necessary at each moment in a succession of moments in order to achieve a particular aim, and hopes that what appears to be necessary to an agent who follows a given path cannot be totally immaterial to what is actually necessary in general. The relationship between apparent necessity and actual necessity is the topic of another discussion later in this work, so I leave it till then. At this point, it only needs to be observed that an apparent necessity constitutes a real force on the agent who observes it, in other words, that it constrains the acts of the agent to whom it appears necessary. Given the freedom of intellect that comes from the reflective criticism of particular developments, a particular agent's particular inquiries are hopefully conceived in such a way as to work toward necessary truths.

 I'm truly sorry man's dominion Has broken Nature's social union, An justifies that ill opinion, Which makes thee startle At me, thy poor, earth born companion, An fellow mortal! — Robert Burns, To a Mouse, [CPW, 131]

Given the nature of particular agency, along with the circumstance that an inquiry must be carried out by a particular agent, an inquiry is apt to proceed in ways that are far from being absolutely necessary, and it is bound to wander on paths that fail to be optimal in the use of time. But this fact — the fact that many departures from necessity are likely to affect the progress of any particular inquiry, and the fact that such contingencies, deficiencies, and facticities are almost sure to apply to one's present inquiry — although its likelihood in general is frequently suspected by a reflective agent and its certainty in theory is probably apparent to a critical agent, its import is usually not clearly known, not in the detailed sense that its application to the moment in question is available to the agent who needs to act on it, and not in the pressing sense that its bearings on the consequences for experience are apparent to the agent who ought to be concerned about their subsequent effects. But the widespread suspicion that what appears to be necessary is not always actually and absolutely necessary, however much it is likely to verge on the truth, remains completely vague in that form, and it does not conjure up enough of an objection to deter action on what appears to be necessary, not unless a concrete alternative also appears.

In this way one is able to see the form of short term independence, the apparent indifference and the seeming lack of correlation that persists in the meantime, between actual necessities and apparent necessities. The apparent necessity continues to subsist as a factitious matter, no matter how grave it appears to the agent who falls within its orbit and no matter how much it constrains the circumstantial actions of the agent to whom it in fact appears necessary. A lack of actual necessity does not prevent an apparent necessity from continuing to appear just as if it were called for. Conversely, a lack of apparent necessity in no way impedes an actual necessity from continuing to rule the total situation. With all due respect to apparent necessities, the fact of their actual facticity is perfectly capable of holding true, however much these very conditions are able to constrain the actions of the particular agents to whom they appear necessary. Moreover, the factitious nature and the virtual force that are severally attributed to an apparent necessity are just as apparently independent of each other, at least, in medias res. The facticity of an apparent necessity continues to hold in fact, however forcefully it actually succeeds in compelling the activities of an agent. The force of an apparent necessity continues to stay in effect, in spite of its actual facticity, right up until the time when it no longer appears to be necessary.

 I doubt na, whyles, but thou may thieve; What then? poor beastie, thou maun live! A daimen icker in a thrave 'S a sma request; I'll get a blessin wi the lave, An never miss't! — Robert Burns, To a Mouse, [CPW, 132]

What I hope that my discussion of The LOS leads to is an inkling of the type of dialogue that is capable of taking place between a formal domain and the informal context in which it lives, the world in which it is born, continues to grow, and even forces to evolve along with its development, the setting at times in which it lies dormant, remaining restively inert for years or simply sleeping through the appointed phases of the night, the fold in which it is able to be reborn, to come to a new life, and to arise afresh. The form of this dialogue is one that suggests the name for itself of a discursion, a word that is coined to carry a wealth of various possibilities: a dialectic recursion or a recursive dialogue, a recursive analysis (RA) or a recursive excursion (RE), perhaps the very form of recursive inquiry (RI) that admits of its decomposition into one or another recursive undertaking (RU) and thereby maintains the very form of its own constitution. This array of acronyms serves to stake out a ready field of discursive research and exploration, one that is open in certain directions to unformalized possibilities of experience, in a sense or in essence, to its own future.

But the question remains whether sign-bearing agents can act, at least, as if they are able to be aware of their bearing as one component of a coherent, competent, and complete code of conduct, even a form of life. And the question continues how interpreters can acquire their faculties for the conscientious development and the deliberate elaboration of the factors that affect their own interpretive activities, in sum, how they can reflect on the factual contingencies that affect their own sign use, on the facticity of the circumstances that constrain these uses, and on the factors that determine the facility of the conditions that lead up to these uses, and then act on the results of all these reflections to make improvements in all these factors. In this way of broaching the subject of reflection, I am forced to drop it almost immediately, with the aim of starting afresh at another point and approaching the topic again, the next time from another direction.

