This site is supported by donations to The OEIS Foundation.

Inquiry Driven Systems • Part 10

From OeisWiki
Jump to: navigation, search

Author: Jon Awbrey

Reflective Interpretive Frameworks

Tell me, good Brutus, can you see your face?
No, Cassius, for the eye sees not itself
But by reflection, by some other things.
'Tis just;
And it is very much lamented, Brutus,
That you have no such mirrors as will turn
Your hidden worthiness into your eye,
That you might see your shadow. …
Into what dangers would you lead me, Cassius,
That you would have me seek into myself
For that which is not in me?
Therefor, good Brutus, be prepared to hear.
And since you know you cannot see yourself
So well as by reflection, I, your glass,
Will modestly discover to yourself
That of yourself which you yet know not of.
  Julius Caesar, 1.2.53–72

The rest of this Section (?), continuing the discussion of formalization in terms of concrete examples and extending over the next 50 (?) Subsections (?), details the construction of a reflective interpretive framework (RIF). This is a special type of sign theoretic setting, illustrated in the present case as based on the sign relations A and B, but intended more generally to constitute a fully developed environment of objective and interpretive resources, in the likes of which an inquiry into inquiry can reasonably be expected to find its home.

An inquiry into inquiry necessarily involves itself in various forms of self application and self reference. Even when the inquiree and the inquirer, the operand inquiry and the operant inquiry, are conceived to be separately instituted and disjointly embodied in material activity, they still must share a common form and enjoy a collection of definitive characteristics, or else the use of a common term for both sides of the application is equivocal and hardly justified. But this depiction of an inquiry into inquiry, if it is imagined to be valid, raises a couple of difficult issues, of how a form of activity like inquiry can be said to apply and to refer to itself, and of how a general form of activity can be materialized in concretely different processes, that is, represented in the parametrically diverse instantiations of its own generic principles. Before these problems can be clarified to any degree it is necessary to develop a suitable framework of discussion, along with a requisite array of conceptual tools. This is where the construction of a RIF comes in.

And now the investigation itself is under investigation.

— President Clinton, August 17, 1998

The task of building a RIF is here approached on two fronts, structural and functional. The structural approach looks to the formal constitution of the framework itself, with an eye to the static logical relationships that potentially exist among its objective and its interpretive elements, that is, the abstract relations that can be permitted through the medium of its use to be brought to light, to be recognized on future occasions, and to be signified to a community of observant and interpretive agents. The functional approach looks to the dynamic and effective conduct of a typical reflective interpreter, with an eye to the medium of operational resources that support its activity, and it seeks to discover amid this defrayal the workings of the act of reflection that makes it all possible.

I was, at that time, in Germany, whither the wars, which have not yet finished there, had called me, and as I was returning from the coronation of the Emperor to join the army, the onset of winter held me up in quarters in which, finding no company to distract me, and having, fortunately, no cares or passions to disturb me, I spent the whole day shut up in a room heated by an enclosed stove, where I had complete leisure to meditate on my own thoughts.

— Rene Descartes, Discourse on Method, [Des1, 35]

Principals and Principles

So it is that these old cities which, originally only villages, have become, through the passage of time, great towns, are usually so badly proportioned in comparison with those orderly towns which an engineer designs at will on some plain that, although the buildings, taken separately, often display as much art as those of the planned towns or even more, nevertheless, seeing how they are placed, with a big one here, a small one there, and how they cause the streets to bend and to be at different levels, one has the impression that they are more the product of chance than that of a human will operating according to reason.

— Rene Descartes, Discourse on Method, [Des1, 35]

Once this much is said and done, one comes to a realization of the fact that a principle, as a point of logic, is not always a principal in the orders of causes, prizes, rights, or times. Even if the word principly, coined to mean in principle, is well formed in principle to serve that purpose, even if it is quickly struck from a readily available syntactic material, strikes true to the types of an adjective or an adverb, easily fills in for a much more cumbersome prepositional phrase, and fills out a formerly empty slot in the language, and even if tenders itself in print as the gentler equal to impress its point, still, it clangs in speech to the point that it is likely to be irrevocably confused with the sound of the already established word principally, and so, by dint of a certain phonological exclusion principle, the expression of its intention in this way is subject to being excised from the language, bowing out in preference to the accidental antecedents that it arrives to find already prevailing on the scene. In sum, an essentially abstract idea can be inhibited from a particular manner of elaboration on what are purely contingent, developmental, evolutionary, and historical grounds.

Here is a problem that vies with the question of the chicken or the egg, asking which of these firsts comes first: the principal or the principle. Without being able to say which first comes to mind, it may be possible to tell, in point of time, which first entered the lists of language or came to express itself in speech, at least, on the assumption that the PEP has import for this case, and that the first item to enter the lexicon blocks the full inflection of the later entry.

From this case of a broken analogy, this example of a missing point of symmetry, or this paradigm of a defective paradigm, in short, from the mere fact that the noun principle fails in its distribution of uses to fill out the available patterns and to become as fully inflected as the noun principal, it is possible to draw a surprising number of lessons:

  1. It happens that accidents of personal, cultural, or evolutionary history can abrade the facility with which one reflects on essences. Accidental properties of one's linguistic and mental constitution can supply the array of means that one has available to approach the most extreme questions, those concerned with original and ultimate meanings. Accidents of history operate to shape and polish, to impair and repair the faculties of reflection, the instruments of language and mind that one uses to reflect on questions of abstract, eternal, formal, ideal, or invariant form, to contemplate general schemes of categories for objects, and to consider matters of fundamental principle. For good or ill, an accumulation of accidents impacts on the character of one's reflection, innately marking or marring the equanimity with which one thinks about the arrays of otherwise indifferent and equally likely alternatives.
  2. A phonological exclusion principle need not apply in syntactic cases or pragmatic situations where interpreters are reliably discerning enough to adequately resolve the textual, verbal, and vocal ambiguities. For instance, it would not matter that the physical signals represented by the words principally and principly fail to be discriminated by the ear of the interpreter if the mind of the interpreter, informed by the practical and the syntactic contexts of their sundry utterances, and guided by the innate sense of what makes sense in each situation, could be relied on to chose the proper interpretation.
  3. This example of a broken analogy or a defective paradigm, and the problem of converting it to instructive uses and positive advantages, brings up the related but more general puzzle that is commonly known as the problem of learning from negative examples. By this is meant, not just being informed by defective or imperfect examples, or learning from examples that are associated with negatively valued consequences, but inducing the laws that apply to a situation from the events that never occur within it.

Returning to the topic of reflection, as approached on the structural and functional fronts …

Progress on the functional or the operational front can be made by taking up once again the informal calculus of applicational operators that I used at the beginning of the current chapter to annotate the analysis of inquiry, by taking further steps toward formalizing this calculus, and by representing the operation of reflection within it. Progress on the structural front can be made by ...

A RIF is intended to formally allow for a specific area of reflection on experience. I want to use reflection as a bona fide form of observation, in the dual sense that one reflects on happenings in the outside world and again on a range of experiences in one's inner world. Moreover, I want to treat reflection as a genuinely empirical form of observation, perfectly capable of making mistakes in the data and the descriptions it provides, but provisionally able to supply the materials that are needed for building up true theories about the reflected domains of experience.

In historical perspective, there is an array of contentious issues that generally arises in this connection to obstruct the carrying out of any such intention. At times the liberty of reflection is simply proscribed as being out of bounds for the aims of empirical and objective science, at least, if it continues to form a source of data and ideas, then the custom is never to credit the source. At times the region of reflection obtrudes so far from within the preserve of a purely private interest to impose on the realm of a properly public concern that little remains to be seen of the world outside, and no room is left over for the forum of concrete reason to proceed in its own right according to its own lights. Since the next subsection, dedicated to the phenomenology of reflection, takes up this host of issues in great detail, a brief discussion of their bearing on the task of building a RIF is all that is needed at this point.

In order to constitute a RIF as an empirical framework, in other words, as a formal apparatus that can serve to facilitate experiential inquiry, it is necessary to rehabilitate the operation of reflection as a genuine form of experiential observation, one that is capable of generating contingent, defeasible, falsifiable, or hypothetical descriptions of what it reflects on, where the field of view for reflection encompasses everything it is given or gains a power to reflect on, including activities in the external world, affective impressions and motivational impulses that arise in the realm of feeling and drives, and the more or less controlled conduct of reflection itself. To do this, it is necessary, in turn, to achieve a resolution of and to reach an understanding on two points:

  1. First, one needs to recognize that empirical necessarily implies experiential and experimental, but that none of these terms is limited of necessity to implying external, at least, not in the sense of an externality that is exclusive of all felt experience.
  2. Finally, one needs to separate the practice of reflection from the herd of incorrigibles it is liable to be confounded with on the modern scene, to sort it out from the "bad company" of its former associates and all their pretensions to (a) immediacy of inference, (b) impeccability of insight, (c) infallibility of introspection, (d) unimpeachability of intuition, and (e) incognizability of reality.

If the reader reflects that I seem to be trying to make reflection out to be a curious sort of hybrid creation, akin on the one side to primitive forms of observation, but akin on the other side to sophisticated forms of contemplation, and that this makes it the main constitutional problem of its temperament to control its own hubris in such a way that it can keep itself from weening over to excessive degrees in either direction, then the reader reflects correctly. If reflection keeps to this middle course, then, whatever its natural disposition or original inclination might be, it can still enjoy the effective qualities and formal virtues that belong to both realms of experience, mediating between the real and the rational, and joining the sensory to the intellectual.

A historical perspective also shows that the task of arrogating modest powers to reflection without reaching over into insupportable realms of imagination is apparently a difficult balancing act for the human mind to maintain. For reasons that will soon become obvious, I find it useful to describe this as the cartesian polarity problem.

Whereas other operations of mental life have to be forced to the point of examining their own conduct, even tricked into it, it is almost the reflex of reflection to reflect once again on its own action, at least, to reflect on whatever array of intermediate insights or whatever sample of partial results it finds itself able to pin down in memorable signs and texts. And yet, aside from the statement of this vacuity, it seems pointless for reflection to personify itself, often to the point of impersonating itself, and difficult for it to find anything interesting to say, without bringing in something else, some other matter to reflect on. Thus, I do not want to fall into the narcissistic trap of thinking that internal reflection, or introspection, is the only source of knowledge that is certain and true, but neither do I want to vanish in the echoistic dissipation of clinging to external reflection, or reflectances, as the only source of inspiration.

The Initial Description of Inquiry

In order to form a more cogent sense of the direction I must take from this point on, I need to make a concise review of the questions that have been raised and the assumptions that have been laid down so far. I can begin this review with the question of the Criterion, and after developing a critical theme that connects it with its antecedent topics, work backward to the questions of the Problem and the Method.

Under the question of a Criterion (§ 1.1.3) a critical assumption was taken to serve as a guiding hypothesis for this inquiry and to provide a tentative model for its conduct:

According to my current understanding of inquiry, and the tentative model of inquiry that will guide this project, the criterion of an inquiry's competence is how well it succeeds in reducing the uncertainty of its agent about its object. (§ 1.1.3).

