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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8|Part 8]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
====7.2.4. Dynamic and Evaluative Frameworks====
====7.2.4. Dynamic and Evaluative Frameworks====
In this subsection I hope to prepare the way for the consideration of more significant examples of sign relations, and to begin demonstrating how this class of formal structures is relevant to the motivated changes or value directed operations of inquiry. In order to see how the rather static and featureless sorts of sign relations considered so far can grow into full fledged examples of inquiry processes it is necessary to develop two additional aspects of their structure.
# The "dynamic" dimension deals with change, permitting the sequential ordering of state positions in a temporal process.
# The "evaluative" dimension deals with comparisons, permitting the preferential ranking of state qualities on a scale of values.
Moreover, each of these additional aspects or dimensions of structure needs to be articulated at two levels of application to sign relations, considering the dynamic changes and the evaluative comparisons that can take place either "within" or "between" individual sign relations.
a. "Within" sign relations. This level involves (1) the changes and (2) the comparisons that are possible between the elements of a single sign relation, that is, between its objects or else between its signs and interpretants.
b. "Between" sign relations. This level involves (1) the changes that transform whole sign relations into others, whether these actions are considered to occur dynamically in time or only virtually in contemplation, and (2) the comparisons that go into ranking whole idividual sign relations on various scales of values.
Since I am using sign relations as models of inquiry, that is to say, as models of potential theories of inquiry, ...
The hardest part of the inquiry into inquiry, as I presently see it, comes down to this: Are there rational ways to argue toward a theory of inquiry? That is to say, are there systematic ways of reasoning toward definitions and axioms in any domain, and can these methods be applied to arrive at a definition of inquiry itself, along with the principles that are necessarily true of inquiry? In other words, can definitions and axioms be criticized and evaluated on rational grounds with regard to how well they describe independently given concepts? These are difficult questions for certain models of science to address, namely, those whose image of science accustoms the mind to starting out from received formulations of experience that prior work has tamed into the facile forms of primitive expressions, and whose sense of scientific procedure always seems to argue from a formal basis in definitions and axioms rather than toward them, oblivious to the import of all those processes, rational or otherwise, that initally supply this foundation.
By the end of this subsection I want to have charted a return to my discussion of formalization, proceeding thereafter by way of increasingly complex but nevertheless still concrete examples of formal models. However, in order to get that far I will have to steer a winding course, encountering a diversity of foundational crises and brushing up against a selection of critical obstacles. Luckily, the immediate aims of this discussion demand no more from me than to touch as lightly as possible on the most prominent points of each apparent dilemma as it looms up, and thus I can hope to clear their main obstructions in a passing way. Perhaps the highest priority is to revisit my guiding intuitions about inquiry, to see whether this constellation of methodological hypotheses permanently constrains the models of inquiry that can be entertained, or whether this tentative model of inquiry incorporates a way to recognize when the process of inquiry happens to go astray, and thus leaves room for its own self improvement and a continuing revision of insights.
Successful inquiry into any domain of phenomena is supposed to reduce the level of uncertainty that an interpreter has about the objects or processes in that domain. In future discussions, I will refer to this supposition about the end of inquiry as the "initial description" (ID) of inquiry.
Employing this ID of inquiry in the application of inquiry to itself, it follows that successful inquiry into inquiry is supposed to decrease the uncertainty that an interpreter experiences, expresses, or exhibits with respect to the nature and conduct of inquiry itself. I will refer this supposition about the end of inquiry into inquiry, a corollary hypothesis that is derived from and contingent on the "self employment" of the ID, as the "self expression" (SE) of the ID.
Since it is presumptuous to think that anything definitive can be said about inquiry until after the inquiry into inquiry has achieved its end, the thesis that I identify as the ID of inquiry will have to pass in the meantime as a nominal definition or a topical hypothesis, in other words, as a tentative conjecture about the character of inquiry that arises from the realms of personal intuition and popular opinion and that needs to serve no greater purpose than to get the discussion off and running in a definite direction, along lines of inquiry whose fruitfulness can be tested without loss of generality at any later stage of investigation.
And so a modicum of presumption must be tolerated, since it cannot be avoided in any case, and a measure of arrogance is involved in every interrogation of nature, to think that one's question deserves an answer and that one is perhaps one to find it or make it in time. But the hope that this manner of approach to the object of inquiry can be successful in the long run is tantamount to a regulative principle of inquiry, one whose plausibility depends on certain conditions being fulfilled, and thus its rational use requires one to deal with a variety of potential obstacles that affect its justification in practice.
Although some measure of presumption must be tolerated, since it is not seemly to assume that every measure of it can be avoided, this does not mean that every presumption must remain immune from correction and therefore eternally incorrigible. Any initial assumption remains subject to being criticized from the standpoints of all the casual contexts that it injects itself into. Since these forms of interjection do not found the contexts they interrupt and interpret, and supply at best convenient springboards for discussion but never essential foundations, their defects can always be remedied as the need arises.
