Inquiry Driven Systems:
An Inquiry Into Inquiry
Jon Awbrey
Oakland University
1. Research Proposal
1.1 Outline of the Project: Inquiry Driven Systems
1.1.1 Problem
This research is oriented toward a single problem: What is the nature of inquiry? I intend to address
crucial questions about the operation, organization, and computational facilitation of inquiry, taking
inquiry to encompass the general trend of all forms of reasoning that lead to the features of scientific
investigation as their ultimate development.
1.1.2 Method
How will I approach this problem about the nature of inquiry? The simplest answer is this:
I will apply the method of inquiry to the problem of inquiry's nature.
This is the most concise and comprehensive answer I know, but it is likely to sound facetious
at this point. On the other hand, if I did not actually use the method of inquiry that I describe
as inquiry, how could the results possibly be taken seriously? Correspondingly, the questions
of methodological self-application and self-referential consistency will be found at the center
of this research.
In truth, it is fully possible that every means at inquiry's disposal will ultimately find application
in resolving the problem of inquiry's nature. Other than a restraint to valid methods of inquiry --
what those are is part of the question -- there is no reason to expect a prior limitation on the range
of methods that might be required.
This only leads up to the question of priorities: Which methods do I think it wise to apply first?
In this project I will give preference to two kinds of technique, one analytic and one synthetic.
The prevailing method of research that I will exercise throughout this work involves representing
problematic phenomena in a variety of formal systems and then implementing these representations
in a computational medium as a way of clarifying the more complex descriptions that evolve.
Aside from its theoretical core, this research is partly empirical and partly heuristic. Therefore,
I expect that the various components of methodology will need to be applied in an iterative or even
an opportunistic fashion, working on any edge of research that appears to be ready at a given time.
If forced to anticipate the likely developments, I would sketch the possibilities roughly as follows:
The methodology that underlies this approach has two components: The analytic component
involves describing the performance and the competence of intelligent agents in the medium of
various formal systems. The synthetic component involves implementing these formal systems
and the descriptions they express in the form of computational interpreters or language processors.
If everything goes according to the pattern I have observed in previous work, the principal facets
of analytic and synthetic procedure will each be prefaced by its own distinctive phase of preparatory
activity, where the basic materials needed for further investigation are brought together for comparative
study. Taking these initial stages into consideration, I can describe the main modalities of this research
in greater detail, as follows.
1.1.2.1 The Paradigmatic &
Process-Analytic Phase. In this phase I describe the performance and competence of intelligent agents in terms of various formal
systems. For aspects of an inquiry process that affect its dynamic or temporal performance I will typically
use representations modeled on finite automata and differential systems. For aspects of an inquiry faculty
that reflect its formal or symbolic competence I will commonly use representations like formal grammars,
logical calculi, constraint-based axiom systems, and rule-based theories in association with different proof
styles.
Paradigm. Generic example that reflects significant properties of a target class of phenomena,
often derived from a tradition of study.
Analysis. Effective analysis of concepts, capacities, structures, and functions in terms of
fundamental operations and computable functions.
Work in this phase typically proceeds according to the following recipe:
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Focus on a problematic phenomenon. This is a generic property or process that attracts one's
interest, like intelligence or inquiry.
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2.
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Gather under consideration significant examples of concrete systems or agents that exhibit the
property or process in question.
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3.
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Reflect on their common properties in a search for less obvious traits that might explain their
more surprising features.
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4.
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Check these accounts of the phenomenon in one of several ways. For example, one
might (a) search out other systems or situations in nature that manifest the critical traits,
or (b) implement the putative traits in computer simulations. If these hypothesized traits
generate (give rise to, provide a basis for) the phenomenon of interest, either in nature or
on the computer, then one has reason to consider them further as possible explanations.
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The last option of the last step already overlaps with the synthetic phase of work. Viewing this procedure
within the frame of experimental research, it is important to recognize that computer programs can fill the
role of hypotheses, testable (defeasible or falsifiable) construals of how a process is actually, might be
possibly, or ought to be optimally carried out.
1.1.2.2 The Paraphrastic &
Faculty-Synthetic Phase. The closely allied techniques of task analysis and software development that are known as
"step-wise refinement" and "top-down programming" in computer science (Wirth 1976, 49, 303)
have a long ancestry in logic and philosophy, going back to a strategy for establishing or discharging
contextual definitions known as "paraphrasis". All of these methods are founded on the idea of providing
meaning for operational specifications, "definitions in use", alleged descriptions, or "incomplete symbols".
No excessive generosity with the resources of meaning is intended, though. In practice, a larger share of
the routine is spent detecting meaningless fictions rather than discovering meaningful concepts.
Paraphrasis. "A method of accounting for fictions by explaining various purported terms away"
(Quine, in Van Heijenoort, 216). See also (Whitehead & Russell, in Van Heijenoort, 217-223).
Synthesis. Regard computer programs as implementations of hypothetical or postulated faculties.
Within the framework of experimental research, programs can serve as descriptive, as modal, or as
normative hypotheses, that is, conjectures about how a process is actually accomplished in nature,
speculations as to how it might be done in principle, or explorations of how it might be done better
in the medium of technological extensions.
For the purposes of this project, I will take "paraphrastic definition" to denote the analysis of formal
specifications and contextual constraints to derive effective implementations of a process or its faculty.
This is carried out by considering what the faculty in question is required to do in the many contexts
it is expected to serve, and then by analyzing these formal specifications in order to design computer
programs that fulfill them.
