Changes

Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)

Revision as of 00:32, 24 May 2007

1,131 bytes added , 00:32, 24 May 2007

markup

Line 111: Line 111:

The steps of this analysis will be annotated below by making use of the following conventions. Lower case letters denote phenomena, processes, or faculties under investigation. Upper case letters denote classes of the same sorts of entities. Special use is made of the following symbols: Y = genus of inquiry; y = generic inquiry; y0 = present inquiry. Compositions of "faculties" are indicated by concatenating their names, as f.g, and are posed in the sense that the right "applies to" the left. The notation "f >= g" indicates that f is greater than or equal to g in a decompositional series, in other words, f possesses g as a component. The coset notation F.G indicates a class of "faculties" of the form f.g, with f in F and g in G. Notations like "{?}", "{?, ?}", and so on, serve as proxies for unknown components and indicate tentative analyses of faculties in question.

−

====1.3.1 Initial Analysis of Inquiry : Allegro Aperto====

+

====1.3.1. Initial Analysis of Inquiry : Allegro Aperto====

If the faculty of inquiry is a coherent power, then it has an active or instrumental face, a passive or objective face, and a substantial body of connections between them. y = {?}.

Line 122: Line 122:

In accord with this plan, the body of this section is devoted to a discussion of formalization. y0 = y.y >= {d, f}{d, f} >= {f}{d}.

−

====1.3.2 Discussion of Discussion====

+

====1.3.2. Discussion of Discussion====

But first, I nearly skipped a step. Though it might present itself as an interruption, a topic so easy that I almost omitted it altogether deserves at least a passing notice. y0 = y.y >= {d, f}{d, f} >= {d}{d}.

Line 130: Line 130:

There's a catch here that applies to all living creatures: In order to keep talking one has to keep living. This brings discussion back to its role in inquiry, considered as an adaptation of living creatures designed to help them deal with their not so virtual environments. If discussion is constrained to the envelope of life and required to contribute to the trend of inquiry, instead of representing a kind of internal opposition, then it must be possible to tighten up the loose account and elevate the digressionary narrative into a properly directed inquiry. This brings an end to my initial discussion of "discussion".

−

====1.3.3 Discussion of Formalization : General Topics====

+

====1.3.3. Discussion of Formalization : General Topics====

Because this project makes constant use of formal models of phenomenal processes, it is appropriate at this point to introduce the understanding of formalization that I will use throughout this work and to preview a concrete example of its application.

−

=====1.3.3.1 A Formal Charge=====

+

=====1.3.3.1. A Formal Charge=====

An introduction to the topic of formalization, if proper, is obliged to begin informally. But it will be my constant practice to keep a formal eye on the whole proceedings. What this form of observation reveals must be kept silent for the most part at first, but I see no rule against sharing with the reader the general order of this watch:

Line 144: Line 144:

3. Ask yourself, with regard to each postulant faculty in the current account, explicitly charged or otherwise, whether you can imagine any recipe, any program, any rule of procedure for carrying out the form, if not the substance, of what it does, or an aspect thereof.

−

=====1.3.3.2 A Formalization of Formalization?=====

+

=====1.3.3.2. A Formalization of Formalization?=====

An immediate application of the above rules is presented here, in hopes of giving the reader a concrete illustration of their use in a ready example, but the issues raised can quickly diverge into yet another distracting digression, one not so easily brought under control as the discussion of discussion, but whose complexity probably approaches that of the entire task.

Line 156: Line 156:

The reader can follow this example with every concept that I mention in the explanation of formalization, and again in the larger investigation of inquiry, and be assured that it is has not often slipped my attention to at least venture the same, though a delimitation of each exploration in its present state of completion would be far too tedious and tenuous to escape expurgation.

−

=====1.3.3.3 A Formalization of Discussion?=====

+

=====1.3.3.3. A Formalization of Discussion?=====

The previous section took the concept of "formalization" as an example of a topic that a writer might try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader. In either case the formalization process, that aims to translate a concept from informal to formal discussion, is itself mediated by a form of discussion: (1) that interpreters conduct as a part of their ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue with a reader (hearer). In view of this, I see no harm in letting the concept of discussion be stretched to cover all attempted processes of formalization. F ? D.

Line 184: Line 184:

On several occasions, this discussion of inquiry will arrive at a form of "aesthetic deduction", in general terms, a piece of reasoning that ends with a design recommendation, in this case, where an analysis of the general purposes and interests of inquiry leads to the conclusion that a certain property of discussion is an admirable one, and that the quality in question forms an essential part of the implicit value system that is required to guide inquiry and make it what it is meant to be, a method for advancing toward desired forms of knowledge. After a collection of admirable qualities has been recognized as cohering together into a unity, it becomes natural to ask: What is the underlying reality that inheres in these qualities, and what are the logical relations that bind them together into the qualifications of inquiry and a definition of exactly what is desired for knowledge?

−

=====1.3.3.4 A Concept of Formalization=====

+

=====1.3.3.4. A Concept of Formalization=====

The concept of formalization is intended to cover the whole collection of activities that serve to build a relation between casual discussions, those that take place in the ordinary context of informal discourse, and formal discussions, those that make use of completely formalized models. To make a long story short, formalization is the narrative operation or active relation that construes the situational context in the form of a definite text. The end product that results from the formalization process is analogous to a snapshot or a candid picture, a relational or functional image that captures an aspect of the casual circumstances.

Line 190: Line 190:

Relations between casual and formal discussion are often treated in terms of a distinction between two languages, the "meta-language" and the "object language", linguistic systems that take complementary roles in filling out the discussion of interest. In the usual approach, issues of formalization are addressed by postulating a distinction between the meta-language, the descriptions and conceptions from ordinary language and technical discourse that can be used without being formalized, and the object language, the domain of structures and processes that can be studied as a completely formalized object.

−

=====1.3.3.5 A Formal Approach=====

+

=====1.3.3.5. A Formal Approach=====

I plan to approach the issue of formalization from a slightly different angle, proceeding through an analysis of the medium of interpretation and developing an effective conception of "interpretive frameworks" or "interpretive systems". This concept refers to any organized system of interpretive practice, ranging from those used in everyday speech, to the ones that inform technical discourse, to the kinds of completely formalized symbol systems that one can safely regard as mathematical objects. Depending on the degree of objectification that it possesses from one's point of view, the same system of conduct can be variously described as an interpretive framework (IF), interpretive system (IS), interpretive object (IO), or object system (OS). These terms are merely suggestive - no rigid form of classification is intended.

Line 212: Line 212:

From this angle of approach, let us try to view afresh the manner of drawing distinctions between various levels of formalization in language. Once again, I begin in the context of ordinary discussion, and if there is any distinction to be drawn between objective and instrumental languages then it must be possible to describe it within the frame of this informally discursive universe.

−

=====1.3.3.6 A Formal Development=====

+

=====1.3.3.6. A Formal Development=====

The point of view I take on the origin and development of formal models is that they arise with agents retracing structures that already exist in the context of informal activity, until gradually the most relevant and frequently reinforced patterns become emphasized and emboldened enough to continue their development as nearly autonomous styles, in brief, as "genres" growing out of a particular "paradigm".

Line 218: Line 218:

Taking the position that formal models develop within the framework of informal discussion, the questions that become important to ask of a prospective formal model are (1) whether it highlights the structure of its supporting context in a transparent form of emphasis and a relevant reinforcement of salient features, and (2) whether it reveals the active ingredients of its source materials in a critically reflective recapitulation or an analytically representative recipe, or (3) whether it insistently obscures what little fraction of its domain it manages to cover.

−

=====1.3.3.7 A Formal Persuasion=====

+

=====1.3.3.7. A Formal Persuasion=====

An interpretive system can be taken up with very little fanfare, since it does not enjoin one to declare undying allegiance to a particular point of view or to assign each piece of text in view to a sovereign territory, but only to entertain different points of view on the use of symbols. The chief design consideration for an interpretive system is that it must never function as a virus or addiction. Its suggestions must always be, initially and finally, purely optional adjunctions to whatever interpretive framework was already in place before it installed itself on the scene. Interpretive systems are not constituted in the faith that anything nameable will always be dependable, nor articulated in fixed principles that determine what must be doubted and what must not, but rest only in a form of self-knowledge that recognizes the doubts and beliefs that one actually has at each given moment.