It is time to examine this hypothesis a bit more carefully, to review the bearing it has on inquiry and the role it has in an inquiry into inquiry. In this regard, the guiding model elected here needs to be interrogated under the twin lights of how it can apply to inquiry in general while it continues to ply itself fully subject to a specific inquiry into inquiry. In its most general implications, the question is: How can any principle profess to master all inquiry whatsoever, and how can the use of such a rule pretend to serve any inquiry at all, at least, so long it waits on the outcome of its own examination and has to operate under a cloud of suspicion that is pursuant to a particular inquiry into inquiry?

To me it seems intuitively certain (IC) that the purpose of inquiry is to reduce the uncertainty of its agent about its object, and that it does this by increasing the clarity of the signs that the agent possesses with respect to the object. For future reference, let me detach the predicate of this observation and refer to it as the initial description (ID) of inquiry.

ID. The purpose of an inquiry is to reduce the uncertainty of its agent about its object, and it does this by increasing the clarity of the signs that the agent possesses with respect to the object.

This ID depicts inquiry in general in terms of its object in general and it allows for more specific inquiries to have more particular objects. And yet, as if by a manner of reflective reflex, no sooner do I express this insight in the form of an intuitively certain hypothesis (ICH) than I begin to suspect it, to have doubts about the certainty of its truth, and to worry about the clarity of its expression.

On reflection, the ID of inquiry, for all the quality of an ICH that once affected it, at least enough to make me identify with it, starts to find itself in another light, much less IC and much more H, and it begins to appear to me as a nearly indifferent object of contemplation, something else to think about, nothing more. The text of its expression, that I took the time to weave its carefully picked signs into, presents itself to my view as an alien object, composed of almost senseless characters, as if designed to ensnare my mind in a medium of false images rather than to liberate my thinking by means of a clear and distinct truth.

This array of doubts, suspicions, and worries is not so much due to the ID of inquiry itself, that I continue to maintain my sympathies with and to preserve my own recognizance of, as it is on account of and for the sake of the other notions that it raises, whose certainty and clarity it cannot rise above, or so it seems. In other words, whatever certainty and clarity may be, it seems sure that the certainty and the clarity of the ID of inquiry cannot be greater than the certainty and the clarity, respectively, of the notions of agency, certainty, clarity, objectivity, and significance that the ID of inquiry invokes, involves, and implicates. But how do I know this, and, indeed, do I really know this?

But, like a man who walks alone, and in the dark, I resolved to go so slowly, and to use such caution in all things that, even if I went forward only very little, I would at least avoid falling.

— Rene Descartes, Discourse on Method, [Des1, 39]

If the ID of inquiry marks a step that I plan to take in an inquiry into inquiry, then I need to raise the following questions about it. How can I tell if it is a step in the right direction? Expressed in other ways: How can I test the utility of this step with the information that I find available to me at my present state of knowledge, or within reach of it? How can I come to know, short of rashly staking my whole enterprise on its trustworthiness, whether it establishes a foothold on a viable path, not just marking a point on a feasible path of investigation, but lying a discrete and reasonable distance in the direction of its goal, and thus being capable of leading toward a state that is ultimately certain (UC) as to what it represents about inquiry?

If all the themes are aptly initialized, then the end of inquiry is met when a condition of equanimity, balance, or harmony is achieved between the facts IC and the facts UC, in other words, when everyone sees the point that each one is trying to make and when everyone understands the line that each one is meant to get across.

If the simple entertainment of a simple hypothesis is enough to change the course of an inquiry in an irremediable, irreversible, or irrevocable way, and in a manner that makes a pragmatically significant difference to the outcome, then all hope is lost of discovering a robust method or developing a self corrective procedure for inquiry, and thus of giving to inquiry an adaptive and evolving form. This means that inquiry is not a feasible endeavor for agents of a fallible sort unless they are capable of taking up a flexible attitude and maintaining the following sorts of stance:

  1. To contemplate a diversity of hypotheses with a reasonable measure of immunity against their actual effects, that is, while remaining moderately well insulated from the consequences these hypotheses would have in execution.
  2. To entertain a wildly incorrect but still corrigible guess with a respectable level of impunity, that is, while preserving the overall ideals of a reparable harmony in their own systems of belief and while operating without loss of ultimate geniality in the community of inquiry at large. Still, it is best not to play on forms of dissonance that do not come tempered with at least an idea of how to atone for themselves in time.

Imagine that an agent begins in a state of almost complete ignorance or near total uncertainty about inquiry, such as might be associated with the mere possession of the name inquiry or reflected by an encounter with another type of nominal pointer to the topic of inquiry in general. Against this background of original sinescience and relative to this condition of initial innocence, the ID of inquiry does indeed appear to give an impression of saying something more definite about inquiry, and thus it does seem to increase the agent's knowledge in some measure, whether in certainty, clarity, or distinctness I cannot say for sure at this point. But how can an agent tell if this appearance is real?

How can I address the array of questions "How?" that I raise as I reflect on the ID of inquiry? The only response I can think of that answers the arraignment of all these challenges is simply to continue with the inquiry itself. The ID of inquiry has something to say about the how of inquiry, expressing its suggestions in terms of the phrase that concerns itself with "increasing the clarity of the signs that the agent possesses with respect to the object". But the implicit charge of this ID, to "clarify the signs that the agent has of the object", is not entirely unambiguous in and of itself, and until it can be rendered free of ambivalence in its own right it is difficult to entertain an effective action on its behalf. On further reflection, it becomes apparent that the charge to clarify signs contains the potential of being interpreted in at least two ways, and thus, for the purposes of effective action, requires a further clarification. Consequently, toward the end of action on the charge yet another inquiry and yet another clarification, this time concerning the character of the charge itself, becomes due.

In accord with this analysis of inquiry as a process of clarification, and of clarification in turn as a process that operates on sign relations, the next few paragraphs consider various interpretations of the clarification task, initiating the process of comparing and contrasting their elements, and ultimately seeking to classify their variety. This discussion notices one general feature that all types of clarification process appear to have in common and it discerns another general feature that splits the genus of clarification processes into a couple of broad moieties or species.

Inquiry, considered as a process of clarification, is the chief way that a sign relation can grow and develop in service to the life of its agent. If not assured as the principal way, at least, while the jurisdictions of automatic adaptation, oblique evolution, and random ramification are yet uncharted and unassessed, it is probably still the most principled way that sign relations have of adapting and evolving to meet the objectives of interpretive agents in their given environments of needs and objects. By way of a general comparison, then, all reasonable interpretations of the clarification task involve the augmentation of sign relations by the addition of elementary sign relations, that is, ordered triples of the form

Treating the process of clarification as one that affects the growth and development of a sign relation, even if constrained to the medium of its syntactic domain, there is, of course, an overwhelming diversity of ways that one can imagine an arbitrary sign relation as growing through time. No matter whether it restrains its labors to the monotonic annexation of ever more triples to the masses of data already accumulated or whether it liberates the full deliberations of a discursive process, thus invoking the ebb and flow of corrective, editorial, reflective, remedial, and reversible processes, not every mode of growth or development that can occur in a sign relation has a bearing on reducing the uncertainty of an agent about an object or has the effect of promoting the clarity of the given signs.

With regard to inquiry as clarification, and clarification in turn as the evolution of a sign relation, it does not matter whether one views it as a process of exploration and discovery, taking place in a preconceived cartesian space and seeking to find clearer signs for each known object, or whether one views it as a process of creation and invention, staking out the syntactic parts of elementary sign relations following the directions of transient clarity to the signs of maximal achievable clarity, making and testing novel combinations with an eye toward present objects, and picking out the clearest indications for inclusion in one's current sign relation.

To review: Inquiry depends on clarification, and clarification depends on the augmentation or the evolution of sign relations in various ways. In order to stay within the realms of possibility that are accessible to computational processes and covered by computational models, it is best to look for varieties of clarification process that are tantamount to recursive forms of development in sign relations, those that one can contemplate being carried out by a recursively defined growth process. Even working under these constraints, there is still an amazingly large variety of different ways that the eking out of initial sign relations and the imping out of fledgling sign relations can proceed.

To expand: Inquiry depends on clarification, and clarification depends on the augmentation or the evolution of sign relations in directions that serve the interests and help to achieve the intentions of their agents. If this is true then it must be possible to say something about the ways that sign relations figure into the interests and intentions of agents. In this connection, the desire to relate sign relations to the objectives of interpretive agents touches on the topics of what are normally called the normative sciences, namely: aesthetics, ethics, and logic. Since the style of pragmatic thought that I am using puts a distinctive twist on the way that these three disciplines are regarded in relation to each other, it is necessary for me to attach a slight gloss on this point. Along the way, related concerns about the topic of "justification" make a natural appearance, and this allows me to set down some initial thoughts about the forms of justification (FOJs) that I contemplate using in this work.

An Early Description of Interpretation

Insofar as the analysis of etymological and other associations existing among familiar and other words can lead up in time to a proper analysis of the underlying concepts involved, the discussion just given can be taken in the spirit with which it is offered, as a body of suggestions about the derivation of an abductive faculty from an advisory function. But insofar as the sole themes that exhibit any novelty about them are easy to lose in the cacophony of verbal clutter that frequently ensues, it may be advisable, one last time, in as summary a refrain as possible, to recapitulate the chief points of originality to which this work gives fanfare. The originality I advert to appears to arise from Aristotle:

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (semeia), are the same for the whole of mankind, as are also the objects (pragmata) of which those affections are representations or likenesses, images, copies (homoiomata).

(Aristotle, On Interpretation, i.16a4–9, p. 115)

Of all the early intimations of the sign relation that have come down to the present time, this depiction is the clearest and the fullest, in the level and the lucidity of the details that it articulates, of any I know. There will be ample occasion to return to its ideas on a recurring basis throughout the rest of this work. For the moment, there are especially a couple of themes, traceable to this locus and running through its text, that I want to draw out and to emphasize, not only for the message that they convey for the sake of the immediate inquiry, but for their manner of bearing it into the current context of applications.

The assumptions and implications of Aristotle's account that are relevant here are first listed briefly, after which all of the points in turn are explored in full detail.

  1. Assumptions of constancy
  2. Compound of fractures
  3. Cognitive coin/currency/ideas are derivative in relation to affective basis/realm/ideas
  4. Concrete material presented by emotions: affects and motives

On Aristotle's account, there is a special path of relationship that can be traced in either direction between the pragmatic objects (pragmata) that attract, concern, or interest the mind and the symbolic signs that the mind exploits to express its feelings or its thoughts, and this route passes through the pathemata, literally, the affects that these objects impress on the mind (psyche). Picturesquely, the image overall is that of a coin, which is cast, minted, or stamped in a die, mold, or template and then split into fragments that serve as tokens of mutual recognition if and when they are ever again caused “to be cast or thrust together” (symballein). Aside from the nuance that distinguishes artificial and cultural symbols (symbola) from biological and natural signs (semeia), the signs that mediate peoples' cognitive processes can be seen to arise as fragments of likenesses of their objects. And so it is appropriate to dub this picture of sign relations as the iconoclastic theory of signs.