1.1.2.3 Reprise of Methods In summary, the whole array of methods will be typical of the top-down strategies that are used in
"artificial intelligence research" (AIR), involving the conceptual and operational analysis of higher-order
cognitive capacities with an eye toward the modeling, the grounding, and the support of these faculties
in the form of effective computer programs. The toughest part of this discipline is in making sure that
one does indeed "come down", that is, in finding guarantees that the analytic reagents and the synthetic
apparatus that one applies are actually effective, reducing the "fat" of speculation into something that
will "wash".
Finally, I ought to observe a hedge against betting too much on this or any other too neat arrangement
of research stages. It should not be forgotten that the flourishing of inquiry evolves its own forms of
organic integrity. No matter how one tries to tease them apart, the various tendrils of research tend
to interleave and to intertwine as they will.
1.1.3 Criterion
When is enough enough? What measure can I use to tell if my effort is working? What information
is critical in deciding whether my exercise of the method is advancing my state of knowledge toward
a solution of the problem?
Given that the problem is "inquiry" and the method is "inquiry", the test of progress and eventual success
is just the measure of any inquiry's performance. 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.
What are the practical tests of whether the results of inquiry succeed in reducing uncertainty? Two gains
are often cited: Successful results of inquiry provide the agent with increased powers of prediction and
control as to how the object system will behave in given circumstances. If a common theme is desired, at
the price of a finely equivocal thread, it can be said that the agent has gained in its power of determination.
Hence, more certainty is exhibited by less hesitation, more determination is manifested by less vacillation.
1.1.4 Application
Where can the results be used? Knowledge about the nature of inquiry can be applied. It can be used
to improve our personal competence at inquiry. It can be used to build software support for the tasks
involved in inquiry.
If it is desired to articulate the loop of self-application a bit further, computer models of inquiry can be
seen as building a two-way bridge between experimental science and software engineering, allowing the
results of each to be applied in the furtherance of the other.
In yet another development, computer models of learning and reasoning form a linkage among cognitive
psychology (the descriptive study of how we think), artificial intelligence (the prospective study of how
we might think), and the logic of operations research (the normative study of how we ought to think in
order to achieve the goals of reasoning).
1.2 Onus of the Project: No Way But Inquiry
At the beginning of inquiry there is nothing for me to work with but the actual constellation of doubts
and beliefs that I have at the moment. Beliefs that operate at the deepest levels can be taken so far for
granted that they rarely if ever obtrude on awareness. Doubts that oppress in the most obvious ways are
still known only as debits and droughts, as the absence of something, one knows not what, and a desire
that obliges one only to try. Obscure forms of oversight provide an impulse to replenish the condition of
privation but never out of necessity afford a sense of direction. One senses there ought to be a way out
at once, or ordered ways to overcome obstruction, or organized or otherwise ways to obviate one's opacity
of omission and rescue a secure motivation from the array of conflicting possibilities. In the roughest
sense of the word, any action that does in fact lead out of this onerous state can be regarded as a form
of "inquiry". Only later, in moments of more leisurely inquiry, when it comes down to classifying and
comparing the manner of escapes that can be recounted, does it become possible to recognize the ways
in which certain general patterns of strategy are routinely more successful in the long run than others.
1.2.1 A Modulating Prelude
If I aim to devise the kind of computational support that can give the greatest assistance to inquiry,
then it must be able to come in at the very beginning, to be of service in the kinds of formless and
negative conditions that I just described, and to help people navigate a way through the constellations
of contingent, incomplete, and contradictory indications that they actually find themselves sailing under
at present.
In the remainder of this section I will try to indicate as briefly as possible the nature of the problem
that must be faced in this particular approach to inquiry, and to explain what a large share of the
ensuing fuss will be directed toward clearing up.
Toward the end of this discussion I will be using highly concrete mathematical models, that is, very
specific families of combinatorial objects, to represent the abstract structures of experiential sequences
that agents pass through. If these primitive and simplified models are to be regarded as something more
than mere toys, and if the relations of particular experiences to particular models, along with the structural
relationships that exist within the field of experiences and again within the collection of models, are not to
be dismissed as category confusions, then I will need to develop a toolbox of logical techniques that can
be used to justify these constructions. The required technology of categorical and relational notions will
be developed in the process of addressing its basic task: To show how the same conceptual categories
can be applied to materials and models of experience that are radically diverse in their specific contents
and peculiar to the states of the particular agents to which they attach.
1.2.2 A Fugitive Canon
The principal difficulties associated with this task appear to spring from two roots.
First, there is the issue of "computational mediation". In using the sorts of sequences that computers
go through to mediate discussion of the sorts of sequences that people go through, it becomes necessary
to re-examine all of the facilitating assumptions that are commonly taken for granted in relating one human
experience to another, that is, in describing and building structural relationships among the experiences of
human agents.
Second, there is the problem of "representing the general in the particular". How is it possible for
the most particular imaginable things, namely, the transient experiential states of agents, to represent
the most general imaginable things, namely, the agents' own conceptions of the abstract categories
of experience?
Finally, not altogether as an afterthought, there is a question that binds these issues together. How does it
make sense to apply one's individual conceptions of the abstract categories of experience, not only to the
experiences of oneself and others, but in points of form to compare them with the structures present in
mathematical models?