Before this project is done I will need to have developed an analytic and computational theory of interpreters and interpretive frameworks. In the aspects of this theory that I can anticipate at this point, an interpreter or interpretive framework is exemplified by a collective activity of symbol-using practices like those that might be found embodied in a person, a community, or a culture. Each one forms a moderately free and independent perspective, with no objective rankings of supremacy in practice that all interpretive frameworks are likely to support at any foreseeable moment in their fields of view. Of course, each interpreter initially enters discussion operating as if its own perspective were "meta" in comparison to all the others, but a well-developed interpretive framework is likely to have acquired the notion and taken notice of the fact that this is not likely to be a universally shared opinion (USO).

−

====1.3.4 Discussion of Formalization : Concrete Examples====

+

====1.3.4. Discussion of Formalization : Concrete Examples====

The previous section outlined a variety of general issues surrounding the concept of formalization. The following section will plot the specific objectives of this project in constructing formal models of intellectual processes. In this section I wish to take a breather between these abstract discussions in order to give their main ideas a few points of contact with terra firma. To do this, I examine a selection of concrete examples, artificially constructed to approach the minimum levels of non-trivial complexity, that are intended to illustrate the kinds of mathematical objects I have in mind using as formal models.

−

=====1.3.4.1 Formal Models : A Sketch=====

+

=====1.3.4.1. Formal Models : A Sketch=====

To sketch the features of the modeling activity that are relevant to the immediate purpose: The modeler begins with a "phenomenon of interest" or a "process of interest" (POI) and relates it to a formal "model of interest" (MOI), the whole while working within a particular "interpretive framework" (IF) and relating the results from one "system of interpretation" (SOI) to another, or to a subsequent development of the same SOI.

Line 240: Line 240:

3. Finally, the IF's and the SOI's always remain partly out of sight, caught up in various stages of explicit notice between casual informality and partial formalization, with no guarantee or even much likelihood of a completely articulate formulation being forthcoming or even possible. Still, it is usually worth the effort to try lifting one edge or another of these frameworks and backdrops into the light, at least for a time.

−

=====1.3.4.2 Sign Relations : A Primer=====

+

=====1.3.4.2. Sign Relations : A Primer=====

To the extent that their structures and functions can be discussed at all, it is likely that all of the formal entities that are destined to develop in this approach to inquiry will be instances of a class of three-place relations called "sign relations". At any rate, all of the formal structures that I have examined so far in this area have turned out to be easily converted to or ultimately grounded in sign relations. This class of triadic relations constitutes the main study of the "pragmatic theory of signs", a branch of logical philosophy devoted to understanding all types of symbolic representation and communication.

Line 340: Line 340:

Therefore, my attention is directed mainly toward understanding the forms of correlation, coordination, and cooperation among the various components of sign relations that form the necessary conditions for carrying out coherent inquiries.

−

=====1.3.4.3 Semiotic Equivalence Relations=====

+

=====1.3.4.3. Semiotic Equivalence Relations=====

If one examines the sign relations L(A) and L(B) that are associated with the interpreters A and B, respectively, one observes that they have many contingent properties that are not possessed by sign relations in general. One nice property possessed by the sign relations L(A) and L(B) is that their connotative components ASI and BSI constitute a pair of equivalence relations on their common syntactic domain S = I. It is convenient to refer to such structures as "semiotic equivalence relations" (SER's) since they equate signs that mean the same thing to somebody. Each of the SER's, ASI, BSI ? S?I = S?S partitions the whole collection of signs into "semiotic equivalence classes" (SEC's). This makes for a strong form of representation in that the structure of the participants' common object domain is reflected or reconstructed, part for part, in the structure of each of their "semiotic partitions" (SEP's) of the syntactic domain.

Line 389: Line 389:

and the semiotic partition: {{"A", "u"}, {"B", "i"}}.

−

=====1.3.4.4 Graphical Representations=====

+

=====1.3.4.4. Graphical Representations=====

The dyadic components of sign relations can be given graph-theoretic representations, as "digraphs" (or "directed graphs"), that provide concise pictures of their structural and potential dynamic properties.

Line 412: Line 412:

The theme running through the last three subsections, that associates different interpreters and different aspects of interpretation with different sorts of relational structures on the same set of points, heralds a topic that will be developed extensively in the sequel.

−

=====1.3.4.5 Taking Stock=====

+

=====1.3.4.5. Taking Stock=====

So far, my discussion of the discussion between A and B, in the picture that it gives of sign relations and their connection to the imagined processes of interpretation and inquiry, can best be described as fragmentary. In the story of A and B, a sample of typical language use has been drawn from the context of informal discussion and partially formalized in the guise of two independent sign relations, but no unified conception of the commonly understood interpretive practices in such a situation has yet been drafted.

Line 422: Line 422:

The next few subsections will be concerned with the most problematic features of the A and B dialogue, especially with the sorts of difficulties that are clues to significant deficits in theory and technique, and that point out directions for future improvements.

−

=====1.3.4.6 The "Meta" Question=====

+

=====1.3.4.6. The "Meta" Question=====

There is one point of common contention that I finessed from play in my handling of the discussion between A and B, even though it lies in plain view on both their Tables. This is the troubling business, recalcitrant to analysis precisely because its operations race on so heedlessly ahead of thought and grind on so routinely beneath its notice, that concerns the placement of object languages within the frame of a meta-language.

Line 433: Line 433:

Sign relations themselves, like any real objects of discussion, are either too abstract or too concrete to reside in the medium of communication, but can only find themselves represented there. The tables and graphs that are used to represent sign relations are themselves complex signs, involving a step of denotation to reach the sign relation intended. The intricacies of this step demand interpretive agents who are able, over and above executing all the rudimentary steps of denotation, to orchestrate the requisite kinds of concerted steps. This performance in turn requires a whole array of techniques to match the connotations of complex signs and to test their alternative styles of representation for semiotic equivalence. Analogous to the ways that matrices represent linear transformations and that multiplication tables represent group operations, a large part of the usefulness of these complex signs comes from the fact that they are not just conventional symbols for their objects but iconic representations of their structure.

−

=====1.3.4.7 Iconic Signs=====

+

=====1.3.4.7. Iconic Signs=====

In the pragmatic theory of signs, an "icon" is a sign that accomplishes its representation, including the projects of denotation and connotation, by virtue of properties that it shares with its object. In the case of relational tables and graphs, interpreted as iconic representations or analogous expressions of logical and mathematical objects, the pivotal properties are formal and abstract in character. Since a uniform translation through any dimension (of sight, of sound, or imagination) does not affect the structural properties of a configuration of signs in relation to each other, this may help to explain how tables and graphs, in spite of their semantic shiftiness, can succeed in representing sign relations without essential distortion.

Line 450: Line 450:

One serious form of contamination can be traced to the accidental circumstance that A and B and I all use the same proper names for A and B. This renders it is impossible to tell, purely from the tokens that are being tendered, whether it is a formal or a casual transaction that forms the issue of the moment. It also means that a formalization of the writer's and the reader's accessory sign relations would have several portions that look identical to pieces of those Tables under formal review.

−

=====1.3.4.8 The Conflict of Interpretations=====

+

=====1.3.4.8. The Conflict of Interpretations=====

One discrepancy that needs to be documented can be observed in the conflict of interpretations between A and B, as reflected in the lack of congruity between their semiotic partitions of the syntactic domain. This is a problematic but realistic feature of the present example. That is, it represents a type of problem with the interpretation of pronouns (indexical signs or bound variables) that actually arises in practice when attempting to formalize the semantics of natural, logical, and programming languages. On this account, the deficiency resides with the present analysis, and the burden remains to clarify exactly what is going on here.

Line 456: Line 456:

Notice, however, that I have deliberately avoided dealing with indexical tokens in the usual ways, namely, by seeking to eliminate all semantic ambiguities from the initial formalization. Instead, I have preserved this aspect of interpretive discrepancy as one of the essential phenomena or inescapable facts in the realm of pragmatic semantics, tantamount to the irreducible nature of perspective diversity. I believe that the desired competence at this faculty of language will come, not from any strategy of substitution that constantly replenishes bound variables with their objective referents on every fixed occasion, but from a pattern of recognition that keeps indexical signs persistently attached to their interpreters of reference.

−

=====1.3.4.9 Indexical Signs=====

+

=====1.3.4.9. Indexical Signs=====

In the pragmatic theory of signs, an "index" is a sign that achieves its representation of an object by virtue of an actual connection with it. Though real and objective, however, the indexical connection can be purely incidental and even a bit accidental. Its effectiveness depends only on the fact that an object in actual existence has many properties, definitive and derivative, any number of which can serve as its signs. Indices of an object reside among its more tangential sorts of attributes, its accidental or accessory features, which are really the properties of some but not all points in the locus of its existential actualization.

