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===6.4. A Formal Point of View===
===6.4. A Formal Point of View===
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In this section the concept of a "point of view" (POV) is taken up in greater detail and subjected to the first few steps of a formalization process. This makes it possible to explore the wider implications of the idea, to pursue the lines of inquiry it suggests to greater lengths, and to apply the tentative formalism to an issue of pressing concern, namely, the question of what kind of distinction ought to be posed between the dynamic and the symbolic aspects of intelligent systems.
If there were nothing but a single POV to entertain, a diversion of attention to matters of perspective would hardly be worth the candle. Accordingly, the dimensions of change and diversity are intrinsic to the worth of the whole idea.
One of the reasons for trying to formalize the concept of a POV is so that this TOI, along with others on its model, can reflectively comment on its own POV, as it progresses from moment to moment, and critically examine it as it develops.
When it comes to the subject of systems theory, a particular POV is so widely propagated that it might as well be regarded as the established, received, or traditional POV. The POV in question says that there are dynamic systems and symbolic systems, and never the twain shall meet. I naturally intend to challenge this assumption, preferring to suggest that dynamic and symbolic attributes are better regarded as different aspects of a single underlying system, as "two sides of the same coin". But first I have to express the assumption well enough to question it.
Beyond the dim inkling of an underlying influence, a sufficiently critical level of reflection on a POV requires a language that is articulate and analytic enough to transform each thesis posed in it into the form of a question. A deliberately reflective technology is needed to bring the prevailing, prejudicial, and hypocritical underpinnings of a POV to light, since biases due to assumptions obscurely held are seldom automatically revealed. This highlights the need for a critical apparatus that can be applied to the typical TOI, supplying its interpreter with the technical means to take up a critical POV with respect to it.
A logical calculus cannot initiate reflection on a text, but it can help to support and maintain it. The raw ability to perceive selected features of an ongoing text and the basic language of primitive terms, that allow one to mark the presence and note the passing of these features, have to be supplied from outside the calculus at the outset of its calculations. In the present text, the means to support critical reflection on its own POV and others are implemented in the form of a propositional calculus. Given the raw ability of a perceptive interpreter to form glosses on the text and to reflect on the contents of its current POV, a logical calculus can serve to augment the text and assist its critique by catalyzing the consideration of alternative POV's and facilitating reasoning about the wider implications of any particular POV.
The discussion so far has dwelt at length on a particular scene, returning periodically to the fragmentary but concrete situation of a dialogue between A and B, poring over the formal setting and teasing out the casual surroundings of a circumscribed pair of sign relations. If the larger inquiry into inquiry is ever to lift itself off from these concrete and isolated grounds, then there is need for a way to extract the lessons of this exercise for reuse on other occasions. If items of knowledge with enduring value are to be found in this arena, then they ought to be capable of application to broader areas of interest and to richer domains of inquiry, and this demands ways to test their tentative findings in analogous and alternative situations of a more significant stripe. One way to do this is to identify properties and details of the selected examples that can be varied within the bounds of a common theme and treated as parameters whose momentary values convey the appearance of complete individuality to each particular case.
Typically, a movement from reduced examples to realistic exercises takes a definite but gradual progression of steps, moving forward through the paces of abstraction, generalization, transformation, and re application. The prospects of success in these stages of development are associated with the introduction of certain formal devices. Principal among these are the explicit recognition of sets of "parameters" and their expression in terms of lists of "variables".
As I understand them, "variables" are a class of beneficially ambiguous or usefully equivocal signs. In effect, variables are just signs, but signs possessed of a more adaptive constitution or affected by a more flexible interpretation than signs of the usual, more "constant" variety. These forms of employment turn variables into a class of reusable signs, converting them into sustainable resources for meaning that can be used in a plurality of ways and deployed to articulate different choices at different times from among the available points of thematic variation.