1.3 Option of the Project: A Way Up To Inquiry
I begin with an informal examination of the concept of inquiry. This section takes as its subjects the
supposed faculty of inquiry in general and the present inquiry into inquiry in particular, and attempts
to analyze them in relation to each other on formal principles alone.
The initial set of concepts I need to get discussion started are few. Assuming that a working set of ideas
can be understood on informal grounds at the outset, I anticipate being able to formalize them to a greater
degree as the project gets under way. Inquiry in general will be described as encompassing particular
inquiries. Particular forms of inquiry, regarded as phenomenal processes, will be analyzed in terms
of simpler kinds of phenomenal processes.
As a phenomenon, a particular way of doing inquiry is regarded as embodied in a faculty of inquiry, as
possessed by an agent of inquiry. As a process, a particular example of inquiry is regarded as extended
in time through a sequence of states, as experienced by its ongoing agent. It is envisioned that an agent
or faculty of any generically described phenomenal process, inquiry included, could be started off from
different initial states and would follow different trajectories of subsequent states, and yet there would be
a recognizable quality or abstractable property that justifies invoking the name of the genus.
The steps of this analysis will be annotated below by making use of the following conventions:
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Lower case letters denote phenomena, processes, or faculties under investigation.
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2.
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Upper case letters denote classes of the same sorts of entities, that is, phenomena, processes,
or faculties of interest in a particular investigation.
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3.
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Special use is made of the following symbols:
Y = genus of inquiry; y = generic inquiry; y0 = present inquiry.
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4.
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Compositions of "faculties" are indicated by concatenating their names, as in "f.g", and
are posed in the sense that the faculty on the right "applies to" the faculty on the left.
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5.
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The notation "f >= g" indicates that f is greater than or equal to g in a decompositional series,
in other words, that f possesses g as a component.
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6.
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The coset notation F.G indicates a class of "faculties" of the form f.g, with f in F and g in G.
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7.
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Notations like "{?}", "{?,?}", and so on, serve as proxies for unknown components and
can be used in an informal way to indicate tentative analyses of the faculties in question.
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1.3.1 Initial Analysis of Inquiry
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Allegro Aperto
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If the faculty of inquiry is a coherent power, then it has an active or instrumental face, a passive or
objective face, and a substantial body of connections between them. y = {?}.
In giving the current inquiry a reflexive cast, as inquiry into inquiry, I have brought inquiry face to face
with itself, inditing it to apply its action in pursuing a knowledge of its passion. y0 = y.y = {?}{?}.
If this juxtaposition of characters is to have a meaningful issue, then the fullness of its instrumental
and objective aspects must have recourse to easier actions and simpler objects. y >= {?,?}.
Looking for an edge on each face of inquiry, as a plausible option for beginning to apply one to the
other, I find what seems a likely pair. I begin with an aspect of instrumental inquiry that is easy to do,
namely "discussion", along with an aspect of objective inquiry that is unavoidable to discuss, namely
"formalization". y >= {disc, form}.
In accord with this plan, the body of this section is devoted to a discussion of formalization.
y0 = y.y >= {d,f}{d,f} >= {f}{d}.
1.3.2 Discussion of Discussion
But first, I nearly skipped a step. Though it might present itself as an interruption, a topic so easy that
I almost omitted it altogether deserves at least a passing notice. y0 = y.y >= {d,f}{d,f} >= {d}{d}.
Discussion is easy in general because its termination criterion is relaxed to the point of becoming otiose.
A discussion of things in general can be pursued as an end in itself, with no consideration of any purpose
but persevering in its current form, and this accounts for the virtually perpetual continuation of many
a familiar and perennial discussion.
There's a catch here that applies to all living creatures: In order to keep talking one has to keep living.
This brings discussion back to its role in inquiry, considered as an adaptation of living creatures designed
to help them deal with their not so virtual environments. If discussion is constrained to the envelope of life
and required to contribute to the trend of inquiry, instead of representing a kind of internal opposition, then
it must be possible to tighten up the loose account and elevate the digressionary narrative into a properly
directed inquiry. This brings an end to my initial discussion of "discussion".
1.3.3 Discussion of Formalization: General Topics
Because this project makes constant use of formal models of phenomenal processes, it is appropriate
at this point to introduce the understanding of formalization that I will use throughout this work and
to preview a concrete example of its application.
An introduction to the topic of formalization, if proper, is obliged to begin informally. But it will be
my constant practice to keep a formal eye on the whole proceedings. What this form of observation
reveals must be kept silent for the most part at first, but I see no rule against sharing with the reader
the general order of this watch:
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Examine every notion of the casual intuition that enters into the informal discussion and inquire
into its qualifications as a potential candidate for formalization.
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2.
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Pay special attention to the nominal operations that are invoked to substantiate each tentative
explanation of a critically important process. Often, but not infallibly, these can be detected
appearing in the guise of "-ionized" terms, words ending in "-ion" that typically connote both
a process and its result.
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3.
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Ask yourself, with regard to each postulant faculty in the current account, explicitly charged
or otherwise, whether you can imagine any recipe, any program, any rule of procedure for
carrying out the form, if not the substance, of what it does, or an aspect thereof.
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1.3.3.2 A Formalization of Formalization? An immediate application of the above rules is presented here, in hopes of giving the reader a concrete
illustration of their use in a ready example, but the issues raised can quickly diverge into yet another
distracting digression, one not so easily brought under control as the discussion of discussion, but whose
complexity probably approaches that of the entire task. Therefore, a partial adumbration of its character
will have to suffice for the present. y0 = y.y >= {d,f}{d,f} >= {f}{f}.