Line 479: Line 479:

Therefore, I consider any supposed form of "ontological descent" to be, more likely, just one among many possible forms of "semantic descent", each one of which details a particular way to reformulate objects as signs of more determinate objects, and every one of which operates with respect to its assumed form of analysis or its tacit analytic framework.

−

=====1.3.4.10 Sundry Problems=====

+

=====1.3.4.10. Sundry Problems=====

There are moments in the development of an analytic discussion when a thing initially described as a single object under a single sign needs to be reformulated as a congeries extending over more determinate objects. If the usage of the original singular sign is preserved, as it often is, then the multitude of new instances that one comes to fathom beneath the old object's superficial appearance gradually serve to reconstitute the singular sign's denotation in the fashion of a plural reference.

Line 493: Line 493:

A related source of conceptual turbulence stems from the circumstance that, even though a certain aesthetic dynamics attracts the mind toward sign relational systems that are capable of reflecting on, commenting on, and thus "counter-rolling" their own behavior, it is still important to distinguish in every active instance the part of the system that is doing the discussing from the part of the system that is being discussed. To do this, interpreters need two things: (1) the senses to discern the essential tensions that typically prevail between the formal pole and the informal arena, and (2) the language to articulate, aside from their potential roles, the moment by moment placement of dynamic elements and systematic components with respect to this field of polarities.

−

=====1.3.4.11 Review & Prospect=====

+

=====1.3.4.11. Review & Prospect=====

What has been learned from the foregoing study of icons and indices? The import of this examination can be sized up in two stages, at first, by reflecting on the action of both the formal and the casual signs that were found to be operating in and around the discussion of A and B, and then, by taking up the lessons of this circumscribed arena as a paradigm for future investigation.

Line 504: Line 504:

Can this manner of recursively searching for explanation be established as well-founded? In order to organize the expanding circle of thoughts and the growing wealth of objects that are envisioned within its scheme, it helps to introduce a set of organizing conceptions. Doing this will be the business of the next four Subsections.

−

=====1.3.4.12 Objective Plans & Levels=====

+

=====1.3.4.12. Objective Plans & Levels=====

In accounting for the special characters of icons and indices that arose in previous discussions, it was necessary to open the domain of objects coming under formal consideration to include unspecified numbers of properties and instances of whatever objects were initially set down. This is a general phenomenon, affecting every motion toward explanation whether pursued by analytic or synthetic means. What it calls for in practice is a way of organizing growing domains of objects, without having to specify in advance all the objects there are.

Line 556: Line 556:

In setting out the preceding characterization, I have reiterated what is likely to seem like an anthropomorphism, prefacing each requirement of the candidate OM with the qualification "it can say". This is done in order to emphasize that an OM's command of a share of its OG is partly a function of the interpretive effability that it brings to bear on the object domain and partly a matter of the expressive power that it is able to dictate over its own development.

−

=====1.3.4.13 Formalization of OF : Objective Levels=====

+

=====1.3.4.13. Formalization of OF : Objective Levels=====

The three levels of objective detail to be discussed are referred to as the objective "framework", "genre", and "motive" that one finds actively involved in organizing, guiding, and regulating a particular inquiry.

Line 695: Line 695:

Some readings of the staging relations are tantamount to statements of (a possibly higher order) model theory. For example, the predicate P : J -> B = {0, 1}, defined by P(j) <=> "j proposes x an instance of y", is a proposition that applies to a domain of propositions, or elements with the evidentiary import of propositions, and its models are therefore conceived to be certain propositional entities in J. And yet, all of these expressions are just elaborate ways of stating the underlying assertion which says that there exists a triple ‹j, x, y› in the genre G(:<).

−

=====1.3.4.14 Application of OF : Generic Level=====

+

=====1.3.4.14. Application of OF : Generic Level=====

Given an ontological framework that can provide multiple perspectives and moving platforms for dealing with object structure, in other words, that can organize diverse hierarchies and developing orders of objects, attention can now return to the discussion of sign relations as models of intellectual processes.

Line 810: Line 810:

This appears to suggest that icons and their objects are icons of each other, and that indices and their objects are indices of each other. Are the results of these symbolic manipulations really to be trusted? Given that there is no mention of the interpretive agent to whom these sign relations are supposed to appear, one might well suspect that these results can only amount to approximate truths or potential verities.

−

=====1.3.4.15 Application of OF : Motive Level=====

+

=====1.3.4.15. Application of OF : Motive Level=====

Now that an adequate variety of formal tools have been set in order and the workspace afforded by an objective framework has been rendered reasonably clear, the structural theory of sign relations can be pursued with greater precision. In support of this aim, the concept of an objective genre and the particular example provided by OG (Prop, Inst) have served to rough out the basic shapes of the more refined analytic instruments to be developed in this subsection.

Line 867: Line 867:

In the discussion of the dialogue between A and B, it was allowed that the same signs "A" and "B" could reference the different categories of things they name with a deliberate duality and a systematic ambiguity. Used informally as a part of the peripheral discussion, they indicate the entirety of the sign relations themselves. Used formally within the focal dialogue, they denote the objects of two particular sign relations. In just this way, or an elaboration of it, the signs "j" and "k" can have their meanings extended to encompass both the objective motifs (OM's) that inform and regulate experience and the object experiences (OE's) that fill out and substantiate their forms.

−

=====1.3.4.16 The Integration of Frameworks=====

+

=====1.3.4.16. The Integration of Frameworks=====

A large number of the problems arising in this work have to do with the integration of different interpretive frameworks over a common objective basis, or the prospective bases provided by shared objectives. The main concern of this project continues to be the integration of dynamic and symbolic frameworks for understanding intelligent systems, concentrating on the kinds of interpretive agents that are capable of being involved in inquiry.

Line 889: Line 889:

The integration of model-theoretic and proof-theoretic aspects of "physical symbol systems", besides being closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant to the job of integrating dynamic and symbolic frameworks for intelligent systems. This is so because the search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where the mathematical materials made available for modeling are further constrained by system-theoretic principles, like being able to say what the states are and how the transitions are determined.

−

=====1.3.4.17 Recapitulation : A Brush with Symbols=====

+

=====1.3.4.17. Recapitulation : A Brush with Symbols=====

A common goal of work in artificial intelligence and cognitive simulation is to understand how is it possible for intelligent life to evolve from elements available in the primordial sea. Simply put, the question is: "What's in the brine that ink may character?"

Line 925: Line 925:

When the IF and the OF sketched here have been developed far enough, I hope to tell wherein and whereof a sign is able, by its very character, to address itself to a purpose, one determined by its objective nature and determining, in a measure, that of its intended interpreter, to the extent that it makes the other wiser than the other would otherwise be.

−

~~<pre>~~

+

=====1.3.4.18. C'est Moi=====

−

1.3.4.18 C'est Moi

+

From the emblem unfurled on a tapestry to tease out the working of its loom and spindle, a charge to bind these frameworks together is drawn by necessity from a single request: "To whom is the sign addressed?" The easy, all too easy answer comes "To whom it may concern", but this works more to put off the question than it acts as a genuine response. To say that a sign relation is intended for the use of its interpreter, unless one has ready an independent account of that agent's conduct, only rephrases the initial question about the end of interpretation.

+

The interpreter is an agency depicted over and above the sign relation, but in a very real sense it is simply identical with the whole of it. And so one is led to examine the relationship between the interpreter and the interpretant, the element falling within the sign relation to which the sign in actuality tends. The catch is that the whole of the intended sign relation is seldom known from the beginning of inquiry, and so the aimed for interpretant is often just as unknown as the rest.

+

These eventualities call for the elaboration of interpretive and objective frameworks in which not just the specious but the speculative purpose of a sign can be contemplated, permitting extensions of the initial data, through error and retrial, to satisfy emergent and recurring questions.

+

At last, even with the needed frameworks only partly shored up, I can finally ravel up and tighten one thread of this rambling investigation. All this time, steadily rising to answer the challenge about the identity of the interpreter, "Who's there?", and the role of the interpretant, "Stand and unfold yourself", has been the ready and abiding state of a certain system of interpretation, developing its character and gradually evolving its meaning through a series of imputations and extensions. Namely, the MOI (the SOI experienced as an object) can answer for the interpreter, to whatever extent that conduct can be formalized, and the IM (the SOI experienced in action, in statu nascendi) can serve as a proxy for the momentary thrust of interpretive dynamics, to whatever degree that process can be explicated.

+

To put a finer point on this result I can do no better at this stage of discussion than to recount the "metaphorical argument" that Peirce often used to illustrate the same conclusion.

−

I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term - or one which has become identified with it, - in short, has an interpretant.