The next major task of this discussion, while continuing to take its bearings from examples as concrete as A and B, is to develop systematic methods for divining the bearing of such isolated examples on issues of real concern. This involves two stages:
1. One needs to detect the invariant features of the currently known examples, in other words, the dimensions along which their values are, knowingly or unknowingly, held to be constant.
2. One needs to try varying the features that are presently held to be constant by imagining new examples that are able to realize alternative features.
The larger issue at stake throughout these stages is how the agent of inquiry can find ways to express the lessons of individual exercises in ways that persist through and rise above their individual attachments to experience, thereby living through detailed experiences while remaining undiverted by their peculiar distractions.
There appears to be a practical necessity in drawing at least a tentative distinction between the role of an object and the role of an interpreter, even if a moment of reflection occasionally requires a single entity to fill both roles, and even though a mass of experience with systems that try to draw hard and fast distinctions between things, once and for all, leads one to see that a need exists for ways to withdraw every pretense of any distinction, redrawing it anew if possible, and drawing on new grounds if necessary. There is never anything initially or immediately obvious about a sign itself that says it destined to represent an object of a particular type, and this makes it necessary to infer the type that ought to be specified from the pattern of references in which the sign is actually observed to be engaged.
A distinction that one is initially tempted to treat as substantial but is later bound to discover as purely interpretive, like that between objects and signs, subjects and predicates, particles and waves, or dynamic and symbolic aspects of systems, can frequently bedevil sensible inquiry for quite some period of time. To deal with this problem, there needs to be a standardly available mechanism for introducing these staple but still provisional distinctions, accepting them on a par with axioms at first, but without precluding the opportunities to later revise the substantive imports of their interpretations.
On the way to integrating dynamic and symbolic approaches to systems there are several different sorts of things that can happen. It can happen that a certain distinction, a natural or artificial feature that separates the outlooks of the dynamic and symbolic perspectives, or the sheer appearance of a distinction, a suggestion of a line that leads an observer to see a difference between the two views in the first place, merely gets erased. Or it can happen that the ostensible distinction between the two standpoints marks in reality a naturally useful border, one that is well worth preserving, and yet a wealth of connections that constitutes the true relationship between the two realms can be marked and remarked with increasing visibility in the meantime. In any case, there are lines of pretended distinction and potential difference that must be crossed, and then recrossed, time after time, until their exact form and precise nature have become marked in their clarity or else transparent in their obliteration.
I would like to detach, for a moment, from the particular contrast of interest here, the one posed between dynamic and symbolic orientations, to examine the general question of relating contrasting aspects or views. In this connection, two distinct but correlated efforts at classification and organization arise in tandem with each other. One concern seeks to classify the attributes, categories, features, properties, or qualities that are used to describe the object observed, while the other project tries to organize the approaches, instruments, methods, perspectives, or views that are used to observe the object described.
To invoke the traditional terminology, natural classes of predicates are referred to as "categories" or "predicaments", making it natural to call the classification and study of predicates by the name of "categoric", while the classification and study of methods is classically referred to as "heuristic" or "methodeutic" (Peirce, CP 2.105 110 & 2.207).
Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: "Category" from Aristotle and Kant, "Functor" from Carnap ..., and "natural transformation" from then current informal parlance.
(Mac Lane 1971, Cat.Work.Math. 29 30).
Categoric. Although this subject is historically referred to as the "theory of categories", in modern times it is necessary to distinguish it from the mathematical subject of "category theory", whose claim to the title is confessedly derived by stealth. By way of suffering unto the older discipline the freshness of the younger subject, the original study and more general classification of predicates can be referred to as the "doctrine of categories" (DOC). This is a fair description, given that optional schemes of basic categories are commonly taken up, maintained, and transmitted in decidedly catechismic and rigidly dogmatic fashions.