To illustrate the formal charge by taking the present matter to task, the word "formalization" is itself
exemplary of the "-ionized" terms falling under the charge, and so it can be lionized as the nominal
head of a prospectively formal discussion. The reader has a right to object at this point that I have not
described what particular action I intend to convey under the heading of "formalization", by no means
enough to begin applying it to any term, much less itself. However, anyone can recognize on syntactic
grounds that the word is an instance of the formal rule, purely from the character of its terminal "-ion",
and this can be done aside from all clues about the particular meaning that I intend it to have at the end
of formalization.
Unlike a mechanical interpreter meeting with the declaration of an undefined term for the very first time,
the human reader of this text has the advantage of a prior acquaintance with almost every term that might
conceivably enter into informal discussion. And "formalization" is a stock term widely traded in the forums
of ordinary and technical discussion, so the reader is bound to have met with it in the context of practical
experience and to have attached a personal concept to it. Therefore, this inquiry into formalization begins
with a writer and a reader in a state of limited uncertainty, each attaching a distribution of meanings in
practice to the word "formalization", but uncertain whether their diverse spectra of associations can
presently constitute or eventually converge to compatible arrays of effective meaning.
To review: The concept of formalization itself is an item of informal discussion that might be investigated
as a candidate for formalization. For each aspect or component of the formalization process that I plan
to transport across the semi-permeable threshold from informal to formal discussion, the reader has
permission to challenge it, plus an open invitation to question every further process that I mention as
a part of its constitution, and to ask with regard to each item whether its registration has cleared up the
account in any measure or merely rung up a higher charge on the running bill of fare.
The reader can follow this example with every concept that I mention in the explanation of formalization,
and again in the larger investigation of inquiry, and be assured that it is has not often slipped my attention
to at least venture the same, though a delimitation of each exploration in its present state of completion
would be far too tedious and tenuous to escape expurgation.
1.3.3.3 A Formalization of Discussion? The previous section took the concept of "formalization" as an example of a topic that a writer might
try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept
to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader.
In either case the formalization process, that aims to translate a concept from informal to formal
discussion, is itself mediated by a form of discussion: (1) that interpreters conduct as a part of their
ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue
with a reader (hearer). In view of this, I see no harm in letting the concept of discussion be stretched to
cover all attempted processes of formalization. F c D.
In this section, I step back from the example of "formalization" and consider the general task of clarifying
and communicating concepts by means of a properly directed discussion. Let this kind of "motivated"
or "measured" discussion be referred to as a "meditation", that is, "a discourse intended to express its
author's reflections or to guide others in contemplation" (Webster's). The motive of a meditation is
to mediate a certain object or intention, namely, the system of concepts intended for clarification or
communication. The measure of a meditation is a system of values that permits its participants to tell
how close they are to achieving its object. The letter "M" will be used to annotate this form of meditation.
F c M c D.
This brings the discussion around to considering the intentional objects of measured discussions and
the qualifications of a writer so motivated. Just what is involved in achieving the object of a motivated
discussion? Can these intentions be formalized? y0 = y.y >= {d,f}{d,f} >= {d}{f}.
The writer's task is not to create meaning from nothing, but to construct a relation from the typical
meanings that are available in ordinary discourse to the particular meanings that are intended to be
the effects of a particular discussion.
In case there is difficulty with the meaning of the word "meaning", I replace its use with references
to a "system of interpretation" (SOI), a technical concept that will be increasingly formalized as this
project proceeds. Thus, the writer's job description is reformulated as follows.
The writer's task is not to create a system of interpretation (SOI) from nothing, but to construct a relation
from the typical SOI's that are available in ordinary discourse to the particular SOI's that are intended to be
the effects of a particular discussion.
This assignment begins with an informal system of interpretation (SOI1), and builds a relation from it to
another system of interpretation (SOI2). The first is an informal SOI that amounts to a shared resource of
writer and reader. The latter is a system of meanings in practice that is the current object of the writer's
intention to recommend for the reader's consideration and, hopefully, edification. In order to have
a compact term for highlighting the effects of a discussion that "builds a relation" between SOI's,
I will refer to this aspect of the overall discussion process by the name of "narration".
It is the writer's ethical responsibility to ensure that a discourse is potentially edifying with respect to the
reader's current SOI, and the reader's self-interest to evaluate whether a discourse is actually edifying from
the perspective of the reader's present SOI.
Formally, the relation that the writer builds from SOI to SOI can always be cast or recast as a three-place
relation, one whose staple element of structure is an ordered or indexed triple. One component of each
triple is anchored in the interpreter of the moment, and the other two form a connection with the source
and target SOI's of the current assignment.
Once this relation is built, a shift in the attention of any interpreter or a change in the present focus
of discourse can leave the impression of a transformation taking place from SOI1 to SOI2, but this is
more illusory (or allusory) than real. To be more precise, this style of transformation takes place on
a virtual basis, and need not have the substantive impact (or import) that a substantial replacement
of one SOI by another would imply. For a writer to affect a reader in this way would simply not be
polite. A moment's consideration of the kinds of SOI-building worth having leads me to enumerate
a few characteristics of "polite discourse" or "considerate discussion".
If this form of SOI-building narrative is truly intended to edify and educate, whether pursued in monologue
or dialogue fashion, then its action cannot be forcibly to replace the meanings in practice a sign already has
with others of an arbitrary nature, but freely to augment the options for meaning and powers for choice in
the resulting SOI.