In the entire discussion so far, I have let myself be guided by the governing couple of casual intuitions or working hypotheses that are formulated in the preceding ID of inquiry and in its subsequent SE, and especially by the implicit rule of hope that is involved in their use. Consequently, it may seem at this juncture that the utility of the whole discussion hinges on the prior certainty of these two cardinal points. In order to proceed with any degree of confidence along the lines of approach I have chosen, I will have to argue that this is not so, that the apparent force of obstruction presented by the practical necessity of making initial constructions does not prevail against the conceptual possibility of inquiry into inquiry nor against the chances of every simple inquiry simply going forward in accord with its own lights.
It becomes the task of continuing discussion to preserve the mode of guidance identified by the ID of inquiry and to persist in the enterprise staked out by its SE without being pinned down too fast or too fixedly by the patently obvious and hopefully transient limitations that these principles betray on a moment to moment basis. It remains the duty of this project to see whether inquiry constitutes a form of progress that can work toward truer and proper definitions of itself or whether it is terminally limited by the first impressions and incipient reflections that it captures of its own character, no matter how sage or insipid these preliminary guesses at a recipe for inquiry may initially be.
Returning to the refrain: Inquiry into any process or phenomenon is supposed to decrease the uncertainty that an interpreter has about that particular object of interest. Inquiry into the process of inquiry is supposed to decrease the uncertainty that an interpreter endures or evinces with respect to the nature and conduct of inquiry itself.
Expressing everything over again in positive terms: Successful inquiry increases the certainty that an interpreter has about the object of its investigation. Successful inquiry into inquiry increases the certainty that an interpreter possesses or manifests with regard to the process of inquiry itself.
There are many things about the ID of inquiry and its SE that will have to be examined with increasing care at various later stages in this work. If the profile of inquiry and its self application depicted here are to be regarded as useful, then each of the concepts invoked in this picture of inquiry needs to be clarified as much as possible, ideally to the point where it can be accepted as a definition and examined with regard to its potential for formalization and quantification. For the moment, I suggest just a few of the additional points that will undoubtedly arise, and then I return to focus on the topics of immediate concern from the standpoint of developing concrete examples of formalization.
Of central concern, the concepts of uncertainty and certainty that are implied by the ID and its SE need to be analyzed in relation to standard concepts of entropy and information that have already been formalized and quantified to an adequate degree. At first sight, the concept of certainty seems to involve the superabundant qualities of "quick wit": (1) as a feature of a state of intellection, something that enables the exercise of ready decision making powers, and (2) as a feature of signs and expressions, something that increases their clarity and alacrity, or augments the accessibility and usability of their information, all of which seems to add up to facilities and capacities that are not guaranteed by the mere possession of information alone.
As always, in carrying out the analysis of a vaguely given idea in relation to a known concept, assuming there really is something to the idea, one has the options: (1) of extending the precursory term to incorporate additional meanings, or (2) of limiting the term of the paradigm to its established senses and inventing distinctive names for the extra components of meaning. The choice between these options is usually decided by how much continuity is perceived along the series of related concepts, as they come to be analyzed.
Until the terms it invokes are formalized, or at least clarified to a greater extent than they are at present, the ID that I presented on behalf of inquiry and the SE that I employed for the sake of inquiry into inquiry will provide little more assistance toward understanding the character of their subject than the vague indication already supplied in the nominal invocation of "inquiry", and even that much progress is purchased at the cost of no small measure of distraction.
Axiomatic presentations, that arrange their subjects as if freshly sprung from undefined terms and unproven axioms, are extremely useful for the purposes of retrospective exposition and rhetorical justification, but they rarely do justice to the actual order and process of discovery or fairly represent with any degree of realism the evolution and growth of their living subject matters. Not even logic and mathematics are such purely deductive enterprises as to remain for long entirely captivated by their still life forms and aesthetically distanced styles of depiction.
Since nothing about inquiry makes sense outside the framework of sign using agents, the ID and SE are able to refer, without loss of generality, to an "interpreter" as forming the generic agent of inquiry, instead of the "agent" or "observer" that might be expected to appear in seemingly more general formulations. The pragmatic theory of signs, that naturally develops in parallel with the pragmatic theory of inquiry, is presented in large part simply to explain what is meant by this "interpreter". As a bonus, the extra dimension of relationship involved in the pragmatic theory of signs can be turned toward the beneficial purpose of constantly maintaining a critical perspective on one's own conceptual constructions.