Perhaps it is the mind's reluctance to revive the uncertainties and to relive the struggles that these schemes were made to resolve, but once the fundamental categories are settled it is nearly impossible to revise them, however poorly they come to fit the current circumstances of life. No matter how original the thinking that leads up to a site where a stable foundation can be poured, the foundation itself is typically laid down as if it were cut from inalterable stone.
I even hope that what I have done may prove a first step toward the resolution of one of the main problems of logic, that of producing a method for the discovery of methods in mathematics. (Peirce, CP 3.364).
Methodeutic. This subject, that C.S. Peirce gave the alternate titles of "speculative rhetoric" or "formal rhetoric", because it is a science that "would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants" (CP 1.444 & 1.559), and that he assigned the task to find "a method of discovering methods" (CP 2.108 & 3.364), is one that clearly has a special relevance to the pursuit of an inquiry into inquiry.
In an effort to gradually begin formalizing these issues, I introduce the concept of a "point of development" (POD). This notion is intended to capture a particular moment in the history of a system or its agent, as it is reflected in the systems of propositions associated with each POD. Relative to a particular POD there can be distinguished, though neither exclusively nor exhaustively, two types of propositions that are said to be "associated" with it. Roughly speaking, these types of propositions reflect the thoughts that are "applied" to a POD and the thoughts that are "attached" to a POD, respectively.
1. A proposition that "applies" to a POD can be formulated in more detail as a "proposition about or on a POD" (PAO'POD). This describes the corresponding POD as though observed from an outside perspective, stating features that locate it within a space of dynamic configurations or that place it in relation to some other medium of common description. This manner of associating propositions with POD's is tantamount to adopting a third person POV on the system or its agent, and it is commonly used to convey an impression of objectivity, no matter whether this standpoint is well taken or not.
2. A proposition that "attaches" to a POD can be formalized in more detail as a "proposition at or in a POD" (PAI'POD). This represents what an agent thinks or believes, entertains or maintains, in sum, what an agent is aware of or willing to assert at a particular POD. By way of filling out the formula, this type of proposition expresses thoughts and is expressed in signs that are likewise regarded as "attached" to the POD in question. In general, propositions at a POD can be formed to express every conceivable modality. Collectively, they can state anything that an agent notes or thinks, observes or imagines at a given moment of its developmental history. They can reflect any aspect of an agent's awareness, belief, conjecture, doubt, expectation, intention, observation, or any other latitude of thought that is actively considered or faithfully preserved throughout the moment in question, and in this sense they are considered to be attached to, bound to, contained in, or localized at a particular POD.
In one sense, propositions about a POD are potentially the general case, since propositions at a POD can be incorporated within their formulation. That is, a proposition about a POD is allowed to make assertions about the propositions at that POD, plus assertions about their relation to propositions at other POD's. But propositions whose references are this involved, articulated as "propositions about propositions at a POD", for instance, are classed as "higher order propositions" (HOP's) and need to be inferred through processes of hypothesis and experiment, conjecture and confirmation, instead of being observed outright. In another sense, propositions at a POD are intrinsically the prototype, since it is from their data that every other type must be constructed.
Propositions about POD's naturally collect into theories about POD's, and at the next level of aggregation these constitute the familiar sorts of dynamic theories that are used to describe the state spaces of systems and the trajectories of agents through them. Concentrating on these types of propositions leads to the kinds of theories about systems where a "neutral observer", not involved in the system itself, is postulated or fancied to stand outside the dynamics of the "observable object system": where this "objective reasoner" is supposedly able to theorize about the observable system without essentially becoming a part of its operations or necessarily being involved as a participant in its actual workings, and where the same "passive agent" never finds itself forced to interact in an irreversible or irrevocable manner with the autonomous course of the object system's action.
The thoughts attached to a POD, the things an agent thinks or believes, entertains or maintains at one POD, in relation to what the agent thinks or believes, is aware of or willing to assert at another POD, is the very form of subject matter that is bound to come to light and bound to fall into play whenever one studies the development of a reflective system, whether the focus of interest is the course of a particular inquiry or the emergence of a generic intelligence.