+

−

Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. ... A thing cannot stand for something without standing to something for that something. Now, what is this that a word stands to? Is it a person?

+

−

We usually say that the word homme stands to a Frenchman for man. It would be a little more precise to say that it stands to the Frenchman's mind - to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what image, what remembrance? Plainly, the one which is the mental equivalent of the word homme - in short, its interpretant. Whatever a word addresses then or stands to, is its interpretant or identified symbol. ...

+

I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term - or one which has become identified with it, - in short, has an interpretant.

−

The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand to something, every symbol - every word and every conception - must have an interpretant - or what is the same thing, must have information or implication. (Peirce, CE 1, 466-467).

+

Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. ... A thing cannot stand for something without standing to something for that something. Now, what is this that a word stands to? Is it a person?

+

We usually say that the word homme stands to a Frenchman for man. It would be a little more precise to say that it stands to the Frenchman's mind - to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what image, what remembrance? Plainly, the one which is the mental equivalent of the word homme - in short, its interpretant. Whatever a word addresses then or stands to, is its interpretant or identified symbol. ...

+

The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand to something, every symbol - every word and every conception - must have an interpretant - or what is the same thing, must have information or implication. (Peirce, CE 1, 466-467).

+

</blockquote>

+

It will take a while to develop the wealth of information that a suitably perspicacious and persistent IF would find implicit in this unassuming homily. The main innovations that this project can hope to add to the story are as follows:

+

1. To prescribe a context of effective systems theory (C'EST), one that can provide for the computational formalization of each intuitively given interpreter as a determinate model of interpretation (MOI). An appropriate set of concepts and methods would deal with the generic constitutions of interpreters, converting paraphrastic and periphrastic descriptions of their interpretive practice into relatively complete and concrete specifications of sign relations.

+

2. To prepare a fully dynamic basis for actualizing interpretants. This means that an interpretant addressed by the interpretation of a sign would not be left in the form of a detached token or abstract memory image to be processed by a hypothetical but largely nondescript interpreter, but realized as a definite type of state configuration in a qualitative dynamic system. To fathom what should be the symbolic analogue of a "state with momentum" has presented this project with difficulties both conceptual and terminological. So far in this project, I have attempted to approach the character of an active sign-theoretic state in terms of an "interpretive moment" (IM), "information state" (IS), "attended token" (AT), "situation of use" (SOU), or "instance of use" (IOU). A successful concept would capture the transient dispositions that drive interpreters to engage in specific forms of inquiry, defining their ongoing state of uncertainty with regard to objects and questions of immediate concern.

−

1.3.4.19 Entr'acte

+

=====1.3.4.19. Entr'acte=====

+

Have I pointed at this problem from enough different directions to convey an idea of its location and extent? Here is one more variation on the theme. I believe that our theoretical empire is bare in spots. There does not exist yet in the field a suitably comprehensive concept of a dynamic system moving through a variable state of information. This conceptual gap apparently forces investigators to focus on one aspect or the other, on the dynamic bearing or the information borne, but leaves their studies unable to integrate the several perspectives into a full-dimensioned picture of the evolving knowledge system.

+

It is always possible that the dual aspects of transformation and information are conceptually complementary and even non-orientable. That is, there may be no way to arrange our mental apparatus to grasp both sides at the same time, and the whole appearance that there are two sides may be an illusion of overly local and myopic perspectives. However, none of this should be taken for granted without proof.

+

Whatever the case, to constantly focus on the restricted aspects of dynamics adequately covered by currently available concepts leads one to ignore the growing body of symbolic knowledge that the states of systems potentially carry. Conversely, to leap from the relatively secure grounds of physically based dynamics into the briar patch of formally defined symbol systems often marks the last time that one has sufficient footing on the dynamic landscape to contemplate any form of overarching law, or any rule to prospectively govern the evolution of reflective knowledge. This is one of the reasons I continue to strive after the key ideas here. If straw is all that one has in reach, then ships and shelters will have to be built from straw.

−

1.3.5 Discussion of Formalization: Specific Objects

+

====1.3.5. Discussion of Formalization : Specific Objects====

+

"Knowledge" is a referring back: in its essence a regressus in infinitum. That which comes to a standstill (at a supposed causa prima, at something unconditioned, etc.) is laziness, weariness --

(Nietzsche, The Will to Power S575, 309).

+

</blockquote>

+

With this preamble, I return to develop my own account of formalization, with special attention to the kind of step that leads from the inchoate chaos of casual discourse to a well-founded discussion of formal models. A formalization step, of the incipient kind being considered here, has the peculiar property that one can say with some definiteness where it ends, since it leads precisely to a well-defined formal model, but not with any definiteness where it begins. Any attempt to trace the steps of formalization backward toward their ultimate beginnings can lead to an interminable multiplicity of open-ended explorations. In view of these circumstances, let me limit my attention to the frame of the present inquiry and try to sum up what brings me to this point.

+

I ask whether it is possible to reason about inquiry in a way that leads to a productive end. I pose this question as an inquiry into inquiry, and I use the formula "y0 = y·y" to express the relationship between the present inquiry, y0, and a generic inquiry, y. Then I propose a couple of components of inquiry, expressed in the form "y >= {d, f}", that appear to be worth investigating. Applying these components to each other, as must be done in the present inquiry, I am led to the current discussion of formalization, y0 = y·y >= f·d.

+

There is already much to question here. At least, so many repetitions of the same mysterious formula are bound to lead the reader to question its meaning.

+

1. The notion of a "generic inquiry" is ambiguous. Its meaning in practice depends on whether this descriptive term is interpreted literally or merely as a figure of speech. In the literal case, the name "y" denotes a particular inquiry, y ? Y, one that is assumed to be plenipotential or prototypical in a yet to be specified way. In the figurative case, the name "y" is simply a variable that ranges over a collection Y of nominally conceivable inquiries.

+

2. On first reading, the recipe "y0 = y·y" appears to specify that the present inquiry is constituted by taking everything denoted by the most general concept of inquiry that the present inquirer can imagine and inquiring into it by means of the most general capacity for inquiry that this same inquirer can muster.

+

3. Given the formula "y0 = y·y", the subordination "y >= {d, f}", and the successive containments "F ? M ? D", the y that looks into y is not restricted to examining y's immediate subordinates, d and f, but it can investigate any feature of y's overall context, whether objective, syntactic, interpretive, whether definitive or incidental, and finally it can question any supporting claim of the discussion. Moreover, the question y is not limited to the particular claims that are being made here, but applies to the abstract relations and the general notions that are invoked in making them. Among the many kinds of inquiry that suggest themselves, there are the following possibilities:

+

a. Inquiry into propositions about application and equality.

Start with the formula "y0 = y·y" itself.

+

b. Inquiry into application (.).

+

c. Inquiry into equality (=).

+

d. Inquiry into indices (e.g. 0).

+

e. Inquiry into terms, namely, constants and variables.

+

What are the functions of "y" and "y0" in this respect?

+

f. Inquiry into decomposition or subordination (>=).

+

g. Inquiry into containment or inclusion. In particular, examine the claim "F ? M ? D" which conditions the chances that a formalization has an object, the degree to which a formalization can be carried out by means of a discussion, and the extent to which an object of formalization can be conveyed by a form of discussion.

+

If inquiry begins in doubt, then inquiry into inquiry begins in doubt about doubt. All things considered, the formula "y0 = y·y" has to be taken as the first attempt at a description of the problem, a hypothesis about the nature of inquiry, or an image that is tossed out by way of getting an initial fix on the object in question. Everything in this account so far, and everything else that I am likely to add, can only be reckoned as hypothesis, whose accuracy, pertinence, and usefulness can be tested, judged, and redeemed only after the fact of proposing it and after the facts to which it refers have themselves been gathered up.

A number of problems present themselves due to the context in which the present inquiry is aimed to present itself. The hypothesis that suggests itself to one person, as worth exploring at a particular time, does not always present itself to another person as worth exploring at the same time, or even necessarily to the same person at another time. In a community of inquiry that extends beyond an isolated person and in a process of inquiry that extends beyond a singular moment in time, it is therefore necessary to consider the nature of the communication process that the discussion of inquiry in general and the discussion of formalization in particular need to invoke for their ultimate utility.

+

Solitude and solipsism are no solution to the problems of community and communication, since even an isolated individual, if ever there was, is, or comes to be such a thing, has to maintain the lines of communication that are required to integrate past, present, and prospective selves - in other words, translating everything into present terms, the parts of one's actually present self that involve actual experiences and present observations, present expectations as reflective of actual memories, and present intentions as reflective of actual hopes. So the dialogue that one holds with oneself is every bit as problematic as the dialogue that one enters with others. Others only surprise one in other ways than one ordinarily surprises oneself.