 Thy wee bit housie, too, in ruin! Its silly wa's the win's are strewin! An naething, now, to big a new ane, O foggage green! An bleak December's win's ensuin, Baith snell an keen! — Robert Burns, To a Mouse, [CPW, 132]

At times one enters a state of mind that seems so rich in possibilities, teems with so many avenues of interesting departures, and unlocks such veins of unsuspected wealth in the world of ideas that one wants to be sure to revisit it again, in order to explore the rest of the thoughts that seem likely to unfold from its locus, its nexus, and its treasury. But the only way that one can be sure to return to anything like the same state of mind is to put reminders of it all about, at every other point that one later passes through and in the vicinity of every locus the neighborhood of which one is likely to visit. Now a state that one experiences at a former time is not always possible to experience again, but it may be possible to make nearby passes or to approach arbitrarily close to the essence of the exact experience at a host of future times. Then consider a manifold of possible states of mind as forming a space that possesses its conceivable extension. And so one gets these ideas: (1) of a manifold that is suffused with the idea of a manifold that is suffused just so, (2) of a manifold that is suffused with more or less accurate ideas of itself, and (3) of a manifold that is suffused with its own idea just far enough that it can serve to maintain the orbits of the agents that pass through it in suffusion with the very idea of doing so.

If the writer can din the reader into an awareness that the repetition of a word does not imply the repetition of a thought, that the repetition of a sign does not imply the repetition of any idea, that the repetition of a state does not mean its repetition forever, then this repetition serves its purpose, however close it verges on absurdity.

The discussion arrives at the question of signs and texts that signify, beyond their ostensible denotations and their obvious connotations, the characters of their authors, the features of their intended readers, and much more besides about the nature of their joint adventures, whatever their levels of participation in them, the processes of communication.

If the question of the interpreter that is signified by a sign reduces to the question of the interpretation that is signified by that sign, and if this reduces to the question of the interpretant that is signified by the sign, then one arrives at the circumstance of sign that relates to its interpretant along several paths.

"effective descriptions and finite texts" (EDAFTs)

 Thou saw the fields laid bare an waste, An weary winter comin fast, An cozie here, beneath the blast, Thou thought to dwell, Till crash! the cruel coulter past Out thro thy cell. — Robert Burns, To a Mouse, [CPW, 132]

At this juncture the discussion comes face to face with a type of text, many of whose signs are subject to different levels of interpretation. Besides denoting characters and creatures of legend and myth that form at first sight the subjects of the text, describing their features, and depicting their various adventures, they also appear to be amenable to recursive or self referent interpretations or to suggest an extra sense for themselves. Indeed, they seem designed to serve an added intention of their author, namely, to say something about the aims of the author, the attributes of the audience, whether hoped or feared, and the nature of the whole attempt to communicate.

Just to indicate the types of self reference that are being contemplated, it helps to introduce a number of informal definitions. Let any suitable set of entities {writer, sign, reader} be called a linkage of the sign in question, and let any suitable set of entities {writer, text, reader} be called a linkage of the text in question. In either of these uses, let the subset of entities {writer, reader} be called the link of that linkage, and let the elements of a link be called its ends or termini. At present, the situations of interest are those in which all of the signs in a text, at least, those that denote anything at all, are considered to share the very same link, which they all bear in common with their text. From now on, this condition is taken for granted unless it is otherwise expressly noted. Given a sign within a text, the union of their linkages is a set of entities {writer, sign, text, reader} that is useful to call a nocking of the sign. Together with the specification of a sign relation that suits a particular condition of interpretation, these constructs go toward defining a communication situation, an interpretive setting, or a pragmatic frame for the sign or the text in question.

Naturally, these constructions require a lot more information about the details of a given interpretation in a given situation in order to pin them down exactly, but this is enough to rough out their general ideas. Their main use in the current setting is simply to provide a ready way of talking about the properties of certain kinds of complex texts, as they are become subject to certain kinds of loopy, recursive, or self-referent interpretations.

If a sign within a text is interpreted as making any kind of denotative reference to its own nocking, namely, to the appropriate set of entities {writer, sign, text, reader}, its elements, or its properties, then it is useful to consider this sign and this text as being self referent in the broad sense that they refer to accessory or instrumental aspects of the pragmatic frame itself, and thus can be said to have an internal aim. This can happen whether or not a sign within a text denotes any object beyond its nocking, and thus can be said to have an external aim.