As conditions for the possibility of considerate but significant narration, there are a couple of requirements
that are placed on the writer and the reader, as appropriate to their respective roles. Considerate narration,
constructing a relation from SOI to SOI in a politic fashion, cannot operate in an infectious or an addictive
manner, invading a SOI like a virus or a trojan horse, but must transfer its communication wholly into the
control of the receiving SOI. Significant communication, in which the receiving SOI is augmented by
options for meaning and powers for choice that it did not have before, requires a SOI on the reader's
part that is truly "extensible" in non-trivial ways.
At this point, the discussion has touched on a topic, in one of its manifold aspects, that it will encounter
repeatedly, under a variety of aspects, throughout this work. In recognition of this circumstance, and
to prepare the way for future discussion, it seems like a good idea to note a few of the aliases that this
protean topic can be found lurking under, and to notice the logical relationships that exist among its
several different appearances.
On several occasions, this discussion of inquiry will arrive at a form of "aesthetic deduction", in general
terms, a piece of reasoning that ends with a design recommendation, in this case, where an analysis of
the general purposes and interests of inquiry leads to the conclusion that a certain property of discussion
is an admirable one, and that the quality in question forms an essential part of the implicit value system
that is required to guide inquiry and make it what it is meant to be, a method for advancing toward desired
forms of knowledge. After a collection of admirable qualities has been recognized as cohering together
into a unity, it becomes natural to ask: What is the underlying reality that inheres in these qualities, and
what are the logical relations that bind them together into the qualifications of inquiry and a definition
of exactly what is desired for knowledge?
1.3.3.4 A Concept of Formalization The concept of formalization is intended to cover the whole collection of activities that serve to build
a relation between casual discussions, those that take place in the ordinary context of informal discourse,
and formal discussions, those that make use of completely formalized models. To make a long story short,
formalization is the narrative operation or active relation that construes the situational context in the form
of a definite text. The end product that results from the formalization process is analogous to a snapshot
or a candid picture, a relational or functional image that captures an aspect of the casual circumstances.
Relations between casual and formal discussion are often treated in terms of a distinction between two
languages, the "meta-language" and the "object language", linguistic systems that take complementary
roles in filling out the discussion of interest. In the usual approach, issues of formalization are addressed
by postulating a distinction between the meta-language, the descriptions and conceptions from ordinary
language and technical discourse that can be used without being formalized, and the object language,
the domain of structures and processes that can be studied as a completely formalized object.
1.3.3.5 A Formal Approach I plan to approach the issue of formalization from a slightly different angle, proceeding through an analysis
of the medium of interpretation and developing an effective conception of an "interpretive framework" or
an "interpretive system". This concept refers to any organized system of interpretive practice, ranging from
those that we use in everyday speech, to the ones that inform technical discourse, to the kinds of completely
formalized symbol systems that are safely regarded as mathematical objects. Depending on the degree of
objectification that it possesses from a particular person's operative point of view, the very same system of
conduct can variously be described as an "interpretive framework" (IF), an "interpretive system" (IS), an
"interpretive object" (IO), or an "object system" (OS). These terms are merely suggestive -- no rigid form
of classification is intended.
Many times, it is convenient to personify the interpretive organization as if it were embodied in the actions
of a typical user of the framework or a substantive agent of the system. I will call this agent the "interpreter"
of the moment. At other times, it may be necessary to analyze the action of interpretation more carefully.
At these times, it is important to remember that this form of personification is itself a figure of speech,
one that has no meaning outside a fairly flexible interpretive framework. Thus, the term "interpreter"
can be a cipher analogous to the terms "X", "unknown", or "to whom it may concern" appearing in
a system of potentially recursive constraints. As such, it serves in the role of an indeterminate symbol,
in the end to be solved for a fitting value, but in the mean time conveying an appearance of knowledge
in a place where very little is known about the subject itself.
A meta-language corresponds to what I call an "interpretive framework". Besides a set of descriptions
and conceptions, this construction embodies the whole collective activity of unexamined structures and
automatic processes that are trusted by agents at a given moment to make its employment meaningful
in practice. An interpretive framework is best understood as a form of conduct, that is, a comprehensive
organization of related activities.
In use, an interpretive framework operates to contain activity and constrain the engagement of agents
to certain forms of active involvement and dynamic participation, and manifests itself only incidentally
in the manipulation of compact symbols and isolated instruments. In short, though a framework may
have "pointer dials" and "portable tools" attached to it, it is usually too incumbent and cumbersome
to be easily moved on its own grounds, at least, it rests beyond the scope of any local effort to do so.
An interpretive framework (IF) is set to work when an agent or agency becomes involved in its
organization and participates in the forms of activity that make it up. Often, an IF is founded and
persists in operation long before any participant is able to reflect on its structure or to post a note
of its character to the constituting members of the framework. In some cases, the rules of the IF
in question forbid the act of reflecting on its form. In practice, to the extent that agents are actively
involved in filling out the requisite forms and taking part in the step by step routines of the IF, they
may have little surplus memory capacity to memorandize the big picture even when it is permitted
in principle.
An object language is a special case of the kind of formal system that is so completely formalized
that it can be regarded as combinatorial object, an inactive image of a form of activity that is meant
for the moment to be studied rather than joined.
The supposition that there is a meaningful and well-defined distinction between object language and
meta-language ordinarily goes unexamined. This means that the assumption of a distinction between
them is de facto a part of the meta-language and not even an object of discussion in the object language.