+

I recognize inquiry as beginning with a "surprising phenomenon" or a "problematic situation", more briefly described as a "surprise" or a "problem", respectively. These are the types of moments that try our souls, the instances of events that instigate inquiry as an effort to achieve their own resolution. Surprises and problems are experienced as afflicted with an irritating uncertainty or a compelling difficulty, one that calls for a response on the part of the agent in question:

+

1. A "surprise" calls for an explanation to resolve the uncertainty that is present in it. This uncertainty is associated with a difference between observations and expectations.

+

2. A "problem" calls for a plan of action to resolve the difficulty that is present in it. This difficulty is associated with a difference between observations and intentions.

To express this diversity in a unified formula: Both types of inquiry begin with a "delta", a compact term that admits of expansion as a debt, a difference, a difficulty, a discrepancy, a dispersion, a distribution, a doubt, a duplicity, or a duty.

Expressed another way, inquiry begins with a doubt about one's object, whether this means what is true of a case, an object, or a world, what to do about reaching a goal, or whether the hoped-for goal is really good for oneself - with all that these questions lead to in essence, in deed, or in fact.

+

Perhaps there is an inexhaustible reality that issues in these apparent mysteries and recurrent crises, but, by the time I say this much, I am already indulging in a finite image, a hypothesis about what is going on. If nothing else, then, one finds again the familiar pattern, where the formative relation between the informal and the formal merely serves to remind one anew of the relation between the infinite and the finite.

−

1.3.5.1 The Will to Form

+

=====1.3.5.1. The Will to Form=====

+

The power of form, the will to give form to oneself. "Happiness" admitted as a goal. Much strength and energy behind the emphasis on forms. The delight in looking at a life that seems so easy. - To the French, the Greeks looked like children.

(Nietzsche, The Will to Power S94, 58).

+

</blockquote>

+

Let me see if can summarize as quickly as possible the problem that I see before me. Each time that I try to express my experience, to lend it a form that others can recognize, to put it in a shape that I myself can later recall, or to store it in a state that allows me the chance of its re-experience, I generate an image of the way things are, or at least a description of how things seem to me. I call this process "reflection", since it fabricates an image in a medium of signs that reflects an aspect of experience. Often this experience can be said to be "of" - what? - something that exists or persists at least partially outside the immediate experience, some action, event, or object that is imagined to inform the present experience, or perhaps some conduct of one's own that obtrudes for a moment into the world of others and meets with a reaction there. In all of these cases, where the experience is everted to refer to an object and becomes the attribute of something with an external aspect, something that is thus supposed to be a prior cause of the experience, the reflection on experience doubles as a reflection on that conduct, performance, or transaction that the experience is an experience "of". In short, if the experience has an eversion that makes it of an object, then its reflection is again a reflection that is also of this object.

+

Just at the point where one threatens to become lost in the morass of words for describing experience and the nuances of their interpretation, one can adopt a formal perspective, and realize that the relation among objects, experiences, and reflective images is formally analogous to the relation among objects, signs, and interpretant signs that is covered by the pragmatic theory of signs. One still has the problem: How are the expressions of experience everted to form the exterior faces of extended objects and exploited to embed them in their external circumstances, and no matter whether this object with an outer face is oneself or another? Here, one needs to understand that expressions of experience include the original experiences themselves, at least, to the extent that they permit themselves to be recognized and reflected in ongoing experience. But now, from the formal point of view, "how" means only: To describe the formal conditions of a formal possibility.

−

1.3.5.2 The Forms of Reasoning

+

=====1.3.5.2. The Forms of Reasoning=====

+

The most valuable insights are arrived at last; but the most valuable insights are methods.

(Nietzsche, The Will to Power S469, 261).

+

</blockquote>

+

A certain arbitrariness has to be faced in the terms that one uses to talk about reasoning, to split it up into different parts and to sort it out into different types. It is like the arbitrary choice that one makes in assigning the midpoint of an interval to the subintervals on its sides. In setting out the forms of a nomenclature, in fitting the schemes of my terminology to the territory that it disturbs in the process of mapping, I cannot avoid making arbitrary choices, but I can aim for a strategy that is flexible enough to recognize its own alternatives and to accommodate the other options that lie within their scope.

If I make the mark of deduction the fact that it reduces the number of terms, as it moves from the grounds to the end of an argument, then I am due to devise a name for the process that augments the number of terms, and thus prepares the grounds for any account of experience.

+

What name hints at the many ways that signs arise in regard to things? What name covers the manifest ways that a map takes over its territory? What name fits this naming of names, these proceedings that inaugurate a sign in the first place, that duly install it on the office of a term? What name suits all the actions of addition, annexation, incursion, and invention that instigate the initial bearing of signs on an object domain? In the interests of a "maximal analytic precision" (MAP), it is fitting that I should try to sharpen this notion to the point where it applies purely to a simple act, that of entering a new term on the lists, in effect, of enlisting a new term to the ongoing account of experience. Thus, let me style this process as "adduction" or "production", in spite of the fact that the aim of precision is partially blunted by the circumstance that these words have well-worn uses in other contexts. In this way, I can isolate to some degree the singular step of adding a term, leaving it to a later point to distinguish the role that it plays in an argument.

+

As it stands, the words "adduction" and "production" could apply to the arbitrary addition of terms to a discussion, whether or not these terms participate in valid forms of argument or contribute to their mediation. Although there are a number of auxiliary terms, like "factorization", "mediation", or "resolution", that can help to pin down these meanings, it is also useful to have a word that can convey the exact sense meant. Therefore, I coin the term "obduction" to suggest the type of reasoning process that is opposite or converse to deduction and that introduces a middle term "in the way" as it passes from a subject to a predicate.

Consider the adjunction to one's vocabulary that is comprised of these three words: "adduction", "production", "obduction". In particular, how do they appear in the light of their mutual applications to each other and especially with respect to their own reflexivities? Notice that the terms "adduction" and "production" apply to the ways that all three terms enter this general discussion, but that "obduction" applies only to their introduction only in specific contexts of argument.

+

Another dimension of variation that needs to be noted among these different types of processes is their status with regard to determimism. Given the ordinary case of a well-formed syllogism, deduction is a fully deterministic process, since the middle term to be eliminated is clearly marked by its appearance in a pair of premisses. But if one is given nothing but the fact that forms this conclusion, or starts with a fact that is barely suspected to be the conclusion of a possible deduction, then there are many other middle terms and many other premisses that might be construed to result in this fact. Therefore, adduction and production, for all their uncontrolled generality, but even obduction, in spite of its specificity, cannot be treated as deterministic processes. Only in degenerate cases, where the number of terms in a discussion is extremely limited, or where the availability of middle terms is otherwise restricted, can it happen that these processes become deterministic.

−

1.3.5.3 A Fork in the Road

+

=====1.3.5.3. A Fork in the Road=====

+

On "logical semblance" - The concepts "individual" and "species" equally false and merely apparent. "Species" expresses only the fact that an abundance of similar creatures appear at the same time and that the tempo of their further growth and change is for a long time slowed down, so actual small continuations and increases are not very much noticed (- a phase of evolution in which the evolution is not visible, so an equilibrium seems to have been attained, making possible the false notion that a goal has been attained - and that evolution has a goal -).

(Nietzsche, The Will to Power S521, 282).

+

</blockquote>

+

It is worth trying to discover, as I currently am, how many properties of inquiry can be derived from the simple fact that it needs to be able to apply to itself. I find three main ways to approach this issue, the problem of inquiry's self-application, or the question of its reflexivity:

+

1. One way attempts to continue the derivation in the manner of a necessary deduction, perhaps by reasoning in the following vein: If self-application is a property of inquiry, then it is sensible to inquire into the concept of application that makes this conceivable, and not just conceivable, but potentially fruitful.

+

2. Another way breaks off the attempt at a deductive development and puts forth a full-scale model of inquiry, one that has enough plausibility to be probated in the court of experience and enough specificity to be tested in the context of self-application.

+

3. The last way is a bit ambivalent in its indications, seeking as it does both the original unity and the ultimate synthesis at one and the same time. Perhaps it goes toward reversing the steps that lead up to this juncture, marking it down as an impasse, chalking it up as a learning experience, or admitting the failure of the imagined distinction to make a difference in reality. Whether this form of egress is interpreted as a backtracking correction or as a leaping forward to the next level of integration, it serves to erase the distinction between demonstration and exploration.