A reasonably useful correspondence is formed between the sign relations of Aristotle and Peirce, respectively, by fashioning the following rough linkages:

  1. Associate the categories of objects in both accounts.
  2. Collapse for the moment the distinction between signs spoken and signs written and put them together in association with a maximally generic class of signs.
  3. Incorporate pathemata as a particular species of mental conditions, determinations, or entities, that is, as a special class of modes of bearing and modes of being affecting the mind, and put them in association with a special class of interpretant signs.

It is only the last part of this likely correspondence that leads to much difficulty and requires a closer examination to untangle its complexities. In accord with the lines of its suggestion affections and impressions are brought together and given their places within a maximally generic class of affective states, cognitive conditions, conceptual formations, ideal forms, motive dispositions, potentially existent states of mind, and virtually existent things in mind. Under these and other terms, a catch-all category is formed that ranges through the entire panorama of mental dispositions and mental entities, encompassing the full spectrum of determinations in the medium of the mind, all of which, for maximum convenience and generality can be referred to most simply as ideas. Granted this endowment of ideas, the suggestion is made to associate all of these ideas, at least, for the purposes of a formal treatment, with the pragmatic domain of interpretant signs.

This recasting of Aristotle's model of interpretation into the molds of Peirce's theory of sign relations, given that the former retains a body of concrete material that the latter casts off from its abstract forms, barely roughs out an interpretation of the theory in terms of the model. And yet this interpretation is still a bit forced in the character of its suggested associations, and it still faces a number of objections to the likelihood of its truth, its utility, or its other potential virtues ever becoming actualized. These objections indicate a daunting array of more obscure obstacles that line up behind and loom into the distance beyond the one or two more obstinate obstructions that make themselves obvious at present, all of which inveigh, inveigle, and weigh against carrying through the completion of a viable work along the lines projected.

Many of the problems with this trial interpretation, in it stands in its currently tentative state of development, can be traced to the fact that I have not fully disentangled the formal and the material aspects of the category of pathemata, or else, I have not distinguished the properties they display by virtue of their roles in a relation from the properties they exhibit by virtue of their inherent natures. Indeed, as the issue now appears to me on reflection, I have not examined thoroughly enough the relation between the two distinctions I just supposed, that between form and matter, and that between relation and essence, nor even asked how and whether any such distinctions can be made on a reliable basis.

One of the things that one means by matter is the mass of instances that one uses to illustrate a common form. In this sense of the terms, the distinction between form and matter has been implicitly relevant to this work, if not especially salient within it, ever since it entered on the course of discussing the process and the product of formalization in terms of a selection of concrete examples. One of the reasons that one chooses to present a formal subject in the medium of its own materials, that is, by means of examples, is that this very form is not yet grasped abstractly enough, that is, by means of clear and distinctive definitions. This choice can be due to the presence of difficulties and obstructions, on the part of the presenter or the presentee, that stand in the way of a more comprehensive form of understanding being achieved all at once.

In the light of these considerations, one can see that this discussion has stayed immersed in the matter of its topic for quite some time now. Indeed, it is fair to describe the current trajectory of this inquiry as “a matter in search of its form”. A distinction between form and matter, if it matters to anyone, is not already finished, but yet to be formed. And yet, no sooner does it form itself in a particular way than it seems, at least with regard to itself, that it was always meant to be that way. And so one encounters a form of distinction that evolves in coincidence with a form of life, taking the essence of its own formation to be a kind of synthetic a priori. Several factors now conspire to make the relevance of this distinction become more acute at this point.

The whole class of affections, cognitions, dispositions, impressions, and motivations of the mind that I include in the category of ideas is the smallest collection I can form that remains connected in its associations, that is, as a class of signs whose interpretations lead in and to itself. But giving this host of ideas a fixed and a simple name, no matter how well it means to unify the manifold of impressions under a simple term, and no matter how well it manages to organize the array of associations under a specious concept of unity, does nothing to dispel the blooming complexity, the boiling diversity, the booming heterogeneity, and the bubbling incongruity of the ideas themselves, which seem to spite every attempt to incorporate their livelier qualities and to regulate their ongoing varieties in the almost purely nominal forms of integrity that mere words can provide.

A purely formal study of sign relations could proceed unhindered from this point, at least, unencumbered by the material aspects of its subject, if only it had a clear definition of what a sign relation is meant to be. And yet, from a purely formal perspective, almost any axioms are worth pursuing, as long as they pick out an interesting class of formal objects and even so long as they manifest a certain elegance in their own right.

It is frequently claimed that the virtues of elegance and interest are qualities that abstract axioms and formal objects can possess quite independently of their anchorage in, bearing on, connection to, or any other crassly pragmatic relationship with a ground, such as might be constituted by an additional application to a concrete subject or by an extraneous utility in a practical matter. I am tempted to agree, though I suspect that there are further difficulties and greater paradoxes still hiding within the word independently. In any case, if the axioms that one selects to characterize sign relations are intended to have empirical applications, objective justifications, and practical motivations, to be justified by reasons that go beyond the contemplation of abstract forms for their own sakes, to be motivated by purposes that reach beyond the purer forms of aesthetic enjoyment, the self justifying and self seeking forms of entertainment, exercise, experiment, and exploration, or the riskier forms of speculation against the chances of their future utility, and until the essential features of a general definition can be grasped, it will be necessary to preserve the data of their material occurrences for whatever insight it can afford into the qualities that determine the worth of signs, and it will be prudent to continue mining the material evidence for exemplary instances of their actual use.

Before this discussion can proceed much further, there are a couple of seeming distinctions that I find myself in need of trying to make real, or otherwise of knowing the reason why they cannot be made in reality. There are reasons why I emphasize the seeming and trying aspects of this situation:

  1. It is not entirely clear to me whether these apparent distinctions, as commonly described and as usually intended, are capable of being maintained in reality, as opposed to what little significance they have while posed on the grounds of mere imagination.
  2. Even if the corresponding forms of distinction are capable of being established in a clear, a proper, and a successful manner, it remains an open question to me at this point how this ought to be done in practice, and the experiences I have had in previous attempts lead me to believe that each of these tasks is far more difficult than it appears at first.

In the process of carrying out this inquiry I find it necessary to make a type of rhetorical transition that can be cast in the stereotyped form: “In the process of doing x I find it necessary to do y.”

Descriptions of the Mind

In the process of interpreting Aristotle's text on interpretation as an early account of sign relations, I invoked a number of distinctions that appeared to be called for to guide the interpretation of the text and to form what I sense to be the most reasonable interpretation of its terms. All of these distinctions are drawn from common practice and are usually assumed to be easy to make in any case. And yet, on reflection, I find that I have little or no faith in their advertised properties or in my right to take them for granted.

For instance, consider the distinction between form and matter. When I reflect on the question of how and whether I can make this distinction, I find myself hard pressed to tell whether the distinction itself is a formal distinction, a material distinction, or something else entirely. Trying to pin it down between the first two cases, it seems to be either, or both, and yet neither, depending on the light that I choose to throw on the question, to consider the alternatives by, and to interrogate the usual answers under. If it is either, then the significance of the other is diminished to nothing, as all that the opposite side of the divide can amount to is sliced away by a gradual slippage down the apposite slope, until the significance of the entire distinction appears but to disappear. If it is both, then it violates the exclusiveness that is usually assumed to hold between the two sides of the distinction. If it is neither, then it invalidates the exhaustiveness that is usually assumed to apply to the distinction between form and matter. Whatever the case, I am called on to assume something unusual. Indeed, it seems I am forced to recognize a tertium quid or a third something, in other words, an option that can supply a novel alternative to the choice between form and matter, a category that the Greeks only hint at obscurely or obliquely allude to under the name of an entelechy, and something that I can well nigh call the interpretive case.

By way of guidance in this innovation, or this novel effort to capture interpretation in and of itself, I adduce two texts that help to show the way that the relationship between form and matter has often been seen.

The first text illustrates the use of this distinction in the context of a psychological investigation.

We describe one class of existing things as substance (ousia); and this we subdivide into three: (1) matter (hyle), which in itself is not an individual thing; (2) shape (morphe) or form (eidos), in virtue of which individuality is directly attributed; and (3) the compound of the two.

Matter is potentiality (dynamis), while form is realization or actuality (entelecheia), and the word actuality is used in two senses, illustrated by the possession of knowledge (episteme) and the exercise of it (theorein).

Bodies seem to be pre-eminently substances, and most particularly those which are of natural origin; for these are the sources from which the rest are derived.

But of natural bodies some have life and some have not; by life we mean the capacity for self sustenance, growth, and decay. Every natural body, then, which possesses life must be substance, and substance of the compound type.

But since it is a body of a definite kind, viz., having life, the body cannot be soul, for the body is not something predicated of a subject, but rather is itself to be regarded as a subject, i.e., as matter.

So the soul (psyche) must be substance (ousia') in the sense of being the form (eidos) of a natural body (soma), which potentially (dynamei) has life. And substance in this sense is actuality (entelecheia).

Aristotle, De Anima, II.i.412a6–412a22

The soul, then, is the actuality of the kind of body we have just described. But actuality has two senses, analogous to the possession of knowledge and the exercise of it.

Clearly actuality in our present sense is analogous to the possession of knowledge; for both sleep and waking depend upon the presence of soul, and waking is analogous to the exercise of knowledge, sleep to its possession but not its exercise.

Now in one and the same person the possession of knowledge comes first. The soul may therefore be defined as the first actuality of a natural body potentially possessing life; …

So one need no more ask whether body and soul are one than whether the wax and the impression it receives are one, or in general whether the matter of each thing is the same as that of which it is the matter; for admitting that the terms unity and being are used in many senses, the paramount sense is that of actuality.

We have, then, given a general definition of what the soul is: it is substance in the sense of a formula; i.e., the essence of such and such a body [a natural body potentially possessing life].

Suppose that an implement, e.g., an axe, were a natural body; the substance of the axe would be that which makes it an axe, and this would be its soul; suppose this removed, and it would no longer be an axe, except equivocally. …

If the eye were a living creature, its soul would be its vision; for this is the substance in the sense of formula of the eye. But the eye is the matter of vision, and if vision fails there is no eye, except in an equivocal sense, as for instance a stone or painted eye. …

The waking state is actuality in the same sense as the cutting of the axe or the seeing of the eye, while the soul is actuality in the same sense as the faculty of the eye for seeing, or of the implement for doing its work. …

It is also uncertain whether the soul as an actuality bears the same relation to the body as the sailor to the ship.

Aristotle, De Anima, II.i.412a22–413a9

The second text illustrates the use of an analogous distinction between form and matter within the context of a logical investigation.

And how can one know the certainty of demonstrations except by examining the argument in detail, the form and the matter, in order to see if the form is good, and then if each premiss is either admitted or proved by another argument of like force, until one is able to make do with admitted premisses alone?

Leibniz, Theodicy, [Leib, 89]

Take once again the distinction between form and matter, and allow me to say that this distinction is interpretive in character or nature. This gives me the option of saying that it is formal in some cases but material in other cases. It can all depend on choice and circumstance. If I interpret it as formal then certain things follow. If I interpret it as material then other things follow. But I can rest with calling it interpretive, leaving it to the moment to actualize what is most fitting. If I interpret it as interpretive, which amounts to a way of holding any further decision in suspense, then I am choosing to remain all the while constantly aware of the circumstances and the conditions that affect the actualization of this distinction as either form or matter, or else to experience the consequences of failing to do so.