From a pragmatic point of view, a belief is a proposition that an agent is prepared to act on. In practice, this means that information about beliefs can be obtained from observations of action, as long as one remembers that this information is almost always partial information, contingent on the sample of actions that are actually observed and limited by the circumstance that not all preparations result in action.
It may be thought that there is an important distinction between belief and knowledge that ought to be recognized in the modes of maintaining propositions at or in a POD. Given the pragmatic definition of belief, however, there is no local mark that can tell belief and knowledge apart. That is, there is no practical difference that can be sustained, in the propositions attached to a single POD, between those that reflect items of contingent belief and those that reflect items of certain knowledge. Even if the propositions at or in a POD are artificially marked in ways that can later be reliably detected, the problem of constantly updating so fleeting a form of distinction makes the accumulating profusion of ephemeral distinctions as immaterial and unenlightening as every other genre of eracist obliterature.
A distinction between belief and knowledge appears to arise only in the interactions and comparisons that can be made between different POD's, either those enjoyed by a single agent in the history of a single system or those passed through by ostensibly different agents and systems. The sense of the distinction can be sustained only if the order of its relational context continues to be recognized, which means that the mark of the distinction cannot be strained to the point of being an absolute. In this context, different systems and their agents are said to be "at" comparable POD's precisely to the degree and exactly to the extent that the propositions "at" and "about" them, respectively, can be compared. In many respects, the comparison of propositions at different POD's is equally complex and problematic whether it is one agent or several that is being considered.
With all this in mind, I can give a formulation of what the practical difference between belief and knowledge consists in. Roughly speaking, an agent says that an agent "knows" something if and only if the one believes what the other believes. More precisely, an agent at one POD has reason to say that an agent at another POD (possibly a former self) knows something about something (or knew something about something) if and only if the one believes what the other believes about it, all things being relative to the POD's that the agents are at.
Propositions associated with a POD are often found in organized bodies, forming more or less logical systems of more or less logical statements. Whatever their type or modality with respect to a POD, "propositions of a feather gather together". That is, they tend to collect into organized bodies of propositions that share compatible types of association and comparable modes of assertion. In logic, an arbitrary collection of propositions is called a "theory", no matter how coherent, complete, or consistent it turns out to be when subjected in time to critical review. Taking up this liberalized notion of a theory in the present setting, a bunch of PAI'POD's forms a "theory at or in a POD" (TAI'POD), while a bunch of PAO'POD's forms a "theory about or on a POD" (TAO'POD).
A reasonably organized system is amenable to having its propositions sorted further, forming collections of propositions that are intended to be interpreted in the same light, and constellating theories that bear on single modes of contemplation or declaration among their propositions.
With respect to the propositions at a POD, the present inquiry into inquiry is mainly concerned with the modalities of expectation, intention, and observation. This is due to a couple of differential modalities, derived in pairs from among these three, that appear to drive every form of inquiry, at least, to some degree.
1. There is the moment of doubt or uncertainty that is encountered in a surprising phenomenon, providing an impulse for the component of inquiry that seeks an explanation to relieve the shock. This factor driving inquiry can be analyzed as deriving from the differences that occur between one's expectations and one's observations.
2. There is the moment of desire or difficulty that is countenanced in a problematic situation, providing an impulse for the component of inquiry that seeks a plan of action to resolve the trouble. This factor driving inquiry can be analyzed as deriving from the differences that occur between one's intentions and one's observations.
It should be obvious that these conceptions represent another attempt to formalize the relationship between dynamic and symbolic approaches to intelligent systems. Once again, the paradigms that are established for dealing with propositions at or about POD's are typically specialized to consider one or the other but seldom both. This leads to the familiar sorts of dichotomies being imposed on a subject matter where the types are more complementary and generative than exclusive and exhaustive. Thus, one finds methodologies in the field that can work well either from an "external" (dynamic, model theoretic, empirical) perspective or from an "internal" (symbolic, proof theoretic, rational) perspective, but that are seldom able to incorporate both technologies into an integrated methodology.