+

Without a clear sense of how many properties of inquiry are necessary consequences of its self-application and how many are merely accessory to it, or even whether some contradiction still lies lurking within the notion of reflexivity, I have no choice but to follow all three lines of inquiry wherever they lead, keeping an eye out for the synchronicities, the constructive collusions and the destructive collisions that may happen to occur among them.

+

The fictions that one introduces to shore up a shaky account of experience can often be discharged at a later stage of development, gradually replacing them with primitive elements of less and less dubious characters. Hypostases and hypotheses, the creative terms and the inventive propositions that one invokes to account for otherwise ineffable experiences, are tokens that are subject to a later account. Under recurring examination, many such tokens are found to be ciphers, marks that no one will miss if they come to be cancelled out altogether. The symbolic currencies that tend to survive lend themselves to being exchanged for stronger and more settled constructions, in other words, for concrete definitions and explicit demonstrations, gradually leading to primitive elements of more and more durable utilities.

−

1.3.5.4 A Forged Bond

+

−

The form counts as something enduring and therefore more valuable;

+

=====1.3.5.4. A Forged Bond=====

−

but the form has merely been invented by us; and however often "the same form is attained", it does not mean that it is the same form -

+

−

what appears is always something new, and it is only we, who are always comparing, who include the new, to the extent that it is similar to the old, in the unity of the "form". As if a type should be attained and, as it were, was intended by and inherent in the process of formation.

+

+

The form counts as something enduring and therefore more valuable; but the form has merely been invented by us; and however often "the same form is attained", it does not mean that it is the same form - what appears is always something new, and it is only we, who are always comparing, who include the new, to the extent that it is similar to the old, in the unity of the "form". As if a type should be attained and, as it were, was intended by and inherent in the process of formation.

(Nietzsche, The Will to Power S521, 282).

+

</blockquote>

+

A unity can be forged among the methods by noticing the following connections among them. All the while that one proceeds deductively, the primitive elements, the definitions and the axioms, must still be introduced hypothetically, notwithstanding the support they get from common sense and widespread assent. And the whole symbolic system that is constructed through hypothesis and deduction must still be tested in experience to see if it serves any purpose to maintain it.

−

1.3.5.5 A Formal Account

+

=====1.3.5.5. A Formal Account=====

+

Form, species, law, idea, purpose - in all these cases the same error is made of giving a false reality to a fiction, as if events were in some way obedient to something - an artificial distinction is made in respect of events between that which acts and that toward which the act is directed (but this "which" and this "toward" are only posited in obedience to our metaphysical-logical dogmatism: they are not "facts").

(Nietzsche, The Will to Power S521, 282).

+

</blockquote>

+

In this section I consider the step of formalization that takes discussion from a large scale informal inquiry to a well-defined formal inquiry, establishing a relation between the implicit context and the explicit text.

+

In this project, formalization is used to produce formal models that represent relevant features of a phenomenon or process of interest. Thus, the formal model is what constitutes the image of formalization.

+

The role of formalization splits into two different cases depending on the intended use of the formal model. When the phenomenon of interest is external to the agent that is carrying out the formalization, then the model of that phenomenon can be developed without doing significant reflection on the formalization process itself. This is usually a more straightforward operation, since it avails itself of automatic competencies that are not themselves in question. However, ...

In a recursive context, a principal benefit of the formalization step is to find constituents of inquiry with reduced complexities, drawing attention from the context of informal inquiry, whose stock of questions may not be grasped well enough to ever be fruitful and the scope of whose questions may not be focused well enough to ever see an answer, and concentrating effort in an arena of formalized inquiry, where the questions are posed well enough to have some hope of bearing productive answers in a finite time.

−

1.3.5.6 Analogs, Icons, Models, Surrogates

+

=====1.3.5.6. Analogs, Icons, Models, Surrogates=====

+

One should not understand this compulsion to construct concepts, species, forms, purposes, laws ("a world of identical cases") as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible: - we thereby create a world which is calculable, simplified, comprehensible, etc., for us.

(Nietzsche, The Will to Power S521, 282).

+

</blockquote>

+

This project makes pivotal use of certain formal models to represent the conceived structure in a phenomenon of interest. For my purposes, the phenomenon of interest is typically a process of interpretation (POI) or a process of inquiry (POI), two nominal species of process that will turn out to evolve from different points of view on the same form of conduct.

+

Commonly, a process of interest presents itself as the trajectory that an agent describes through an extended space of configurations. The work of conceptualization and formalization is to represent this process as a conceptual object in terms of a formal model. Depending on the point of view that is taken from moment to moment in this work, the formal model of interest may be cast either as a model of interpretation (MOI) or as a model of inquiry (MOI). As might be guessed, it will turn out that both descriptions refer essentially to the same subject, but this will take some development to become clear.

+

In this work, the basic structure of each MOI is adopted from the pragmatic theory of signs and the general account of its operation is derived from the pragmatic theory of inquiry. The indispensible utility of these formal models hinges on the circumstance that each MOI, whether playing its part in interpretation or in inquiry, is always a "model" in two important senses of the word. First, it is a model in the logical sense that its structure satisfies a formal theory or an abstract specification. Second, it is a model in the analogical sense that it represents an aspect of the structure that is present in another object or domain.

−

1.3.5.7 Steps & Tests of Formalization

+

=====1.3.5.7. Steps & Tests of Formalization=====

+

This same compulsion exists in the sense activities that support reason - by simplification, coarsening, emphasizing, and elaborating, upon which all "recognition", all ability to make oneself intelligible rests. Our needs have made our senses so precise that the "same apparent world" always reappears and has thus acquired the semblance of reality.

(Nietzsche, The Will to Power S521, 282).

+

</blockquote>

+

A step of formalization moves the active focus of discussion from the "presentational object" or source domain to the "representational object" or "target domain" that constitutes the relevant MOI. If the structure in the source context is already formalized then the step of formalization can itself be formalized in an especially elegant and satisfying way as a structure-preserving map, homomorphism, or "arrow" of category theory.

+

The test of a formalization being complete is that a computer could in principle carry out the steps of the process exactly as represented in the formal model or image. It needs to be appreciated that this is a criterion of sufficiency to formal understanding and not of necessity relevant to material re-creation. The ordinary agents of informal discussion who address the task of formalization do not disappear in the process of completing it, since it is precisely for their understanding that the step is undertaken. Only if the phenomenon at issue were by its very nature solely a matter of form could its formal analogue constitute an authentic reproduction. But this potential consideration is far from the ordinary case I need to discuss at present.

+

In ordinary discussion, agents depend on the likely interpretations of others to give their common notions and shared notations a meaning in practice. This means that a high level of implicit understanding is relied on to ground each informal inquiry in practice. The entire framework of logical assumptions and interpretive activities that is needed to shore up this platform will itself resist analysis, since it is precisely to save the effort of repeating routine analyses that the whole infrastructure is built.

−

1.3.5.8 ~~Puck, the Ref~~

+

=====1.3.5.8. The Referee=====

+

Our subjective compulsion to believe in logic only reveals that, long before logic itself entered our consciousness, we did nothing but introduce its postulates into events: now we discover them in events - we can no longer do otherwise - and imagine that this compulsion guarantees something connected with "truth".

(Nietzsche, The Will to Power S521, 282-283).

+

</blockquote>

+

In a formal inquiry of the sort projected here, the less the discussants need to depend on the compliance of understanding interpreters the more they will necessarily understand at the end of the formalization. It might be thought that the ultimate zero of understanding expected on the part of the interpreter would correspond to the ultimate height of understanding demanded on the part of the formalizer, but this neglects the negative potential of misunderstanding, the sheer perversity of interpretation that true human creativity can bring to bear on any text. But computers are initially just as incapable of misunderstanding as they are of understanding. Therefore, it actually forms a moderate compromise to address the task of interpretation to a computational system, something that is known to begin from a relatively neutral intitial condition.

−

1.3.5.9 Partial Formalizations

+

=====1.3.5.9. Partial Formalizations=====

+

It is we who created the "thing", the "identical thing", subject, attribute, activity, object, substance, form, after we had long pursued the process of making identical, coarse and simple. The world seems logical to us because we have made it logical.

(Nietzsche, The Will to Power S521, 283).

+

</blockquote>

+

In many discussions the source context remains unformalized in itself, taking form only according to the image it receives in this or that individual MOI. In this case, the step of formalization is not a total function but limited to a partial mapping from the source to the target. Such a partial representation is analogous to a sampling operation. It is not defined on every point of the source domain but assigns values only to a proper selection of source elements. Thus, a partial formalization can be regarded as achieving its form of simplification in a loose way, by ignoring elements of the source domain and collapsing material distinctions in an irregular fashion.