But then, on marking any distinction, a moment's reflection brings me to ask: “Who or what makes this distinction that I mark?” And whether I say that it is I, or you, or whoever else agrees in marking it with us, whose activity constitutes the making of this distinction, or whether I think it is someone other or something else that makes this distinction that all of us merely mark and remark, and whether it is decided in the end that the maker is always coincident or sometimes distinct in regard to the marker, then I find myself still having to ask: “How and why is this distinction being marked, in particular, what side or sides, with respect to each other, are its maker and its marker on?”

For these reasons, it is necessary to use an indirect strategy in order to approach the questions of these distinctions that I want to consider. The ostensible distinctions are first described in very rough terms and introduced in the ways that they are naturally and usually thought of. Thus, without taking for granted the clarity, fidelity, sensibility, or validity of their formulations, the distinctions are initially presented in the terms by which they are commonly indicated, intended, suggested, or regarded as being established. This manner of approach is demanded in order to keep from assuming, if at all possible, the prior worth of the very formulations that are being examined and tested, and it tries to make it a separate question whether these intentions to distinguish can continue to be maintained in the very same terms and formulations. Once this preliminary investigation is carried through to a conclusion, positive or negative, I can then return to analyze more carefully and more generally the whole process of making such distinctions.

  1. The rough idea of one distinction is to sort the properties of things into two categories: the “properties that things have” versus the “properties that things are given”. More specifically, and in reference to a typical agent, the former class is intended to include the properties that things have, in and of themselves, independently of any agent, whereas the latter class is intended to include the properties that things are given by an agent. Now, it is clear that the common usage of words like have and give leaves a wide range of ambiguity still remaining that needs to be resolved by the right interpretation. (essential vs imputed properties)
  2. The rough idea of another distinction is to sort signs and ideas, no matter whether they are considered severally or together, into two categories: “signs and ideas as they actually occur” versus “signs and ideas in an abstract vacuum”. More specifically, and with reference to a particular class, community, or population of interpretive agents, the former category is intended to include signs and ideas as they actually occur among these agents, for example, as actualized, embodied, implemented, operationalized, or realized, whether consciously or not, among human beings, whereas the latter category leaves unanswered the question of embodiment and is therefore open to any suggestion as to how these signs and these ideas are intended to be conceived. (empirical and material vs theoretical and formal signs and ideas)

[Alternative text?] The form of distinction that I need at this point tagging “signs and ideas as they actually occur”, for example, as actualized, embodied, and realized, whether consciously or not, in human beings, and leaving “signs and ideas in a vacuum” untagged by any special mark.

Suppose I need to draw a distinction, that marks out a special dominion from its more general domain, but I want to be careful to emphasize the inclusion of the species within the genus, as much as their separation. So let me paint the distinction this way, that it overlays a distinctive tincture on the species but not on the genus, and thus it highlights the special dominion as it resides within the grounds of its generic domain. Given this special form of distinction, it deserves to be given a name. It is fitting to describe it as a partial functional distinction (PFD), by way of recognizing the partial function that assigns a special value to the species, but not necessarily any value to the rest of the genus. A better nickname, more compact than the verbose description and more mnemonic than the acronym, is served by coining the term distincture. In this context, let the species that is distinguished by a particular distincture be referred to as the content of that distincture, and let the remains of the genus be referred to as the discontent or even as the distent of that distincture. Notice that a distinction, as it is ordinarily understood, has at least two distinctures associated with it, where each especially values what the other does not necessarily value, and where the content of either one is the discontent of the other one. It should also be noted that I have not said anything yet about these partial functions being computable, only that they are conceivable.

I use the terms figure, ground, and [?] to indicate the species, the remains, and the genus, respectively, of a PFD or distincture. Notice that the figure and the ground are not treated symmetrically, but that each element of the figure is given an extra feature, a mark of attention or a tincture of distinction, that it does not have before the distinction is made, even if it is nothing more than a recognition or a representation, explicitly given by an agent to an element, of a feature that the element already possesses. Notice the asymmetry that occurs between the treatment of the figure and the treatment of the ground. Given this special form of distinction, and appreciating this asymmetry, …

There are several ways of studying sign relations that avoid the realm of affects and motives, at least, they seem to get around it for a while, thereby obviating the problems of delving into this refractory material. A purely combinatorial approach …

It seems to me that every impression has something in the way of an impulse about it, in other words, that every affective condition is analogous, equivalent, or identical in some sense to a motive disposition. For this reason, I comprehend the category of pathemata to comprise a generic class of double duty ideas that one is free to interpret in either a passive or an active sense, in short, as affects or motives, respectively. To sum up the understanding of these terms that I reach at this point: The category of pathemata, encompassing both affective impressions and motive impulses, can be treated as a species of ideas. Ideas constitute a genus of mental conditions, dispositions, or entities that are theoretically tantamount to mental signs. Whereas ideas can be understood as signs in the mind, it is perhaps best to regard them as signs of the mind, or even as the mind in signs, that is, as all the ways that the mind conducts itself and continues to live in signs.

Affects and motives, by way of giving them a conventional placement in the larger class of ideas that inhabit the mind of a particular agent, can be seen as belonging somewhat closer to the body of their agent, since they are especially concerned with maintaining the health and the life of that body, and they preserve an interest in the viability, the vitality, and the overall well being of the particular agent concerned. Accordingly, whatever else the signs called pathemata are about, they are partly about the body of functions and structures that are required to maintain their agent in a viable form. No matter what other objects their signals of conditions and their suggestions of actions may have, they are partially intended to serve a particular form of materially constituted agent and to help it preserve its own accustomed nature.

To form a better sense of how affects and motives fit within the category of ideas, or mental signs, and of how they can be located within a suitable domain of interpretant signs, I give these pathemata the somewhat arbitrary collective name of motives or themes (MOTs), intended to suggest little more than the common coin of emotions and motivations, and then I quickly divide this overly bulky, burdensome, and burgeoning class of meanings into three subdomains:

  1. The ostensibly ultimate interpretants (OUIs) comprise whatever aspects of affirmative and definite sense are available to these MOTs. They constitute the ultimate meanings that appear to be achievable and affirmable at a given moment in the development of an interpreter or in the evolution of an interpretation. At any given time, they seem to be the ultimate interpretants that all properly directed mental processes are tending toward, and yet none of this stands in the way of diverse interpretants being taken as the ultimate achievables at other times.
  2. The almost never objective notions (ANONs)
  3. The never objective notions (NONs)

Talk of mental impressions, whether taken literally, as being the forms that objects are imagined to impress on the mind, or taken figuratively, as bearing the information that objects are recognized to transfer into the medium afforded by the mind, is frequently criticized as a metaphor that leads to many false, misleading, specious, or spurious impressions. For instance, the very idea of a mental impression is often censured on the grounds that it promotes an offshoot of illegitimate instructivist notions, themselves the outgrowth of commonly discredited essentialist doctrines, teaching something to the effect that objects have the power to “instruct” the mind about their essential natures or true properties, thereby directly, literally, and materially imbuing, informing, infusing, and “instructuring” the mind, not just about their actual characters, but fully in their ideal forms and wholly with their real natures.

Obviously, construing the word impression in that strict a fashion, hobbling it to senses that remain as naively literal as they favor the purely material, is bound to raise a welter of absurdities in the mind. The notion that an object itself can provide instruction in its nature is not invidious in itself. It is only the refractory implication that often accompanies it, the uncritical, unexamined, and unreflective assumption that this degree of directness affords a quality of infallibility to what nature teaches, insofar as its lessons can be imparted to the finite mind. Regarded in this light, the fallacies imputed to essentialist doctrines and instructivist notions are not essential to the elements of validity that a charitable interpretation could find in them, but only variations on the same old theme, the pervasive illusion that any mode of infallible cognition is available to a finite mind.

What can be said about this fundamental fallacy, to wit, the presumption of infallibility that so persistently appears to affect the minds of the very agents who least deserve to claim its prerogative with any justice, that so frequently appears to remain as incorrigible as it is devoted to preserve its unregenerate state? If one inquires into the origin of this delusion and into the source of its effects on the mind, then the issue can be divided into two branches, distinguishing the mechanisms of its operation from the motives of its enterprise, the how from the why. When it comes to the mechanisms that are capable of accomplishing the effects of this illusion, it seems to be through the creations of the imagination and the ingenuities of speculative thought, in short, through the inventions of wishful thinking that it manages to maintain itself. When it comes to the motives that can be held responsible for mounting the measures of effort that the work on this web of deception requires, they seems to harbor their most fugitive aspiration in the overwhelming need to find some perfection somewhere. This is tantamount to a desire or a disposition, affecting the conduct of agent who falls subject to it, that expects a promise of perfect certainty at some point or other, and thus insists on placing a measure of absolute trust in a point of dogma or a rule of method.

Wherever there is an prevailing need to believe that one already knows, to think with respect to a question that the answer is already found, then there will be no genuine inquiry occurring in that direction.

If it pertinent to characterize the kind of agent that behaves this way, it is almost as if the agent imagines that it cannot actually be, neither begin to act, nor continue to act, without such a guarantee of certainty. But what kind of surety would that be, but another specious certificate? Perhaps this character of conduct is due to an excessive sensitivity to the “irritation of doubt” or an exaggerated intolerance for existing in a state of uncertainty. But no amount of finite intuition can purchase an instruction so authoritative that it can ever be interpreted as infallible. In summary, if essentialism and its oftentimes corollary instructivism are interpreted perversely, that is, taking at face value the excessively literal images and the extremely material senses that their underlying thematic metaphors are able to bring to mind, then they are definitely capable of leading to ridiculous conclusions, but if they are interpreted in figurative and formal manners, then there may be a sufficient amount of interpretive elbow room for them to convey a measure of sense.

In this work I intend to give a liberal interpretation to the issue of what kinds of forms are able to impress their shapes on the mind. I consider it likely that they can take the forms, among other things, of probability distributions, in other words, patterns of amplitude, density, frequency, intensity, or likely value that can be predicated of events in the world or impressions in the mind with equal felicity. If these forms are still too concretely cast, then still more formal forms are available. Abstracting from the contents of a strictly probabilistic interpretation, one is left with functions from domains of elementary events articulated in the world or existential experiences affecting the mind, respectively, to ranges of a common value, the height of which has the sole utility of indicating to different degrees the diverse elements under its dominion. In the resulting spaces of functions, forms of dispensation or patterns of distribution accumulate over the domains of external events and the domains of internal experiences, respectively, like crowns of foliage above the branches of the corresponding trees. It is trees like these, nothing more literal, that provides the material for mental impressions. In summary, the medium of functional forms is able to furnish a common ground for the exchange of information between events and experiences and to supply a mode of comparison that connects any domain of objects with any domain of ideas.

Granted the liberality of this interpretation, and given the looseness of this resulting constructions, while recognizing the general fallibility of all the mind's affections and impressions, and also remembering that the essences of some substantial objects are formal, relational, or structural rather than absolute, literal, or material, the force of common objections to essential instructions is blunted or diffused on these points, that is, the potential charges of essentialist and instructivist fallacies become defused in their application to these forms of distributed interpretation.