The concept of a POD in the history of a system, with its associated division of propositions into those that apply exterior to it and those that attach interior to it, is yet another way of approaching a recurring subject, "the being and the role of the interpreter", that the general concept of an "objective concern" (OC), broached at an earlier point of development in this text, is also intended to capture. Advancing as if from a pair of complementary and convergent directions, the notion of a POD, in the way it supplies a footing to the propositions about or on it and serves to encapsulate the propositions at or in it, equips a growing SOI with all the pivotal, trophic, and vital functions that the notion of an "objective motif" (OM) realized in an "interpretive moment" (IM) is likewise meant to provide.
The relationship between a POD and an OM at an IM can be understood as follows. ...
In order to continue formalizing the discussion of POV's and POD's within the text that uses them, I introduce the following notations:
j : x | y, x |j y, x | y : j,
j : x / y, x /j y, x / y : j,
j : (x , y), (x , y)j, (x , y) : j.
All of these expressions are intended to indicate a set of circumstances that could otherwise be rendered as follows:
1. j appears to see a distinction between x and y.
2. j partitions a dimension of discourse between x and y.
3. j sees x and y as mutually exclusive and exhaustive possibilities.
In this scheme, "x" and "y" indicate logical dimensions of variation or propositional features of description that govern an agent's possibilities of action and perception. Used as primitive logical terms they denote the distinctive features that determine an agent's spaces of performance and experience. In combination with logical operators they generate a descriptive framework that encompasses both: (1) the methodological "approaches" or "perspectives" toward objects that an agent can adopt, and (2) the categorical "aspects" of objects, the independently coherent systems of properties and qualities that characterize the hypothetically unified object system.
In practice, it does not matter whether one regards x and y as logical features or as boolean variables, so long as the full set of positive and negative features { x, (x), y, (y) } is initially available to classify the relevant space of object perceptions or interpretive actions. Analogous to its role in the staging relations { < , > }, the label "j" indicates the active interpreter, that is, the system and moment of interpretation or the state of the interpretive system that is held to be responsible for finding, making, testing, or following through the consequences of posing the contemplated distinctions.
Dual to the statements of momentary interpretive distinctions (MID's) are the respective statements of momentary interpretive coincidences (MIC's):
j : x = y, x =j y, x = y : j,
j : x <=> y, x <=>j y, x <=> y : j,
j : ((x , y)), ((x , y))j, ((x , y)) : j.
Each of these expressions is intended to indicate a set of circumstances that could otherwise be rendered by any one of the following, logically equivalent statements:
1. j appears to see a coincidence between x and y.
2. j draws no distinction between the dimensions x and y.
3. j sees x and y as manifestly equivalent ranges of possibilities.
The introduction of explicit names for systems of interpretation, as well as for their interpretive moments, models of interpretation, objective concerns, points of development, and situations of use, is intended to flesh out the lifeless idiom or insipid brand of "assignment statements" that are currently found in CL settings, which are typically rendered so abstractly as to constitute a entire style of "anonymous", "passive", or "unattributed" excuses for fully executable commands.
In a related usage, one is permitted to reparse the "anonymous" or "passive" form of assignment statement:
"x := y", read as "x is set equal to y",
converting it into the corresponding "attributive" or "active" form of assignment statement:
"j : x = y", read as "j sets x equal to y".
Returning to the present application, the "categorical" project leads one to seek something in the object itself, some factor that divides up its dynamic and symbolic aspects, some plane of cleavage that explains the natural divisions between different types of object system, while the "methodeutic" outlook leads one to wonder whether the specialized mode of being that is beheld in the object is not in fact due to something in the style and direction of approach, some artifact of method that is being cast on the object system from the eye of the beholder.