 That wee bit heap o leaves an stibble, Has cost thee monie a weary nibble! Now thou's turn'd out, for a' thy trouble, But house or hald, To thole the winter's sleety dribble, An cranreuch cauld! — Robert Burns, To a Mouse, [CPW, 132]

In the pragmatic theory of signs it is often said, “The question of the interpreter reduces to the question of the interpretant.” If this is true then it means that questions about the special interpreters that are designated to serve as the writer and the reader of a text are reducible to questions about the particular sign relations that independently and jointly define these two interpreters and their process of communication. The assumptions and the implications that are involved in this maxim are best explained by retracing the analysis that leads to this reduction, setting it out in the following stages:

In the pragmatic theory of signs it is often said, “The question of the interpreter reduces to the question of the interpretant.” If this is true then it means that questions about the special interpreters that are designated to serve as the writer and the reader of a text are reducible to questions about the particular sign relations that independently and jointly define these two interpreters and their process of communication. The assumptions and the implications that are involved in this maxim are best explained by retracing the analysis that leads to this reduction, setting it out in the following stages:

1. By way of setting up the question of the interpreter, it needs to be noted that it can be asked in any one of several modalities. These are commonly referred to under a variety of different names, for instance:

1. What may be: the "prospective" or the "imaginative";
also: the contingent, inquisitive, interrogative, optional, provisional, speculative, or "possible on some condition".

2. What is: the "descriptive" or the "indicative";
also: the actual, apparent, definite, empirical, existential, experiential, factual, phenomenal, or "evident at some time".

3. What must be: the "prescriptive" or the "imperative";
also: the injunctive, intentional, normative, obligatory, optative, prerequisite, or "necessary to some purpose".

It is important to recognize that these lists refer to modes of judgment, not the results of the judgments themselves. Accordingly, they conflate under single headings the particular issues that remain to be sorted out through the performance of the appropriate judgments, for instance, the difference between an apparent fact and a genuine fact. In general, it is a difficult question what sorts of relationships exist among these modalities and what sorts of orderings are logically or naturally the best for organizing them in the mind. Here, they are given in one of the possible types of logical ordering, based on the idea that a thing must be possible before it can become actual, and that it must become actual (at some point in time) in order to qualify as being necessary. That is, being necessary implies being actual at some time or another, and being actual implies being possible in the first place. This amounts to thinking that something must be added to a condition of possibility in order to achieve a state of actuality, and that something must be added to a state of actuality in order to acquire a status of necessity.

 But Mousie, thou art no thy lane, In proving foresight may be vain: The best laid schemes o mice an men Gang aft agley, An lea'e us nought but grief an pain, For promis'd joy! — Robert Burns, To a Mouse, [CPW, 132]

All of this notwithstanding, it needs to be recognized that other types of logical arrangement can be motivated on other grounds. For example, there are good reasons to think that all of one's notions of possibility are in fact abstracted from one's actual experiences, making actuality prior in some empirically natural sense to the predicates of possibility. Since a plausible heuristic organization is all that is needed for now, this is one of those questions that can be left open until a later time.

1. Taking this setting as sufficiently well understood and keeping these modalities of inquiry in mind, the analysis proper can begin. Any question about the character of the interpreter that is acting in a situation can be identified with a question about the nature of the process of interpretation that is taking place under the corresponding conditions.

2. Any question about the nature of the process of interpretation that is taking place can be identified with a question about the properties of the interpretant that follows on a given sign. This is a question about the interpretant that is associated with a sign, in one of several modalities and as contingent on the total context.

In summary: The question of the interpreter that is signified to act reduces to the question of the interpretation that is signified to occur, and thus to the question of the interpretant that is signified to follow the given sign under the given conditions. Expanding over the various modalities: The question of the interpreter reduces to the question of the interpretation that is determined, designed, or depicted to occur, and this in turn reduces to the question of the interpretant that is indicated, intended, or imagined to be associated with the given sign.

To follow this reduction in stages, the character of the interpreter that can be signified in some modality to be acting in a situation is identified with the nature of the process of interpretation that can be signified in that same modality to be taking place in that same situation, and this is the matter of the kind of interpretant that can be signified in that same modality to be following on the sign that is given in that same situation.

 Still thou art blest, compar'd wi me! The present only toucheth thee: But och! I backward cast my e'e, On prospects drear! An forward, tho I canna see, I guess an fear! — Robert Burns, To a Mouse, [CPW, 132]