Given that reasonable interpretations are available for the language of mental impressions, that serve to make talk about mental impressions at least potentially sensible, then what explains the very real problems that nevertheless continue to arise from this usage? As far as I can detect, the real problem with the supposition of an instructive mechanism of transfer is a steady bias, arising especially in certain corners of the modern scene, toward material rather than formal interpretations of the forms, the patterns, or the shapes that are taken as being impressed on the mind.

Of Signs and the Mind

In the process of trying to clarify my initial description of inquiry, I worked my way back through several modern animadversions, credulous and critical at turns, to an original classical source for many of the ideas that are involved in it. In the process of attempting to understand this text, encountered as a foundation stone in the discussion of sign relations, I found myself invoking, almost reflexively, a number of distinctions, for instance, that between figure and letter, as they are used to mark a manner of interpretation, and that between form and matter, as they concern the content of an indication, and each distinction in its turn seemed to be necessary just in order to outline a sufficient indication of what I sense to be a proper reading of this text.

But the mere formation and the occasional invocation of these words, no matter how familiar the sound of them, is of little benefit to my reader if I cannot explain the sense of them, whether long established meanings or any new gleanings that I intend, and the instrumentality intended for these distinctions can be of little use to anyone unless I can say, with regard to each conceivable distinction, how it is made or how I make it. In accordance with this reflection on the making of distinctions, I am thus led to ask: “Who makes these distinctions, and how are they made? Are they made before us, by us, or after us?”

I think I began innocently enough, with no predominating desire either to dispatch or else to vindicate any particular line of thought, but simply to trace the effects of certain ideas, and this means tracking them down to their sources, in whatever places they are to be found, whether ancient or modern, as well as trying to deduce or to foresee their consequences in theory or in action, whether for good or for ill. And now this form of investigation, more like a process of divestiture, brings me to an array of questions that I have only the slightest clues how to answer.

All of the leads that I do have arise from noticing the things that are left still lying about, the remains of the case that led to the inquiry. This includes, beyond the intentional products of focal investigations, the artifacts of analysis that still disturb the development of a clear and complete picture, the circumstantial evidence that fails to fit my nearest approximation to the facts, and the incidental residues that are supposed to have their sole function only in servicing the machinery of method, and yet that seem to litter the grounds around my present site.

For example, it was among this array of clutter on the workbench that I first noticed the distinction between form and matter. It appears as an element or tool that I have been using all along without much reflection on its qualities. And yet there is nothing simple in the way it appears, on the one hand, as a constituent of construction, on the other hand, as an instrument of interpretation. And then, the moment I start to reflect on it, to become aware of the contingent facticity of the distinction, as if for the very first time, I find I must confess that I have lost all my formerly implicit faith in the trustworthiness, the unquestioned utility, and the ultimate validity of even this apparently innocuous distinction. There is nothing then to do about it but to begin again, to examine the worth of this now hypothetical distinction, to see whether the old trust in it can be reconstructed, whether a new justification for it needs to be devised, whether anything like it has to be entirely dispensed with, or whether alternative forms of distinction and even much different types of relation are required to take its place.

Is it conceivable that the proper application of these bits and pieces to themselves and to each other can lead to a reconstruction of the rationality desired?

For instance, consider the distinction between form and matter.

No matter what distinction forms the interest of the moment, there is that which discerns, draws, finds, follows, grasps, makes, sees, or seizes the distinction in question, an experimental agency that might as well be called an interpreter, a maker, or an observer of that distinction. With regard to any form of distinction, the agency of a distinguisher or a former is a role that seems to suit what the Greeks fairly often described, but just barely hinted at, under the name of an entelechy. In general, this is a somewhat mysterious designation, stemming from a complex of terms whose various connotations are commonly translated as actuality or reality, and often as actualization or realization, seeming to suggest actualizer or realizer for the duty of this agent. Sticking more literally to its etymology, the function of an entelechy can be taken to mean “that which has or is its end in itself”, and thus “that which exists for its own sake” or “that which is complete as it is”. Whether the interpreter actively creates the distinction as it is drawn or passively discovers the distinction as it is traced is not yet the issue of interest, and I leave this matter to a future distinction.

The relevance of the distinction between form and matter can be traced, not solely by way of illustration, to another passage from Aristotle:


One should not let the phrases tertium quid or third something lead one astray, going so far as to think that an additional essence, a new kind of material, or a novel substance is implied, when it might be only a third way of being, mode of existence, degree of freedom, dimension of motion, or an extra role in a relation that is actually required.

To this seminal account of interpretation the pragmatic theory of signs adds an array of general and specific elaborations, equipping it with a fully developed corpus of formal, instrumental, and material features. Since the pragmatic line of development is in some sense an alternative track to what is usually called the modern line, the naive enlightenment, or the cartesian tradition, and yet shares many aims and basic methods with this still current mode of inquiry, it is necessary to distinguish these different trends, to detect their different impacts on the present scene, and to discern their different imports for the future of inquiry. The accidental, intentional, and specific differences that the pragmatic theory of sign relations, in its currently developing form, is able to deploy over and above the ancient account, along with the differential circumstances that exist in the context of its present day applications, are taken up next, starting with the most salient augmentations and the most significant extensions of its overall lines of growth.

Some of the most important general features that mark out the pragmatic theory of sign relations from its original material are instrumental in character and arise largely due to changes in the technological base, formally speaking, between the ancient and the present times, that is, by innovations in the formal languages and the technical methods that are made available for carrying out the discussion. Three of these general instrumental features are taken up next.

  1. In conformity with the modern facility for thinking of relations in general in extensional terms, as collections of ordered n tuples of domain components that belong to the relation in question, current versions of the theory of signs render it easiest to think of each given sign relation as a particular collection of ordered triples. Elements of a sign relation are called elementary sign relations (ESRs), and the data of each given element of the sign relation can be represented as an ordered triple, of the form that names its object, sign, and interpretant, respectively.
  2. Among the other props on the modern stage, the pragmatic theory of sign relations can make especially good use of the bounteous logics of relations and algebras of relative terms that are currently available, as expressed in any one of several symbolic calculi with approximately the power of predicate logic. Indeed, many of these algebras, calculi, and logics of relations received their first “modern&redquo; formulations in the work of C.S. Peirce, and in the very process of trying to deal with the problems presented by the classical theory of signs. As it happens, this coincidence of origins and this parallelism of derivations may help to account for the appearance of a quality of pre-established harmony that is presently manifested between the general subject of relations and the special subject of sign relations.
  3. Developments in other fields in the intervening times have caused the prevailing paradigms to shift a number of times. For starters, the lately recognized inescapability of participatory observation, and the multitude of constraints on knowledgeable action that the necessity of this contingency implies, that ought to have always been clear in marking the horizons of anthropology, economics, politics, psychology, and sociology, and the phenomenological consequences of this unavoidability that have recently forced themselves to the status of physical principles and tardily made their appearance in the symbolic rites of the attendant formalities, against all the fields of reluctance that physics can generate, and in spite of the full recalcitrance that its occasional ancillary, mathematics, can bring to heel. These cautions leave even the casual observer nowadays much more suspicious about declaring the self evident independence of diverse aspects and axes of experience, whether assuming the disentanglement of different features of experiential quality or presuming on the orthogonality of their coordinate dimensions of formal quantity, for instance, as represented by the aspects of particles versus waves, or the axes of space versus time. Features and dimensions of experience that appear as relevant or arise into salience at one level of action, exchange, or observation can disappear from the scene of relevant regard at other stages of participation and weigh imponderably on other scales of transaction. In relation to one another, aspects and axes of experience that appear unrelated just so long as they are considered at one level of interaction and perception may not preserve their appearance of indifference and independence if the scales of participation under consideration are radically shifted, whether up or down in their order of magnitude. As a result, the sort of consideration that makes a line of experience conspicuous as it falls on one plane of existence is seldom enough to draw it through every plane of being. In a related fashion, the brand of consideration whose bearing on an intermediate scale of treatment causes one to regard two features or dimensions of experience as moderately independent or as relatively orthogonal is rarely ever relevant to all levels of regard and is almost never enough to justify one's calling these aspects absolutely independent or to support one's calling these axes "perfectly orthogonal".

Next, I examine the more specific features of the pragmatic theory of sign relations, focusing on attributes that are augmented in the degrees of their development and that acquire a distinctive emphasis along with the extension and growth of this theory. These features happen to be material in character, that is, they concern the contents of individual sign relations, affecting the aspects of relational structure and the orders of relational complexity that become especially conspicuous from the pragmatic point of view. Two of these specific material features are taken up next.

  1. Direct relation between objects and signs.
  2. Irreducibly triadic sign relations.

A few more things can now be said about the conditions that are usually taken for granted in the theoretical use of sign relations. Although it is often the case that the structure of the object domain is marked for reconstruction, part for part, in the partition of the syntactic domain, as one says, in the divisions of its quotient structure, or equally, in the structure of its semantic equivalence classes (SECs), which are also called its semantic orbits, it is advisable not to imagine, except in the most abstractly artificial and purely formal cases, that an object is “nothing but” an orbit of signs. In every situation of concrete or practical interest, the object domain is something that has a real existence, one that is independent of the syntactic domain to some degree, and to a degree of qualified independence that can be specified, for example, as absolutely, moderately, or relatively. That is, an object exists in a manner that is more or less independent of both the signs and the interpretants that are used to talk and to think about it, as one sooner or later discovers in any real case where one is tempted to ignore the implications of this fact.

But this explanation of the status intended for objects only serves to elevate into prominence the subordinate question: What is meant by the relation independent of? Outside the realm of mathematics, where the necessity has long been recognized of declaring one's independence in the form of an explicit and public definition, one that makes clear the sense of the term that one plans to uphold, this is an issue that still manages to incite an uproarious confusion of obvious claims and often just as obvious counter claims, each of which is just as insistent in what it attributes to the terms of its relation as the actual basis for what it considers evident is kept implicit.

One thing does appear certain, at least, once the issue is addressed: Whatever it means, and however it is qualified, the relation of being independent of does not mean a relation of being not in relation to. After all, did I not just call this, with all due justice, a relation? Indeed, independently of all questions of independence, the very notion of there being a relation not in relation to is a self cancelling nullity. Perhaps the closest that one can approach to conceiving of relations like not related to or not a relative of, in short, perhaps the simplest analogues or approximations to such a relation that one can devise are: considered as not in relation to or treated as not in relation to, prompting the questions: considered by whom? and treated by whom?, all of which goes to make it manifest that a triadic relation is the minimal support needed for any such brand of speculative relation.

In trying to reach a form of relation that is minimal in a certain regard, the analysis comes to a point where it is forced to reverse its direction and to synthesize a complex relation, one that possesses a higher arity than might be expected of a structure intended as a primitive rudiment. What is ultimately suggested is a triadic relation that formulates the idea of a consideration, a regard, or a treatment. This involves an agent that acts as the overseer of the consideration, the regard, or the treatment in question along with a couple of other entities that fall in a dyadic relation to each other under this consideration, this regard, or this treatment. The way to treat this triadic relation as sparingly as possible, in regard to the level of consideration that is assigned to it, is to let the agency of this oversight ignore as much as it possibly can about all the relations that conceivably exist between the overseen pair, the couple of agents, entities, or objects that fall within its purview. Thus, the least that the overseer can manage to do is to mark a relation between the other two parties, without codifying, conveying, recording, or retaining any information about the particular kind of relation it is. At any rate, this is the best interpretation that I find myself able to contrive at present for “ regards as not in relation to ”.