A slippery slope begins here. A failure to build reflective capacities into an interpretive framework can
let go unchallenged the spurious opinion that presumes there can be only one way to draw a distinction
between object language and meta-language.
The next natural development is to iterate the supposed distinction. This represents an attempt to formalize
and thereby "objectify" parts of the meta-language, precipitating it like a new layer of pearl or crystal from
the resident medium or "mother liquor", and thereby preparing the decantation of a still more pervasive and
ethereal meta-meta-language. The successive results of this process can have a positivistically intoxicating
effect on the human intellect. But a not so happy side-effect leads the not quite mindful cerebration up and
down a blind alley, chasing the specious impression that just beyond the realm of objective nature there lies
a unique fractionation of permeabilities and a permanent hierarchy of effabilities in language.
The grounds of discussion that I am raking over here constellate a rather striking scene, especially for
a level of conceptual architecture that is intended as a neutral backdrop. Unlike other concerns, the points
I am making seem obvious to all reasonable people at the outset of discussion, and yet the difficulties that
follow as inquiry develops get all the muddier and more grating the more one probes and stirs them up.
A large measure of the blame, I think, can be charged to a misleading directive that people derive from
the epithet "meta", leading them to search for higher and higher levels of meaning and truth, on beyond
language, on beyond any conceivable system of signs, and on beyond sense. Prolonged use of the prefix
"meta", without due reflection on its side-effects, leads people to act as if a meta-language were step outside
of ordinary language, or an artificial platform constructed above and beyond natural language, and then they
forget that formal models are developments internal to the informal context. For this reason among others,
I suggest replacing talk about rigidly stratified layers of object languages and meta-languages with talk
about contingent, transcient, and variable forms of interpretive frameworks.
To avoid the types of cul-de-sac (cultist act) encountered above, I am taking some pains to ensure
a reflective capacity for the interpretive frameworks I develop in this project. This is a capacity that
natural languages always assume for themselves, instituting specialized discourses as developments
that take place within their frame and not as constructs that lie beyond their scope. Any time that the
levels of recursive discussion become too involved to manage successfully, one needs to keep available
the resource of "instant wisdom", the modest but indispensable quantum of ready understanding, that
restores itself on each return to the "ordinary universe" (OU).
From this angle of approach, let us try to view afresh the manner of drawing distinctions between
various levels of formalization in language. Once again, I begin in the context of ordinary discussion,
and if there is any distinction to be drawn between objective and instrumental languages then it must
be possible to describe it within the frame of this informally discursive universe.
1.3.3.6 A Formal Development The point of view that I take on the origin and development of formal models is that they arise with
agents retracing structures that already exist in the context of informal activity, until gradually the most
relevant and frequently reinforced patterns become emphasized and emboldened enough to continue their
development as nearly autonomous styles, in brief, as "genres" growing out of a particular "paradigm".
Taking the position that formal models develop within the framework of informal discussion, the questions
that become important to ask of a prospective formal model are (1) whether it highlights the structure of its
supporting context in a transparent form of emphasis and a relevant reinforcement of salient features, and
(2) whether it reveals the active ingredients of its source materials in a critically reflective recapitulation
or an analytically representative recipe, or (3) whether it insistently obscures what little fraction of its
domain it manages to cover.
1.3.3.7 A Formal Persuasion An interpretive system can be taken up with very little fanfare, since it does not enjoin one to
declare undying allegiance to a particular point of view or to assign each piece of text in view
to a sovereign territory, but only to entertain different points of view on the use of the symbols
involved. The chief design consideration for an interpretive system is that it must never function
as a virus or an addiction. Its suggestions must always be, initially and finally, purely optional
adjunctions to whatever interpretive framework was already in place before it installed itself on
the scene. Interpretive systems are thus not constituted in the faith that anything nameable will
always be dependable, nor articulated in fixed principles that determine what must be doubted
and what must not, but rest only in a form of self-knowledge that recognizes the doubts and the
beliefs that one actually has at each given moment.
Before this project is done I will need to have developed an analytic and computational theory
of interpreters and interpretive frameworks. In the aspects of this theory that I can anticipate at
this point, an interpreter or an interpretive framework is exemplified by a collective activity of
symbol-using practices like those that might be found embodied in a person, a community, or
a culture. Each one forms a moderately free and independent perspective, with no objective
rankings of supremacy in practice that all interpretive frameworks are likely to support at any
foreseeable moment in their fields of view. Of course, each interpreter initially enters discussion
operating as if its own perspective were "meta" in comparison to all the others, but a well-developed
interpretive framework is likely to have acquired the notion and taken notice of the fact that this is not
likely to be a universally shared opinion (USO).
1.3.4 Discussion of Formalization: Concrete Examples
The previous section outlined a variety of general issues surrounding the concept of formalization.
The following section will plot the specific objectives of this project in constructing formal models
of intellectual processes. In this section I wish to take a breather between these abstract discussions
in order to give their main ideas a few points of contact with terra firma. To do this, I examine a selection
of concrete examples, artificially constructed to approach the minimum levels of non-trivial complexity,
that are intended to illustrate the kinds of mathematical objects I have in mind using as formal models.
1.3.4.1 Formal Models: A Sketch To sketch the features of the modeling activity that are relevant to the immediate purpose: The modeler
begins with a phenomenon or process of interest (POI) and relates it to a formal model of interest (MOI),
the whole while working within a particular interpretive framework (IF) and relating the results from one
system of interpretation (SOI) to another, or to a subsequent development of the same SOI.
