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=====5.2.11.9. Pragmatic Certainties=====
=====5.2.11.9. Pragmatic Certainties=====
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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 "ego 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 "C", "L", and "M" 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 "C" 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 "L" 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 "M" 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, "seems X" = "X", for X = C, L, M. 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 C, L, M, 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 X of a claim or a concept be greater than the X of the subordinate claims and concepts that it calls on, where "X" 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 monotonely 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.
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=====5.2.11.10. Problems and Methods=====
=====5.2.11.10. Problems and Methods=====