The preceding analysis may appear to lead up to a trivial point, but the argument just recounted is formally identical to a demonstration that is basic to pragmatic thinking, namely, that “we have no conception of the absolutely incognizable” (Peirce, CP 5.265). Whether or not one wishes to say that there are such things as the “absolutely incognizable”, we have no conception of them. Any concept that we do have cannot truly be a concept of them, that is, it cannot be held to be true of them, since this all by itself would amount in fact to making them cognizable. The idea that a successful conception is intended by its very nature to result in a true concept is critical and crucial in this regard. If one merely wants to point out the triviality that we can have false concepts of anything we please, for example, the false concepts that are attached to the verbal formula “absolutely incognizable”, then it is easy enough to stipulate that we are likely to have false conceits and misleading concepts about very many things indeed.

Since the pragmatic theory of sign relations welcomes partial symbols and verbal formulas of every species of description as well as mental impressions, concepts, and ideas of every genus and level of generation into the same broad class of entities that it takes as signs, the idea of an object that is not the object of a sign imparts a formal impression within its material that is identical, or at least indistinguishable in the structure of the relations that it suggests, to the idea of a relation that fits the verbal formula or the specious specification not in relation to. A rigorous critique of these very ideas is required in order to prevent their specious impressions from flowering into malign oppressions that obsess both the mind and the spirit. The pragmatic critique of prior philosophy and the pragmatic theory of signs are intended, in part, precisely to address this task of weeding out delusive ideas.

Questions of Justification

There is a singular misunderstanding of this pragmatic perspective that needs to have its equally singular but bad effects blunted at this point. There is a definition of good conduct that is implicit in the pragmatic ordering of the normative sciences, but it is a characterization whose true import is frequently misinterpreted by seizing too quickly on one partial formulation or another of its full intention. If the pragmatic definition of good conduct is properly considered, in light of the full circumstances of its intended application, it does not lead to the bad end often associated with the fallacy of “the ends justifying the means”. In fact, the bad effects accountable to even so facile a formulation of the pragmatic desideratum, can be seen to result, in actual practice, from a faulty application of its own stated principle, going even so far as to ignore the expressly indicated pluralities of “ends” and “means”. But that is merely a verbal scruple. In the end, it does not matter whether one speaks of “ends” or the “end”. What really matters is that the term not be interpreted in too singular a way, but only with regard to the whole conceivable effect of each contemplated form of conduct.

Accordingly, in order to counteract the brands of bad faith that arise from ignoring this holistic sense, one needs to remember that an action has many consequences. Since an action has a multitude of results, a plurality of which conceivably contribute in significant ways to a truly balanced judgment of its goodness, an action is good only in so far as all of these results are good. If an action, intended primarily for the purpose of achieving a particular good, however successful it is toward that end, nevertheless has collateral consequences that are not so good, then the action is to that degree not so good as it otherwise might be. These are moral trivialities, of course, but just as easily trifled with, and apparently as likely to slip into oblivion for all concerned as they are likely to be slighted by some. But this is the nature of singularity.

From this pragmatic point of view, it is possible to deal with many questions of justification by invoking the contexts of amenities that surround the reasoning process, outside of which it cannot be pursued and without which it makes no sense. In this frame, one can say that reason is justified by its alternative, that is to say, by unreason, but only in the peculiar sense that reason is justified by considering the properties of unreason, by contemplating the ethical consequences of acting according to its dictates, and by recognizing the aesthetic fact that one does not like these consequences. Of course, this strategy of argument does not amount to a justification of reason in any positive sense of the word justification. In logical force it is tantamount to the aesthetic tautology of simply insisting that one likes what one likes, but I see nothing unreasonable about this form of justification (FOJ), at least, as it is employed in this case. The whole point of noticing the placement of logic within the concentric spheres of ethics and aesthetics is that logical arguments depend on prior considerations of ethical and aesthetic casts, so a logical argument that merely recovers and iterates this context is acting in conformity with the only objective it knows.

By way of concrete examples, FOJs of a negative character frequently arise in situations that are affected by a genuine dilemma, where it is necessary to choose just one action from a set of two or more actions, where it is impossible to do nothing and impossible to do everything, and where each action excludes all the others. At such a juncture the structure of that very situation, or a reference to it as described, is itself a sufficiently valid FOJ for choosing some action, even if not yet a full justification for any one specific choice. If an agent challenged: “Why did you do that?”, responds: “It was necessary to do something!”, then that is “just” as far as it goes, to a general not a specific extent. In summary, one finds that there are FOJs of a negative character, that proceed by the rejection of an alternative, but that are perfectly valid in their doing so. These FOJs of a negative character exist in contrast to the more familiar FOJs, at least, the more often expressed FOJs, all of which are positive and transitive in character, identical or analogous to the various forms of logical implication and logical consequence.

The dictum to the effect that there is no argument in matters of taste, for what it is worth, enjoins an argument to, not an argument from. An aesthetic principle or judgment, that I prefer to live, for example, can have definite logical consequences, even if every justification I can expect to find for it is ultimately circular, tautologous, or logically speaking, trivial in form: “Why do I like it?” — “Just because I do!” To me, this cannot help but seem, if challenged in a case of this kind, to be a perfectly adequate and a reasonably sufficient answer. But to maintain this reason means to preserve this life, and that in its turn has decidedly logical consequences. It is likely that artisans and engineers have an easier time understanding this pragmatic principle, what it means in active practice and the wisdom it holds in general, than many varieties of logicians, mathematicians, philosophers, and scientists, although if I say that I pick my axioms with an eye to the beauty of what they can shape, in other words, that I select my logical and mathematical principles for what are essentially aesthetic reasons, then there are evidently some in these guilded ilks who already know what I mean.

Socrates not only used irony but was so dedicated to irony that he himself succumbed to it.

Kierkegaard, The Concept of Irony, [Kier, 5]

A person who drinks an extract of hemlock for what he says is a reason of logic either suffers from a confusion of priorities or acts according to a higher aesthetic than that of saving his own small portion of life. But a person who drains the tendered glass for lack of lighting quickly enough on a reason why not is a person who has let his extract of logic turn to a poison in its own right.

The Experience of Satisfaction

Die unbegreiflich hohen Werke
Sind herrlich wie am ersten Tag.
The world's unwithered countenance
Is bright as on the earliest day.
  Goethe, Faust, …,
  quoted in Weyl, The Open World, [Weyl, 29].

With these considerations freshly in mind, it is possible to return to the more immediate questions:

Why is it useful to keep a store of memory?
How does a record of past experiences serve an agent in meeting its present goals and thereby in achieving future satisfactions?

Assuming that an agent, however accidentally, elliptically, obliquely, occasionally, partially, or transiently it may happen, ever experiences a state of satisfaction, as reflects its achievement of one of its objects or as marks its identity with one of its goals, then it is likely to be useful for that agent to try to keep track of all the incidental experiences that accompany or surround this "experience of satisfaction" (EOS). Because the questions of causal order and even of purely temporal simultaneity are difficult in general to resolve in real time, in medias res, it is advisable for the agent not to focus too fixedly on trying to sort out the precedents from the consequents, at least, at first. But why is it likely to be useful? And what does it mean to be useful? Responding to these questions requires another apparent departure, as follows.

What does it mean to be useful? It means to further the purpose of an agent's present, continued, or future satisfaction. It means to help an agent achieve a specified goal, or else, failing the possibility of that, to help an agent know the reasons why a particular goal is impossible. Taking this as a satisfactory answer on this score, for now, it leads to the question of why a record of previous experience is likely to further the purpose of future satisfactions. Looking forward to the point when these issues of justification are out of the way, I will then be able to focus on the purely technical task of showing how sign relations can be used to construct many varieties of extremely flexible memory stores, not just accumulating the images of past experience, but indexing their elements in ways that make it possible to analyze their logical imports.

If there is any consistency to experience, in other words, any form of lawful relationship between one sample of experience and other samples of experience, then it follows that almost any kind of memory structure, any facility for attention and retention that an agent can contrive to organize the interaction between transient experience and the orders of its more persistent signs, any faculty that allows an agent to note the sundry aspects of a satisfying experience or the circumstantial details of a satisfying situation, any organization of processes that permits an agent to fashion periodic or persistent notes of the tangent experiences that surround an EOS, whether these stores are internal to its initially given body of resources or external to its innate endowment, is likely to be of service in achieving future satisfactions. Properly organized for quick access, the whole index of past experience can serve as a catalyst for future achievements, in other words, it can act on the whole as the sort of sign that is conducive to actualizing its object.

One may well ask: Is there any form of lawful relationship between one sample of experience and other samples of experience? To say yes too quickly is practically vacuous, that is, it is empty of anything beyond the vaguest hopes of an implication for action, until one is willing to risk the assumption of a specific form of lawful relationship. For the sake of proposing a non trivial stake, what one needs and desires is an informative form of lawful relationship. I am not making any form of fixed assumption here, but merely contemplating the forms of hypotheses that I am able to consider as possible. I admit to occasionally having experiences that cause me to question all the more frequently exploited answers to this question, that tempt me to say no even to this modest quantum of presumption, but then I note that it is particular varieties of experience that lead me to say this and specific brands of laws that I am led to question. Then I notice that all the forms of contrariety, disagreement, discord, discrepancy, disharmony, disparity, dispersion, dissension, distribution, diversification, incongruity, and opposition that I encounter at these junctures are themselves distinctions with a difference, and each in its way renders a generic form of distinction, “which, taken at the flood, leads on to fortune”, to wit, a wealth of unsuspected approaches to the problems that positive experience poses. Without being tempted to classify or to enumerate the full diversity of logical forms by which differing samples of experience come to grate on and to grind against each other, it is possible at this point to notice their essentially differential, negative, and oppositional characters.

In this way, I arrive at the conclusion that forms of negation (FONs), or fundamentally negative logical relations, are unavoidable necessities, needed to anchor any adequate basis for stating the forms of interaction among different samples of experience. One finds, instead of a positive foundation, that irreducibly negative operations are inescapable notions, needed to support any satisfactory system of notations for detailing the collisions and the collusions that particles of experience impart to one another. In spite of the aura of negativity that chances to shade their logical aspects, to color their evidential impacts, and to weigh against their positive receptions, the counter exemplary characters and conducts of these bearings of experience on experience do, at a minimum, contrive to convey “informative forms of lawful relationship between one sample of experience and other samples of experience”.