The vast abstraction schematized by means of the single word "has" — that I sought to flesh out in a highly selective sample of its senses: via the conditions an interpreter "experiences", "expresses", "exhibits", ranging in meaning through all the categories from passive to active modes, from "endures" to "evinces", from "possesses" to "manifests" — this is a complex of interpretive possibilities that will take some time to develop and clarify, not the least because it resonates with the twin themes of the "fugitive canon" that I alluded to early on in this study. In quick order, within a framework that permits the creation of artificial mediations between sequences of experiential states, between successions of felt conditions such as pain or relief, doubt or belief, what kinds of formally effective models could possibly be subtle enough to convey the substance of these persistent general categories while working within the limitations of transient particular states?
Certainty = Information + Clarity + Alacrity + ...
One of the ways that the supposed information can be expressed is in the form of propositions that the interpreter observes about its object. Thus, different states of information about an object can be constituted or represented by different collections of propositions about that object. In logic, an arbitrary collection of propositions is called a "theory", a title of no particular significance until one has examined the consistency and validity of the supposed theory.
Using this form of description, an interpretive agent can be conceived as moving through a space of information about an object, whose points are characterized by different amounts of uncertainty versus information about an object, and where each state of information with regard to an object is associated with a theory about that object.
====7.2.5. Discussion of Examples====
====7.2.5. Discussion of Examples====
At this point, in order to make further use of the pragmatic theory of signs without distorting its character too severely, I am forced, even for the sake of this simple example, to broach a difficult and potentially controversial topic that, for good or ill, can no longer be avoided. For future reference, let me entitle this issue as a question about "the general versus the restricted theory of sign relations". The problem for pragmatic theory and practical application is how to steer a middle course between the riptide of vague generalities and the narrow idols of reductive procedure.
In general, questions about the relationship of signs and interpretants, both inside and outside a computational framework, form a major concern of the pragmatic theory of signs, and will continue to be revisited throughout this discussion. Time and time again, questions about the true character of the interpretant role are found to abide at the heart of the problem, forming the cardinal points of investigation on which everything else hinges. The reason for this appears to be yet another brand of recursion or self similarity affecting the domain of inquiry. Namely, interpretants fill a role within their individual sign relations that is analogous to the role that sign relations used as formal models fill within the larger inquiry, providing a controlled mediation between the wide open domains of phenomena and language.
In the general theory of sign relations, which concerns itself with the formal properties of thinking processes, the interpretant domain is meant to encompass the full variety of mental impressions and affections: ideas, concepts, intuitions, intentions, impulses and dispositions to act, and every sort of intellectual construct, both cognitive and affective. This heady brew is not yet on the table for current consumption, but all of it imbues the aspirations of artificial intelligence with a measure of essential enthusiasm, and a spirit to which even those whose scope is focused on the objective dynamics of intelligent systems cannot turn down a glass.
Working within the constraints of formally effective descriptions (FED's), this project can explore nothing more than pale scattered shadows of these connotative and ideational dimensions of meaning. In the pragmatic theory of signs, it is held that all thought takes place in signs. Ideas, concepts, and other mental constructs are regarded as signs in the mind, in other words, as modifications of their peculiar medium that affect the states of their conducting agents. But with regard to their pertinent formal structure, namely, the sign relations that shape their action as signs, mental signs are no different from the generic brand of signs. In sum, all signs are defined as signs precisely in terms of their relative associations and formal operations, and not according to the marks of any absolute material essence.
Still, there falls within the sweep of this enlarged scope an element of crucial importance to all forms of pragmatic thinking. This is the notion that a solid store of meanings for signs and ideas can be found, not quite in the individual actions of an agent that come and go with the moment, so transient and irrepeatable in themselves, but in the agent's conative character, informed conduct, and consummate disposition to act. This realm includes both inborn and borne in patterns of inclination, broadly conceived plans of action, and generalized contingent resolutions to act in definite ways under prescribed conditions.
If this description sounds familiar, it is with good reason. The formal realm that shares these features is precisely the domain of operational definitions and effective programs whose use in clarifying concepts is being explored in this project. The upshot is, that whatever vague signs are allowed into the sign domain simply on the chance that they might mean something to somebody sometime, there is a more critical property demanded of the interpretant domain that is intended to play a role in deliberate inquiry. For a sign relation to serve inquiry in a positive way its interpretant domain ought to make available to its agent explicit expressions of program like entities that can define with maximal clarity the imports of its signs and ideas.
====7.2.6. Information and Inquiry====
====7.2.6. Information and Inquiry====
Given my initial description of inquiry as a process that reduces the uncertainty of an inquirer (any observant agent or interpretive system) about the state of an object system, and combining this with the characterization of interpreters in concrete form as sign relations, there arises an obvious question that must be addressed by this project: How is the state of uncertainty of an agent about an object system to be defined from the data present in a sign relation?