−

1.3.5.10 A Formal Utility

+

=====1.3.5.10 A Formal Utility=====

+

Ultimate solution. - We believe in reason: this, however, is the philosophy of gray concepts. Language depends on the most naive prejudices.

(Nietzsche, The Will to Power S522, 283).

+

</blockquote>

+

The usefulness of the MOI is that it provides discussion with a compact image of the whole source domain.

+

The use of formalization as a pretermination criterion. One of the primary benefits of the requirement of formalization is to serve as a pretermination criterion.

+

A benefit of adopting the objective of formalization is that it equips discussion with a pretermination criterion.

The purpose of formalization is to identify a simpler version or to fashion a simpler image of a difficult inquiry, one that is well-defined and simple enough to assure its termination in a finite interval of space-time.

+

In formalization one tries to extract a simpler image of the larger inquiry, a context of participatory action that one is too embroiled in carrying out step by step to see as a whole.

In the context of the recursive inquiry I have outlined, the step of formalization is intended to bring discussion appreciably closer to a solid base for the operational definition of inquiry.

−

1.3.5.11 A Formal Aesthetic

+

=====1.3.5.11. A Formal Aesthetic=====

+

</blockquote>

Now we read disharmonies and problems into things because we think only in the form of language - and thus believe in the "eternal truth" of "reason" (e.g., subject, attribute, etc.)

(Nietzsche, The Will to Power S522, 283).

+

</blockquote>

+

Recognizing that the Latin word "forma" means not just "form" but also "beauty" supplies a clue that not all formal models are equally valuable for a purpose of interest. There is a certain quality of formal elegance, or select character, that is essential to the practical utility of the model.

+

The virtue of a good formal model is to provide discussion with a fitting image of the whole phenomenon of interest. The aim of formalization is to extract from an informal discussion or locate within a broader inquiry a clearer and simpler image of the whole activity. If the formalized precis or image is unusually apt it might be prized as a recapitulation or gnomon and said to capture the essence, the gist, of the nub of the whole affair.

+

A pragmatic qualification of this virtue requires that the image be formed quickly enough to take decisive action on. So the quality of being a result often takes precedence over the quality of the result. A definite result, however partial, is frequently reckoned to be better than having to wait for a complete picture that may never develop.

+

But an overly narrow or premature formalization, where the quality of the original phenomenon is too severely reduced in the formalized image, may result in destroying all interest in the result that does result.

−

1.3.5.12 A Formal Apology

+

=====1.3.5.12. A Formal Apology=====

+

We cease to think when we refuse to do so under the constraint of language; we barely reach the doubt that sees this limitation as a limitation.

(Nietzsche, The Will to Power S522, 283).

+

</blockquote>

+

Seizing the advantage of this formal flexibility makes it possible to take abstract leaps over a multitude of material obstacles, to reason about many properties of objects and processes from knowledge of their form alone, without having to know everything about their material content down to the depths that matter can go.

−

1.3.5.13 A Formal Suspicion

+

=====1.3.5.13. A Formal Suspicion=====

+

Rational thought is interpretation according to a scheme that we cannot throw off.

(Nietzsche, The Will to Power S522, 283).

+

</blockquote>

+

I hope that the reader has arrived by now at an independent suspicion that the process of formalization is a microcosm nearly as complex as the whole subject of inquiry itself. Indeed, the initial formulation of a problem is tantamount to a mode of "representational inquiry". In many ways this first effort, that stirs from the torpor of ineffable unease to seek any sort of unity in the manifold of fragmented impressions, is the most difficult, subtle, and crucial kind of inquiry. It begins in doubt about even so much as a fair way to represent the problematic situation, but its result can predestine whether subsequent inquiry has any hope of success. There is very little in this brand of formal engagement and participatory representation that resembles the simple and disinterested act of holding a mirror, flat and featureless, up to nature.

+

If formalization really is a form of inquiry in itself, then its formulations have deductive consequences that can be tested. In other words, formal models have logical effects that reflect on their fitness to qualify as representations, and these effects can cause them to be rejected merely on the grounds of being a defective picture or a misleading conception of the source phenomenon. Therefore, it should be appreciated that software tailored to this task will probably need to spend more time in the alterations of backtracking than it will have occasion to trot out parades of ready-to-wear models.

+

Impelled by the mass of assembled clues from restarts and refits to the gathering form of a coherent direction, the inkling may have gradually accumulated in the reader that something of the same description has been treated in the pragmatic theory of inquiry under the heading of "abductive reasoning". This is distinguished from inductive reasoning, that goes from the particular to the general, in that abductive reasoning must work from a mixed collection of generals and particulars toward a middle term, a formal intermediary that is more specific than the vague allusions gathered about its subject and more generic than the elusive instances fashioned to illustrate its prospective predicates.

+

In a recursive context, the function of formalization is to relate a difficult problem to a simpler problem, breaking the original inquiry into two parts, the step of formalization and the rest of the inquiry, both of which branches it is hoped will be nearer to solid ground and easier to grasp than the original question.

−

1.3.5.14 The Double Aspect of Concepts

+

=====1.3.5.14. The Double Aspect of Concepts=====

+

Nothing is more erroneous than to make of psychical and physical phenomena the two faces, the two revelations of one and the same substance. Nothing is explained thereby: the concept "substance" is perfectly useless as an explanation. Consciousness in a subsidiary role, almost indifferent, superfluous, perhaps destined to vanish and give way to a perfect automatism - (Nietzsche, The Will to Power S523, 283).

+

</blockquote>

+

This work is a particular inquiry into the nature of inquiry in general. As a consequence, every conceptual construct that appears in it will take on a double aspect.

+

To illustrate, let take the concept of a "sign relation" as an example and let me use it to speak about my own agency in this inquiry. All I need to say about a sign relation at this point is that it is a three-place relation, and therefore can be imagined as a relational data-base with three columns, in this case naming the "object", the "sign", and the "interpretant" of the relation at each moment in time of the corresponding "sign process".

At any given moment of this inquiry I will be participating in a certain sign relation that constitutes the informal context of my activity, the full nature of which I can barely hope to conceptualize in explicitly formal terms. At times, the object of this informal sign relation will itself be a sign relation, typically one that is already formalized or one that I have a better hope of formalizing, but it could conceivably be the original sign relation with which I began.

+

In such cases, when the object of a sign relation is also a sign relation, the general concept of a sign relation takes on a double duty:

+

1. The less formalized sign relation is used to mediate the inquiry. As a conceptual construct, it is not yet fully conceived or constructed at the moments of inquiry being considered. Perhaps it is better to regard it as a "concept under construction". Employed as a contextual apparatus, this sign relation serves an instrumental role in the study or construal of its objective sign relation.

+

2. The more formalized sign relation is mentioned as a substantive object to be contemplated and manipulated by the inquiry. As a conceptual construct, it exemplifies the role intended for it best if it is already as completely formalized as possible. It is being engaged as a substantive object of inquiry.

I have given this project a reflective or a recursive cast, describing it as inquiry into inquiry, and one of the consequences of this is that every concept employed in the work will take on a double aspect, divided role, or dual purpose. At any moment, the object inquiry of the moment is aimed to take on a formal definition, whereas the active inquiry ...

−

1.3.5.15 A Formal Permission

+

=====1.3.5.15. A Formal Permission=====

+

If there are to be synthetic a priori judgments, then reason must be in a position to make connections: connection is a form. Reason must possess the capacity of giving form.

(Nietzsche, The Will to Power S530, 288).

+

</blockquote>

+

=====1.3.5.16. A Formal Invention=====

−

~~1.3.5.16 A Formal Invention~~

+

Before there is "thought" (gedacht) there must have been "invention" (gedichtet); the construction of identical cases, of the appearance of sameness, is more primitive than the knowledge of sameness.

(Nietzsche, The Will to Power S544, 293).

+

</blockquote>

+

====1.3.6. Recursion in Perpetuity====

−

~~1.3.6 Recursion in Perpetuity~~

+

Will to truth is a making firm, a making true and durable, an abolition of the false character of things, a reinterpretation of it into beings. "Truth" is therefore not something there, that might be found or discovered - but something that must be created and that gives a name to a process, or rather to a will to overcome that has in itself no end - introducing truth, as a processus in infinitum, an active determining - not a becoming-conscious of something that is in itself firm and determined. It is a word for the "will to power".

(Nietzsche, The Will to Power S552, 298).