The circumstance that absence, necessity, and privation are the mothers of invention, possibility, and plenitude is a difficult fact of logic to accustom oneself to, apparently because of the mind's innate blind spots in regard to its own nature and partly due to the mind's acquired bias in favor of positive relationships. Against these blocks and in accord with this bias, the aspects of nullity and vacuity that arise in respect of logical FONs are frequently responsible for leading the mind astray, for instance, into supposing that these FONs are:

  1. Purely derivative abstractions from wholly positive contents and structures of experience,
  2. Partially selective extractions from primary materials of experience and primitive elements of reasoning,
  3. Secondary, tertiary, and higher order constructions that are based on and built from basically positive forms of empirical and rational connection, and
  4. Wholly dependent for their practical utility and their rational justification on contents of positive experience to fill out their sparingly minimal forms.

By way of contrast, it is possible to identify a couple of dimensions along which the variety of clarification tasks can be classified into coherent associations among themselves and coordinated with each other.

  1. One interpretation of the clarification task fixes the object and the class of signs that figure in as implied arguments of the operation, and thus it understands the task as a process of refining the quality of significance that stems from the individual signs, that is, developing a clearer interpretant for each sign given in the input class. I refer to this brand of clarification as a modeling process, for several reasons:

    1. Speaking of signs in the generic sense, this mode of clarification process involves the finding or the making of model signs to serve as their clarified interpretants. In other words, it takes in signs of an arbitrary quality of clarity and replaces them with their canonical, normal, or standard equivalents, ones that have an improved or optimal level of clarity.

    2. Speaking of signs in the sense of logical expressions, this mode of clarification process involves the detection, enumeration, and organization of their logical "models", that is, their logically satisfying interpretations.

    Overall, this brand of clarification can be viewed a purely cognitive, intellectual, syntactic, or rational process, one that goes on in the absence of any interaction with the object domain beyond the initial sample of signs.

  2. Another interpretation of the clarification task allows the object, or the information that the object avails of itself, to change over time. It is not that agents always have a lot of choice in the matter of whether changes occur or what changes take place, but only that they do have the option to envision the possibility of changes in the objects or the data, and accordingly to contrive systematic ways of tracking these changes and accounting for the developments of objects and signs through time. This rendition of the general requirement to “increase the clarity of the signs that the agent possesses about the object” comprehends the task of clarification as a matter of increasing the quantity of the agent's possessions in that regard, and it leads to a class of strategies in which agents proceed by gathering each new sign that they find of the object into the class of signs that forms their sample.

An Organizational Difficulty

Moreover, I did not wish to begin to reject completely any of the opinions which might have slipped earlier into my mind without having been introduced by reason, until I had first given myself enough time to make a plan of the work I was undertaking, and to seek the true method of arriving at knowledge of everything my mind was capable of grasping.

Rene Descartes, Discourse on Method, [Des1, 39-40]

At this point in my text I run into what I think of as an organizational difficulty (OD). I have already written sixty plus pages of this text and, if the stacks of notes and previous drafts that I find around me are any evidence, I am likely to write many pages more. …

Pragmatic Certainties

This brings me to the point of asking: What does certainty mean in practice, that is, what meanings can be revealed for the concept if one attempts to translate the intentions behind it into operational terms? Once one bothers to ask this eminently practical question, it becomes reasonably clear almost immediately that no brand of absolute certainty is ever in required practice. For practical purposes, only a moderate amount of certainty is demanded, just enough for a particular agent to settle on a particular course of action. A question about the kind of certainty expected or the level of certainty needed in order to make a decision is itself an interpretive issue. In other words, no matter whether its instances remain to be decided on a case by case basis, or whether a general rule can be formed to cover them, their resolution occurs in a manner that retains an irreducible degree of arbitrariness about it, since it must relate to the degrees of freedom possessed by the agents who arbitrate the matter in question. In the final analysis, this is an issue that devolves upon the nature and the constitution of the very form of agency that finds itself concerned with the question and exerts itself according to its interest in the action. Namely and solely, this form of agency can be comprised of nothing other than the particular agents and the communities of agents who are compelled or inspired to act at the moment in question.

The idea that certainty is needed to begin, whether to start thinking or to get moving in any direction of conduct, is one of the most paralyzing traps that the mind can let itself fall into. This is why the pragmatic theory of inquiry emphasizes uncertainty as the literal start of inquiry, since there is certainly no difficulty about the mind finding itself in a state of uncertainty. Thus, there is no scarcity of events to throw the mind into confusion, no trouble at all getting into trouble, and so this renders the whole fabric of one's experience rife with moments of doubt. But what is the mind to make of this dubious resource, and what is the ultimate good of noticing this abundance of ambivalence in the mind?

There is much that is curious in the picture of uncertainty that I just presented. The paradoxical phrase “certainly no difficulty”, that seemed to pop up from nowhere in my description of the situation, is evidently an artifact of reflection, that is, due to the reflective character of the description but not an element of the situation described. Specifically, it focuses on what appears at first to be a purely incidental triviality: How easy it is to find oneself in a state of uncertainty. More carefully, since to "find oneself" may be still too much to expect at such an early stage of the game, it may be said: How easy it is to be for the moment or to end up momentarily in a state of uncertainty. And yet, with yet another reflection, one is forced to ask: To what exactly, whether an aspect of the original situation, a newly introduced amendment to it, or a newly generated outlook on the situation, do all these attributions of certainty, ease, freedom from trouble, and lack of difficulty apply? Since it seems a contradiction to attribute these predicates to the problematic state of uncertainty itself, that is to say, they are not what's the matter in the original situation, they must belong either to the attitude of approach that is capable of reflection, to the ensuing state that is entered on reflection, or to the manner of viewing the whole situation.

Thus, it is possible to distinguish between two collections of properties, or, if one prefers, between two different applications of the same set of predicates:

  1. Those that affect the state of inquiry, its matter, and
  2. Those that affect the attitude toward it, the manner of regarding it, whether of absorption and irreflection or reflection and understanding.

In order to keep track of this distinction, I introduce the designations of lower order (LO) and higher order (HO) properties, attitudes, or applications of predicates.

“Aha!” you might say, here is the hidden certainty that is needed to begin the inquiry, the initial knowledge of its true motive force that makes the whole process of inquiry feasible, the unshakable faith in its prime mover that is required to rest before the rest can get started, or the ultimate security that is necessary to sustain the entire endeavor. But it is not that, not yet. The particular brand of HO certainty that arises in this situation is actually of very little use in resolving the original uncertainty. Although it can provide a modicum of security, a small peace of mind, and serve as a sop to Cerberus at critical times, the invitations to this escape can be as distracting as the delights of its certainties are in fact seductive, and the exercise of this method to the exclusion of risking the perils of real experience can just as easily become the main obstruction to the further progress of inquiry.

This business of being certain that one is uncertain, the enterprises of reasoning that vie to capitalize on its purely derivative securities, the foundations of thought that try to indemnify themselves against all risk and against all hope through the guarantees of its instruments, the certificates of its stocks, and the surety of its bonds, the companies of philosophers, incorporated and limited, who leave their precious earnings so heavily invested in the specious lightness of its bearing, and all the subsidiary entertainments that are produced in pursuit of this spectacle, that grow in the absence of more penetrating lights to delight the hosts of spectators, to enrich the parasites of apparent productivity, that accrue in lieu of more genuine profits to all the participants and their silent partners who count themselves party to this form of gamble, and that provide nothing more than a nominal incentive, both for those who stake their personal fortunes on the receipts of the intervening days and those who bet their pari mutuel interests on the outcome of running along this track — this entire business, that strives to busy itself at any cost whatsoever, to protect its investment for its own sake, and to insure its continuance by means of any excuse it can arrange for itself, eventually leads to the following strategy: to institute a discipline whose rationale is precisely that of issuing warrants for unnamed and probably unnameable apprehensions, of handing down sealed indictments whose principals on principle remain as impeccable as they are obscure, and of rendering forms of certification for forms of belief that have already surrendered their original contents — this tiresome business can easily become so all consuming and global in its sphere of influence, while curiously remaining so provincial and local in its motives, that it totally derails the original train of thought.

What accounts for the fact that one way to certainty, the ostensibly “higher” order, so often gets favored to the exclusion of the other? Perhaps it is something in the nature of the one track mind that only one brand of certainty can be pursued at a time. Perhaps it is partly due to the implicit judgments of “lower” and “higher” and partially on account of the adventitious implications that cannot help but slip into their making. Although these terms originally attach themselves to the discussion as convenient labels, intended solely to mark the sides of a purely formal distinction, and in spite of all the arbitrary characters that go into their nominal conventions, the nature of the associative mind is such that these tokens are almost bound to mount up in time to the point where they come to represent judgments of value, to symbolize in intuitively suggestive or in strictly illicit manners something beyond their original intentions, and thus to connote guilt or gilt by means of their informal associations. Absurd, I know, almost as if the even more innocuous words left and right could come to represent significant value judgments. Still, it happens.

As a guard against the deleterious effects that frequently emerge from the drawing of a distinction between LO and HO attitudes of certainty, no matter whether the division concerns the attributions of properties or the applications of predicates, and that commonly arise from making the various lines of LO and HO tracks express enough to carry between them a significant import but not equal enough for both to carry their share of the moment, I must take care that the tracks laid down in the building of a RIF, and all the actions conducted on their basis, are always adequate to facilitating both levels of inquiry in parallel.

Triadic relations are a staple element of architecture that can serve the purpose of coordinating LO and HO inquiries, since a triadic relation can incorporate the dyadic relation that describes the transition from one state of inquiry to a subsequent state of inquiry, while still keeping track of its relationship to developments occurring on the other track. This allows the orders of developments taking place within each inquiry, and the sequences of states extracted from their processes, to proceed uninterrupted, but not uninterpreted, by each other's concerns, and to exhibit a partial independence, but an adequate correlation, with each other's progress.

In order to carry this discussion of certainty through with a maximum of ease, I need to find a battery of descriptive terms for the situation of uncertainty that is neutral with respect to two interpretations, that covers with equal facility the two kinds of uncertainty that one usually faces in a situation: (1) uncertainty about what is true in a situation, and (2) uncertainty about what to do in a situation. Along these lines, I describe the typical situation of uncertainty, encompassing both kinds of doubt that are fraught with peril for an agent, as junctures.

For the sake of a convenient classification, I label the juncture that presents a problematic phenomenon, a surprising or unexpected state of affairs, with the generic name of a surprise, and I label the juncture that presents a phenomenal problem, a demanding or unintended state of affairs, with the generic name of a problem. Junctures do not always sort themselves out into cases that are clearly one or the other type, but when they do it simplifies the manners of addressing, approaching, and ultimately resolving the difficulties they present for the agent.

  1. If it is the aspect of a surprise that is dominant at a juncture, or the role of a spectator that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding an explanation, a statement expressing a way of looking at the juncture that renders it less of a surprise.
  2. If it is the aspect of a problem that is dominant at a juncture, or the role of an actor that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding a plan of action, a statement expressing a way of moving from the juncture that renders it less of a problem. Of course, it remains for the plan or theoretical resolution to be carried out in practice before the problem itself can disappear.

If the uncertainty that one experiences in facing a juncture reflects the complexity of the juncture that faces one there, and if these are related to the difficulty that one is likely to have in resolving the juncture, then the appropriate analysis of these complexities, difficulties, and uncertainties into several parts can serve to advance the process of their resolution.