I would like to articulate a systematic hypothesis that prevails over the scene of this work, tacitly imposing the deliberately hopeful assumption that there is always some sort of hypostatic unity to be found beneath the manifold diversity of phenomena. It is not just my own presumption or personal preference to say this. I find it to be a likely and common assumption, constantly being used to address all sorts of interesting phenomena and almost every process of note, whether or not it is ever expressly enunciated.
This hypothesis is probably implicit in the very idea of a "system", that is to say, in the notion of "things standing together", and it is central to the very conception of a systematic universe or a universal system. Nevertheless, I will have to take responsibility for the particular way that this premiss is expressed and developed in this text. Because it amounts to the underlying hope that there is always a unified system, some one thing that subsists beneath every form of phenomenal process and that remains available to substantiate and explain whatever manner of diversity in appearances is encountered, something or other that is always ready to be explicated but seldom necessary to declare, I call this assumption the "hypostatically unified system hypothesis" (HUSH).
In accord with this tacit assumption, that rules the entire realm of systems theory, it can be presumed that there is an integral system, prior in its real status to the manifold of observable appearances, that is somehow able to manifest itself in the severally projected roles of a dynamic process and a symbolic purpose. But to harvest any practical consequences from the employment of this inchoative precept, the twin yoke of questions, categorical and methodeutic, must now be taken up:
1. What constitutes the differences between the dynamic and symbolic aspects of the hypothetically unified intelligent system?
2. What features divide the two perspectives that find these aspects respectively salient?
The integration of symbolic and dynamic approaches to systems thinking requires a significant level of reconstructive effort, one that is capable of extending its energies in both the analytic and synthetic directions. It may be nothing more than a metaphor to describe it this way, but there is something like a dynamic economy of energy exchanges that goes on in facilitating the required "metaboly of symbols" (Peirce).
In this vein, there seem to be laws analogous to conservation principles that govern the transactions between subordinate processes, determining the interactions that are most likely to occur between the breaking down of old conceptual bonds and the creation of new configurations of ideas at higher and lower levels of conceptual equilibrium. Brought to bear on the present task, the specific manifestations of "mental energy" that are called on to accomplish the current work of integration have a potential for raising questions about the relation of "logic" to "time", and thus revive an issue that goes back to the very birth of thought.
The relation of logical and temporal realms, of rational ideas to real experiences, is an ancient and fundamental question, one whose initial answers were laid down in their present form at the very beginnings of reflective inquiry and whose sedimented contents now lie metamorphosed into the deepest bedrocks of our native and systematic philosophies. The distribution of current opinion on the matter regards the question as being (1) "previously settled" or (2) "incapable of solution", with little thought given to a "tertium quid", or a more fluid medium that could moderate between the extremes of these fixed alternatives.
Unfortunately, the customary and habitual classification of a problem as "insoluble", even when justified, can work against the recognition of methods that are available to ameliorate its more objectionable impacts. When it comes to the relationship of logic to time, I believe that the resources are currently available that could advance our understanding of this issue in new directions. All it would take is the will to reconfigure those resources in the appropriate ways.
To expand the formula: The realm of "logic" is typified by rational concepts regarding invariant patterns, virtually, by ideas about forms, while the rule of "time" is filled out by realistic experiences with changing qualities, ultimately, by feelings of content and discontent. The application of the integrative effort to intelligent systems in general and to "inquiry driven systems" (IDS's) in particular only sharpens the question of logic and time to the point of self application.
Considerations like these, as old and as constant as the hills, and as much over our heads as the eternally renewed and inconstant weather, are deserving of occasional notice, yet their relevance to the work of the moment is doomed by their very quality of necessity to fade into the backgound of present concerns, and their saliency as problematic phenomena quickly recedes from the scope of any perspective so bent on immediate application as that falling within my present focus.
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===6.5. Three Styles of Linguistic Usage===
===6.5. Three Styles of Linguistic Usage===