The POI's that define the intents and purposes of this project are the closely related processes of inquiry
and interpretation, so the MOI's that must be formulated are models of inquiry and interpretation, species
of formal systems that are even more intimately bound up than usual with the IF's employed and the SOI's
deployed in their ongoing development as models.
Since all of the process models and interpretive systems mentioned here come from the same broad family
of mathematical objects, the different roles that they play in this investigation are mainly distinguished by
variations in their manner and degree of formalization:
1.
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The typical POI comes from natural sources and casual conduct. It is not formalized in itself
but only in the form of its image or model, and just to the extent that aspects of its structure and
function are captured by a formal MOI. But the richness of any natural phenomenon or realistic
process seldom falls within the metes and bounds of any finite or final formula.
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2.
|
Beyond the initial stages of investigation, the MOI is postulated as a completely formalized object,
or is quickly on its way to becoming one. As such, it serves as a pivotal fulcrum and a point of
application poised between the undefined reaches of "phenomena" and "noumena", terms that
serve more as directions of pointing than as denotations of entities. What enables the MOI to
grasp these directions is the mathematical fact that there can be well-defined and finite relations
between entities that are infinite and even indefinite in themselves. Indeed, exploiting this handle
on infinity is the main trick of all computational models and effective procedures. It is how a finitely
informed creature (FIC) can "make infinite use of finite means". Thus, my reason for calling the MOI
pivotal or cardinal is that it forms a model in two senses, logical and analogical, integrating twin roles
of the model concept in a single focus.
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3.
|
Finally, the IF's and SOI's always remain partly out of sight, caught up in various stages of explicit
notice between casual informality and partial formalization, with no guarantee or even a very great
likelihood of a completely articulate formulation being possible. Still, it is usually worth the effort
to try lifting one edge or another of these frameworks and backdrops into the light, at least for a time.
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1.3.4.2 Sign Relations: A Primer To the extent that their structures and functions can be discussed at all, it is likely that all of the formal
entities destined to develop in this approach to inquiry will be instances of a class of three-place relations
called "sign relations". At any rate, all of the formal structures that I have examined so far in this area have
turned out to be, if not manifestly sign relations themselves, erither easily convertible to, or else ultimately
grounded in, some variation on sign relations. This class of triadic relations constitutes the main study
of the "pragmatic theory of signs", a branch of logical philosophy that is devoted to understanding
all manners of symbolic representation and all types of significant communication.
There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.
In fact, the correspondence between the two studies exhibits so many parallels and coincidences that it is
often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the
process by which sign relations come to be established and continue to evolve. In other words, inquiry,
"thinking" in its best sense, "is a term denoting the various ways in which things acquire significance"
(Dewey). Thus, there is an active and intricate form of cooperation that needs to be appreciated and
maintained between these converging modes of investigation. Its proper character is best understood
by realizing that the theory of inquiry is adapted to study the developmental aspects of sign relations,
a subject which the theory of signs is specialized to treat from structural and comparative points of view.
Because the examples in this section have been artificially constructed to be a simple as possible,
their detailed elaboration can run the risk of trivializing the whole theory of sign relations. Still,
these examples have subtleties of their own, and their careful treatment will serve to illustrate
important issues in the general theory of signs.
Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their
expressive and interpretive practice that involves the use of the following nouns and pronouns:
"Ann", "Bob", "I", "You".
The "object domain" of this discussion fragment is the set consiting of two people {Ann, Bob}.
The "syntactic domain" or the "sign system" of their discussion is limited to the set of four signs
{"Ann", "Bob", "I", "You"}.
In their discussion, Ann and Bob are not only the passive objects of nominative and accusative
references but also the active interpreters of the language they use. The system of interpretation (SOI)
associated with each language user can be represented in the form of an individual three-place relation
called the "sign relation" of that interpreter.
Understood in terms of its set-theoretic extension, a sign relation R is a subset of a cartesian product OxSxI.
Here, O, S, and I are three sets called the "object domain", the "sign domain", and the "interpretant domain",
respectively, of the sign relation R c OxSxI. In general, the three domains of a sign relation can be any
sets whatsoever, but the kinds of sign relation contemplated in a computational framework are usually
constrained to having I c S. In this case, interpretants are just a special type of signs, and this makes
it convenient to lump signs and interpretants together into a "syntactic domain". In the forthcoming
examples, S and I are identical as sets, so the very same elements appear in two distinct roles of the
pertinent sign relations. When it is necessary to refer to the whole set of objects and signs in the
union of the domains O, S, and I for a given sign relation R, I will call this the "world of R" and
write W = W(R) = O U S U I.
To facilitate an interest in the abstract structures of sign relations, and to keep the notations as brief
as possible when the examples get more complicated, I introduce the following abbreviations:
O = object domain;
|
S = sign domain;
|
I = interpretant domain.
|
O
|
=
|
{ Ann, Bob }
|
=
|
{ A, B }.
|
S
|
=
|
{"Ann", "Bob", "I", "You"}
|
=
|
{"A", "B", "i", "u"}.
|
In the present examples, S = I = syntactic domain.
Tables 1 and 2 give the sign relations associated with the interpreters A and B, respectively, putting
them in the form of relational databases. Thus, the rows of each Table list the ordered triples <o, s, i>
that make up the corresponding sign relations: A, B c OxSxI. The issue of using the same names for
objects and for relations involving these objects will be taken up later, after the less problematic features
of these relations have been treated.