With this picture of an agent at a juncture, appraising the uncertainties that affect the agent in that situation, indicating the complexities and the difficulties that the situation presents for the agent to resolve, sketching the forms of analysis that are called for in the process of resolution, and suggesting the relationships that obtain among these diverse ingredients of the situation, it is feasible to return to the problem of the cartesian step, the one that moves from dubito to ergo sum, and that simultaneously, as if perforce its very passing, creates the distinction between the LO and the HO attitudes of certainty. Can the cartesian step be viewed in this light, that is, can it be placed in a suitable way within this picture of junctures and resolutions, to be specific, posing a form of analysis that advances the cause of certainty? And if so, how does it appear when regarded in this light, that is, how well does it perform with respect to its conjectural role in reducing a fundamental uncertainty of the agent concerned?

In a sense, the cartesian step splits the agent's initial juncture into a couple of parts, or subjunctures. In this attempt at resolution, there is a part identical to the initial juncture, and thus with an uncertainty of the original severity, plus a part that the agent is sure of, and thus with an uncertainty of zero. But this sort of analysis only works if it brings to light subjunctures of the initial juncture, or subsituations of the initial situation, that are actual ingredients, proper components, or non trivial constituents of it. When the HO certainty does not have an effective bearing on resolving the LO uncertainty, then the pretense of analysis is only a distraction, not a step toward a genuine resolution.

Unless the HO answer that is revealed by dint of the cartesian step has an application to the LO question that instigated the original inquiry, one that reduces the LO uncertainty that initially justified the effort, then it does not have a genuine bearing on the LO juncture that led to putting this inquiry in gear and setting its proceedings into motion, and it cannot bring to bear on the ensuing activity or the ongoing process the modicum of traction that is needed to put a brake on its continuing. But a partition of a level of uncertainty into the very same amount plus a quantity of zero is hardly a sum, however much it seems on the level, that inspires much confidence in either the practical sincerity or the ergo nomic utility of the putative sum.

When Descartes set about the reconstruction of philosophy, his first step was to (theoretically) permit scepticism and to discard the practice of the schoolmen of looking to authority as the ultimate source of truth. That done, he sought a more natural fountain of true principles, and thought he found it in the human mind; …

Self-consciousness was to furnish us with our fundamental truths, and to decide what was agreeable to reason. But since, evidently, not all ideas are true, he was led to note, as the first condition of infallibility, that they must be clear. The distinction between an idea seeming clear and really being so, never occurred to him.

(Peirce, CP 5.391).

In the discussion that follows, I am going to use the letters to stand for three generic features or classes of properties, yet to be fully analyzed or completely specified, that are commonly appreciated, desired, or valued as virtues of signs and expressions. For now, a list of adjectives appropriate to each class can give a sufficient indication of their intended characters, even though it is easily possible and eventually necessary to find important distinctions that exist among the items in each given list of exemplary properties.

  1. The class is suggested by the adjectives certain, cogent, compelling, or convincing, and, in some of their senses, by apparent, evident, obvious, or patent.
  2. The class is suggested by the adjectives clear, lucid, perspicuous, plain, relevant, or vivid. To the geometric imagination, these terms suggest a bluntness (of surfaces) or a sharpness (of edges).
  3. The class is suggested by the adjectives distinct, decided, defined, definite, determinate, different, differentiated, or discrete, and, within a stretch of the imagination, by acute, conspicuous, eminent, manifest, poignant, salient, or striking. To the geometric imagination, these terms suggest a pointedness.

In this frame of thought, it needs to be understood that the intended sense of these last two classes excludes the common usage of words like clear, clearly, and so on, or distinct, distinctly, and so on, as elliptic figures of speech that are intended to be taken in a more literal way to mean clearly true, and so on, or distinctly true, and so on.

In this connection, when I mention one of these properties it is only meant as a representative of its class. Also, as they are used in this context, these terms are intended only in what is diversely called their impressionistic, nominal, subjective, superficial, or topical sense, implying the sorts of qualities that one can judge “by inspection” of the expression and its immediate situation, and without the need of a prolonged investigation. Thus, none of their intentions is damaged for this purpose by prefacing their proposal with an attitude of seeming. For all one cares in these concerns, for This makes the judgment of these qualities a matter of seeming syntax and seeming semantics, involving only the sorts of decision that are commonly and easily made without carrying out complex computations or without delving into the abstruse equivalence classes of expressions.

People frequently use the adverbs immediately or intuitively to get this sense across, and even though these terms have technical meanings that prevent me from using them in this way in anything but a casual setting, they can do for the moment. Still, when I use immediately in this sense it is meant in contrast only to ultimately, and more or less synonymous to mediately, suggesting that which holds in the meantime. In a pinch, a determination of seeming certainty or seeming clarity is enough to put an inquiry on hold for a time being, but the distinction between seeming so to me, for now and seeming so to all, forever still holds, with only the latter deserving the title of being so.

These observations on im/mediate, intuitive, or meantime determinations of certainty, clarity, and distinctness have a bearing on the styles of mathematical formulation and the modes of computational implementation that are candidates for mediating a natural style of inquiry, in other words, the sort of inquiry that a human being can relate to. Because a decision that a sign or expression has one of the virtues even to a mediate, a moderate, or a modest degree, is often enough to end an inquiry on a temporary basis, it becomes necessary to recognize a form of recursive foundation that also rests on a temporal basis. And yet, because these modes of judgment are all the while fallible and subject to change, it is possible that deeper foundations remain to be found.

What does this mean for the topic of reflection? Well, reflection is precisely that mode of thinking that is capable of beginning with the axioms and working backward, that is, of searching out the more basic forms that conceivably underlie one's received formulations.

I thereby concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing; so that this “I”, that is to say, the mind, by which I am what I am, is entirely distinct from the body, and even that it is easier to know than the body, and moreover, that even if the body were not, it would not cease to be all that it is.

Rene Descartes, Discourse on Method, [Des1, 54]

And voila, I have, finally, spontaneously returned to there where I wanted to be. For because it now be known to me that bodies themselves are properly perceived not by the senses or by the faculty of imagining, but rather by the intellect alone, and that bodies are perceived not from thence that they would be touched or seen, but rather from thence only that they were to be understood, I cognize overtly that nothing can be perceived by me more easily or more evidently than my mind.

Rene Descartes, Meditations on First Philosophy, [Des2, 117]

On reflection, the observation that appeared just before these last questions arose can be seen to make a very broad claim about a certain class of properties affecting expressions, namely, all those properties that can be analogous to the ordered measures of expressive quality. For future reference, let me call this the monotone assumption (MA). This generatrix of so many future and specious assumptions takes for granted a sweeping claim about the ways that an order of analysis of expressions translates into an order of comparison of their measures under one of these properties. But this entire and previously unstated assumption is itself just another manner of working hypothesis for the mental procedure or the process of inquiry that makes use of it, and its proper understanding is perhaps better served if it is rephrased as a question: Can the of a claim or a concept be greater than the of the subordinate claims and concepts that it calls on, where stands for certainty, clarity, or any one of the corresponding class of measures, orders, properties, qualities, or virtues?

Rather than taking this claim for granted, suppose I go looking for any properties, that might be similar to certainty or clarity, for which the measure of a whole expression is capable of exceeding the measure of its parts. Is there an order property that is dependent on the constitution of the whole expression and a function of its analytic constituents but not necessarily tied down to monotonically conservative relationships like the sum, the average, or the lowest common denominator of the measures affecting its syntactic elements? Once I take the trouble to formulate the question in explicit terms, any number of familiar examples are free to come to mind as fitting its requirements. Indeed, since the notions of dependency and independence that accompany the use of mathematical functions and mathematical forms of decomposition do not by themselves implicate the more constrained types of dependency and the more radical types of independence that arise in relation and in reaction to the MA, it is rather easy to think of many that will do.

Problems and Methods

The relationship between a “problem” and a “method” needs to be given another look, in view of the discussion that has transpired since the initial steps of this proposal. …

To approach the distinction between problem and method in the present setting, in the light of the discussion that has transpired since I naively assumed a distinction between them, …

What is the nature of the relationship between a problem and a method? What is the distinction between them, and what sort of difference is it? These questions are made especially acute in view of the fact that the present inquiry nominates “inquiry” to both of these roles, proposing to take “inquiry” as naming both a problem and a method. If it makes any sense to do this, and if there is anything to the distinction between a problem and a method, then it must be a distinction of relational roles rather than a distinction of absolute essences. Trying to make sense of this requires me to ask: What manner of common, generic, indifferent, or shared existence do a problem and a method both possess, logically prior to taking on their distinctive roles in relation to each other?

In approaching the distinction between a problem and a method, I use a piece of advice that is helpful in approaching any important distinction, especially a distinction that is naively taken as given or a distinction that has been taken for granted for too long a spell of time, like the distinction between the problem and the method, the work and the tool, or the object and the sign. This recommends that one stand back from a full involvement in the drawing of the distinction under review, to partially withdraw one's commitment to having it drawn the way it is, and to contemplate how it came to be drawn that way in the first place, in other words, to consider the process that initially draws it and that keeps on drawing it in just the way that it presently appears.

If this is done, then one realizes that the problem and the method are both constituted in part by the way their distinction is drawn, by the sort of distinction that one takes it to be, whether a sign of the roles that entities take up in relation to each other or a mark of the natures that entities have in and of themselves, and by the items that one takes as instances on either side of the distinction. In this way, every form of distinction, with respect to the contents of its counterposed sides, plays the role of a mediator in their mutual constitution of each other.

Standing back from the picture a little further, one can see that the distinction between a problem and a method is itself a tool of method, and one that is not ordinarily considered to be a problem. To see this, notice that distinction is an -ionized term, and thus denotes both a process and a result, the process being the drawing of the distinction and the product being the distinction drawn, so any form of distinction is available for consideration in the light of its instrumental meaning. In this regard, the distinction between a problem and a method is itself an instrumentality of reasoning, a procedural means to an end, in short, a method or a tool. This particular distinction, between a problem and a method, falls among those of a very basic order, the kind that one takes as given without hesitation or reflection, uses to construe almost every situation that one finds oneself in, and does not usually question the utility of, until, as presently, some special attention is drawn to it. In summary, the distinction that is drawn between the problem seen and the method used, the conventional form of designation that says what is the work and what is the tool, is itself an artifice, a construct, an invention of the mind, or an intervention of the thinking process whose correspondence with anything else in reality and whose constitution as an enduring reality in itself is something that demands to be tested.

If the terms problem and method refer to phenomena and activities that take place in the world, then that is one mode of existence they have in common. If the “world” is further circumscribed to the kinds of phenomena that have effective descriptions, that is, computational models, and the kinds of activities that have effective prescriptions, that is, computational implementations, then the mode of existence one commonly denotes by means of programs, codes, effective procedures, or other practical recipes is another domain that is capable of providing instances that fill both the roles of a problem or a method. Taking a clue from this interpretation, I can shift my approach to the question and consider the medium of signs that is used to address the things in comparison. By starting with the syntactic side of the issue I avail myself of ready made handles on the question, even if the mechanism of these conventional modes quickly becomes a difficulty in its own right, blocking further progress and demanding to be tackled in terms of the influential biases and the instrumental characters it brings to bear.