In spite of the bare construction of the A and B dialogue it is possible to elaborate a few scenarios on its basis that illustrate the relevance of sign relations to inquiry situations. To devise motivating stories for these inquiries and still be able to obtain the needed variations from such sparce materials, I will be forced to re use many elements of the sign relations A and B in non standard ways. Because they lack most of the analytic refinements that will be needed for complete clarity, these inventions risk the introduction of a few confusions. However, the exercise of untangling potential confusions in a simple example can provide useful practice, highlighting problems before they grow too complex to tackle, and training the attention to detect what features really matter in defining a situation of inquiry.
One type of inquiry might begin with A having no idea what B will say next, except for the certain knowledge that it must be confined to the syntactic domain S = {"A", "B", "i", "u"}. I will refer to this as a "syntactic" type of inquiry, since the object system appropriate to the inquiry situation, as described, is identical to the syntactic domain S. As a rough approximation, this inquiry can be viewed as a degenerate spin off from the original dialogue, one in which the true object domain has been lost, and attention has devolved to mere banter over signs. More carefully regarded, the relationship of the syntactic inquiry to the original situation could be described as deriving new sign relations Syn (A) and Syn (B) from the old sign relations A and B, in each case replacing O with S and splitting the stock of ordered triples in a corresponding fashion, as shown in Tables ** and **.
In this sort of "syntactic inquiry", the state of uncertainty on the part of A about the state of the object system S is a condition of maximum entropy with respect to the outcomes in S and can be represented as a uniform distribution of probabilities over S. In this scenario, A has log2|S| = log2(4) = 2 bits of uncertainty about what B will say next. If A hears B say "A" next, say, then A has no remaining doubts about the issue. As a result of receiving this sign, A comes to reside in a state with 0 bits of uncertainty about the question now past. The same reasoning applies to each of the other signs in S. Altogether, each sign in S conveys 2 bits of information to the interpreter A with respect to the prior condition of maximum uncertainty about the state of the object system S. The "average uncertainty reduction per symbol", in this case 2 bits, is called the "capacity of the information channel", as this channel is defined by the entire set up of the inquiry situation.
<pre>
Table **. Sign Relation of Interpreter X
Object Sign Interpretant
"A"A A "A"A
"B"A A "B"A
"i"A A "i"A
"u"A A "u"A
"A"B B "A"B
"B"B B "B"B
"i"B B "i"B
"u"B B "u"B
Table **. Sign Relation of Interpreter Syn (B)
Object Sign Interpretant
A "A" "A"
A "A" "u"
A "u" "A"
A "u" "u"
B "B" "B"
B "B" "i"
B "i" "B"
B "i" "i"
</pre>
Another type of inquiry might begin with A wondering what object B will denote next. Here, the object system referred to as a part of the inquiry situation is identical with the object domain O of the sign relations A and B.
'''Fragments'''
To deliver the logical functionality that is required to support inquiry, a computational framework must incorporate the ability to work with both empirical and rational knowledge. To do this it needs to have signs that refer to particular experiences and symbols that represent types of experience, and it needs, not only the capacity to examine the bearings of each upon the other, but a means to express the gist of this result in an integral form.
If these references and representations are to avoid the various ways of violating the bounds of sense — something they can do either by failing to have sufficient denotation from the outset or by exceeding the bounds of consistency and tractability at any stage of attempting to process their indications — then ...
# Operating on corrupt arguments or initially senseless indications. Attempting to start out from a state of empty nonsense, from a logically pointless or impoverished point of view, and trying to pursue a moment of semantic irreference on the impulse of a direction with null import. Drawing on resources that are logically empty and following instructions that are semantically nil.
# Transgressing the bounds of consistency or tractability at any subsequent stage of computation and thereby becoming logically empty or effectively vacuous, conceptually inconsistent or computationally intractable at an intermediate stage of investigation.
Even though the present discussion is focussed on isolated cases of sign relations, it cannot illustrate the properties of these examples in an adequate way without considering extended multitudes of other relations, both those that share the same properties and those that do not. Thus, to get the comparative study of sign relations started on a casual basis, something that is helped in addition by placing sign relations within the larger field of n place relations, I will exploit a few devices of taxonomic nomenclature, intending them to be applied for the moment in a purely informal way.
dimensions of temporal evolution and deliberate evaluation
coordinating temporal evolution with directed evaluation
partial specification: approximate, deficient, imperfect, incorrect
partial satisfaction: approximate, deficient, imperfect, incorrect
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• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6|Part 6]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 7|Part 7]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8|Part 8]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Appendices|Appendices]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
• [[Directory:Jon Awbrey/Papers/Inquiry Driven Systems : References|References]]
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[[Category:Artificial Intelligence]]
[[Category:Artificial Intelligence]]