+

</blockquote>

+

Life is founded upon the premise of a belief in enduring and regularly recurring things; the more powerful life is, the wider must be the knowable world to which we, as it were, attribute being. Logicizing, rationalizing, systematizing as expedients of life.

(Nietzsche, The Will to Power S552, 298-299).

+

</blockquote>

+

Man projects his drive to truth, his "goal" in a certain sense, outside himself as a world that has being, as a metaphysical world, as a "thing-in-itself", as a world already in existence. His needs as creator invent the world upon which he works, anticipate it; this anticipation (this "belief" in truth) is his support.

(Nietzsche, The Will to Power S552, 299).

+

</blockquote>

−

1.3.7 Processus, Regressus, Progressus

+

====1.3.7. Processus, Regressus, Progressus====

+

From time immemorial we have ascribed the value of an action, a character, an existence, to the intention, the purpose for the sake of which one has acted or lived: this age-old idiosyncrasy finally takes a dangerous turn - provided, that is, that the absence of intention and purpose in events comes more and more to the forefront of consciousness.

(Nietzsche, The Will to Power S666, 351).

+

</blockquote>

+

Thus there seems to be in preparation a universal disvaluation: "Nothing has any meaning" - this melancholy sentence means "All meaning lies in intention, and if intention is altogether lacking, then meaning is altogether lacking, too".

(Nietzsche, The Will to Power S666, 351).

+

</blockquote>

+

In accordance with this valuation, one was constrained to transfer the value of life to a "life after death", or to the progressive development of ideas or of mankind or of the people or beyond mankind; but with that one had arrived at a progressus in infinitum of purposes: one was at last constrained to make a place for oneself in the "world process" (perhaps with the dysdaemonistic perspective that it was a process into nothingness).

(Nietzsche, The Will to Power S666, 351).

+

</blockquote>

+

====1.3.8 Rondeau : Tempo di Menuetto====

−

~~1.3.8 Rondeau Tempo di Menuetto~~

+

And do you know what "the world" is to me? Shall I show it to you in my mirror? This world: a monster of energy, without beginning, without end; a firm, iron magnitude of force that does not grow bigger or smaller, that does not expend itself but only transforms itself; as a whole, of unalterable size, a household without expenses or losses, but likewise without increase or income; enclosed by "nothingness" as by a boundary; not something blurry or wasted, not something endlessly extended, but set in a definite space as a definite force, and not a space that might be "empty" here or there, but rather as force throughout, as a play of forces and waves of forces, at the same time one and many, increasing here and at the same time decreasing there; a sea of forces flowing and rushing together, eternally changing, eternally flooding back, with tremendous years of recurrence, with an ebb and a flood of its forms; out of the simplest forms striving toward the most complex, out of the stillest, most rigid, coldest forms toward the hottest, most turbulent, most self-contradictory, and then again returning home to the simple out of this abundance, out of the play of contradictions back to the joy of concord, still affirming itself in this uniformity of its courses and its years, blessing itself as that which must return eternally, as a becoming that knows no satiety, no disgust, no weariness: this, my Dionysian world of the eternally self-creating, the eternally self-destroying, this mystery world of the twofold voluptuous delight, my "beyond good and evil", without goal, unless the joy of the circle is itself a goal; without will, unless a ring feels good will toward itself - do you want a name for this world? A solution for all its riddles? A light for you, too, you best-concealed, strongest, most intrepid, most midnightly men? - This world is the will to power - and nothing besides! And you yourselves are also this will to power - and nothing besides!

(Nietzsche, The Will to Power S1067, 549-550).

+

</blockquote>

+

I have attempted in a narrative form to present an accurate picture of the formalization process as it develops in practice. Of course, accuracy must be distinguished from precision, for there are times when accuracy is better served by a vague outline that captures the manner of the subject than it is by a minute account that misses the mark entirely or catches each detail at the expense of losing the central point. Conveying the traffic between chaos and form under the restraint of an overbearing and excisive taxonomy would have sheared away half the picture and robbed the whole exchange of the lion's share of the duty.

At moments I could do no better than to break into metaphor, but I believe that a certain tolerance for metaphor, especially in the initial stages of formalization, is a necessary capacity for reaching beyond the secure boundaries of what is already comfortable to reason. Plus, a controlled transport of metaphor allows one to draw on the boundless store of ready analogies and germinal morphisms that every natural language provides for free.

Finally, it would leave an unfair impression to delete the characters of narrative and metaphor from the text of the story, and especially after they have had such a hand in creating it.

Even the most precise of established formulations cannot be protected from being reused in ways that initially appear as an abuse of language.

+

One of the most difficult questions about the development of intelligent systems is how the power of abstraction can arise, beginning from the kinds of formal systems where each symbol has one meaning at most. I think that the natural pathway of this evolution has to go through the obscure territory of ambiguity and metaphor.

+

A critical phase and a crucial step in the development of intelligent systems, biological or technological, is concerned with achieving a certain power of abstraction, but the real trick is for the budding intelligence to accomplish this without losing a grip on the material contents of the abstract categories, the labels and levels of which this power interposes and intercalates between essence and existence.

+

If one looks to the surface material of natural languages for signs of how this power of abstraction might arise, one finds a suggestive set of potential precursors in the phenomena of ambiguity, anaphora, and metaphor. Keeping this in mind throughout the project, I will pay close attention to the places where the power of abstraction seems to develop, especially in the guises of systematic ambiguity and controlled metaphor.

Paradoxically, and a bit ironically, if one's initial attempt to formalize semantics begins with the aim of stamping out ambiguity, metaphor, and all forms of figurative language use, then one may have precluded all hope of developing a capacity for abstraction at any later stage.

−

1.3.9 Reconnaissance

+

====1.3.9. Reconnaissance====

−

In every sort of project there are two things to consider: first, the absolute goodness of the project; in the second place, the facility of execution.

+

−

In the first respect it suffices that the project be acceptable and practicable in itself, that what is good in it be in the nature of the thing; here, for example, that the proposed education be suitable for man and well adapted to the human heart.

+

−

The second consideration depends on relations given in certain situations - relations accidental to the thing, which consequently are not necessary and admit of infinite variety.

+

In every sort of project there are two things to consider: first, the absolute goodness of the project; in the second place, the facility of execution.

+

In the first respect it suffices that the project be acceptable and practicable in itself, that what is good in it be in the nature of the thing; here, for example, that the proposed education be suitable for man and well adapted to the human heart.

+

The second consideration depends on relations given in certain situations - relations accidental to the thing, which consequently are not necessary and admit of infinite variety.

Rousseau, Emile, or On Education, [Rou1, 34-35]

+

</blockquote>

+

This section provides a glancing introduction to many subjects that cannot be treated in depth until much later in this work, but that need to be touched on at this point, if only in order to "prime the canvass" or to "set the tone" for the rest of this work, that is, to suggest the general philosophy, the implicit assumptions, and the basic conceptions that guide, limit, and underlie this approach to the subject of inquiry. In the process of achieving the aims of this preliminary survey, it is apparently necessary for me, on this occasion, to pick my way through a densely interwoven web, to wit, a pressing but by no means a clear context of informal discussion, and to work my way across and around a nearly invisible warp, a whit less wittingly, a network of not yet fully formalized thought that nevertheless informs discussion in its own way.

+

At every stage my work is bound by dint of the necessities that appear, to me, to occasion it, and thus my initial overture to a more developed inquiry is bound to continue in an indirect style. As this venture and each of its tentative subventures is compelled to try their supervening and intervening subjects in an array of oblique and incidental manners, I am continually forced to detect my likeliest directions of progress by gently teasing out only the most readily exposed clues from the context of tangent discourse, and I am consequently obliged to clarify my local chances of success by provisionally tugging loose only the most roughly isolated threads from this gradually explicated and formulated network. Accordingly, a reconnaissance of the immediate surroundings affords but a minimal opportunity to exercise options for creativity and imagination, and there is little choice but to pick up each subordinate subject in the midst of its action and to let go of it again while it is still in progress.

+

In the process of carrying out the present reconnaissance it is useful to illustrate the pragmatic theory of signs as it bears on a series of slightly less impoverished and somewhat more interesting materials, to demonstrate a few of the ways that the theory of signs can be applied to a selection of genuinely complex and problematic texts, specifically, poetic and lyrical texts that are elicited from natural language sources through the considerable art of creative authors. In keeping with the nonchalant provenance of these texts, I let them make their appearance on the scene of the present discussion in what may seem like a purely incidental way, and only gradually to acquire an explicit recognition.

+

<pre>

1.3.9.1 The Informal Context

On either side the river lie

Jon Awbrey

12,080

edits