These Tables codify a rudimentary level of interpretive practice for the agents A and B, and provide
a basis for formalizing the initial semantics appropriate to their common syntactic domain. Each row
of a Table names an object and two co-referent signs, making up an ordered triple <o, s, i> called an
"elementary relation", that is, one element of the relation's set-theoretic extension.
Already in this elementary context, there are several different meanings that might attach to the project
of a "formal semantics". In the process of discussing these alternatives, I will introduce a few terms that
are occasionally used in the philosophy of language to point out the needed distinctions.
Table 1. Sign Relation of Interpreter A
Table 2. Sign Relation of Interpreter B
One aspect of semantics is concerned with the reference that a sign has to its object, which is often
called its "denotation". For signs in the most general type of situation, neither the existence nor the
uniqueness of a denotation is guaranteed. Thus, the denotation of a sign can refer to a plural, to a
singular, or to a vacuous number of objects. In the pragmatic theory of signs, these references of
signs to their objects are formalized as certain types of dyadic sub-relations that are found embedded
in the triadic sign relations. When it comes to dealing with the degenerate cases of signs that do not
denote, it is necessary to introduce what is, strictly speaking, a slightly more general concept than
a sign relation proper, namely, what is called a "sign-relational complex". But that is the subject
of a much later discussion. For now, I shall keep to signs which are known to have one or more
objects among their denotations.
The dyadic relation that constitutes the "denotative component" of a sign relation R is denoted by
"Den (R)". Information about the denotative component of semantics can be derived from R by taking
its "dyadic projection" on the object and sign domains, indicated by any one of the equivalent forms
"ProjOS(R)", "ROS", or "R12", and defined as:
Den (R) = ProjOS(R) = ROS = R12 = {<o, s> C OxS : <o, s, i> C R for some i C I}.
Looking to the denotative aspects of the present example, various rows of the Tables specify that
A uses "i" to denote A and "u" to denote B, whereas B uses "i" to denote B and "u" to denote A.
It is utterly amazing that even these impoverished remnants of natural language use have properties
that quickly bring the usual prospects of formal semantics to a screeching halt.
The other dyadic aspects of semantics that might be considered concern the reference that a sign has to its
interpretant and the reference that an interpretant has to its object. As before, either type of reference can
be multiple, unique, or empty in its collection of terminal points, and both can be formalized as different
kinds of dyadic sub-relations that can be found embedded in the triadic sign relations.
The connection that a sign makes to an interpretant is called its "connotation". In the general theory of
sign relations, this aspect of semantics includes the references that a sign has to ideas, concepts, affects,
intentions, and to the whole realm of an agent's mental states and allied activities, broadly encompassing
intellectual associations, emotional impressions, and motivational impulses. This complex ecosystem of
references is unlikely ever to be mapped in much detail, much less completely formalized, but the tangible
warp of its accumulated mass is commonly alluded to as the "connotative" import of language. Given a
particular sign relation R, the dyadic relation that constitutes the "connotative component" of R is denoted
by "Con (R)".
The bearing that an interpretant has toward a common object of its sign and itself has no standard name.
If an interpretant is considered to be a sign in its own right, then its independent reference to an object
can be taken as belonging to another moment of denotation, but this omits the mediational character
of the whole transaction.
Given the service that interpretants supply in furnishing a locus for critical, reflective, and explanatory
glosses on objective scenes and their descriptive texts, it is easy to regard them as "annotations" of both
objects and signs, but this function points in the opposite direction to what is needed in this connection.
What does one call the inverse of the annotation function? More generally asked, what is the converse
of the annotation relation?
In light of these considerations, I find myself still experimenting with terms to suit this last-mentioned
dimension of semantics. On a trial basis, I will refer to it as the "ideational", "intentional", or "canonical"
component of the sign relation, and I will try calling the reference of an interpretant sign to an object its
"ideation", "intention", or "conation". Given a particular sign relation R, the dyadic relation that constitutes
the "intentional component" of R is denoted by "Int (R)".
A full consideration of the connotative and intentional aspects of semantics would force a return to
difficult questions about the true nature of the interpretant sign in the general theory of sign relations.
It is best to defer these issues to a later discussion. Fortunately, omission of this material does not interfere
with understanding the purely formal aspects of the present example.
Formally, these new aspects of semantics present no additional problem. The connotative component
of a sign relation R can be formalized as its dyadic projection on the sign and interpretant domains,
defined as:
Con (R) = ProjSI(R) = RSI = R23 = {<s, i> C SxI : <o, s, i> C R for some o C O}.
The intentional component of semantics in a sign relation R, or the "second moment of denotation",
is captured by its dyadic projection on the object and interpretant domains, defined as:
Int (R) = ProjOI(R) = ROI = R13 = {<o, i> C OxI : <o, s, i> C R for some s C S}.
Indeed, the sign relations A and B in the present example are fully symmetric with respect to exchanging
signs and interpretants, so all the structure of AOS and BOS is merely echoed in AOI and BOI, respectively.
The concern of this project is not with every conceivable sign relation but only with those that are capable
of supporting inquiry processes. In these, the relationship between the denotational and connotational
aspects of meaning is not wholly arbitrary. Instead, this relationship must be naturally constrained or
deliberately designed in such a way that it (1) supports the achievement of particular purposes that
have intentional value for the agent and (2) represents the embodiment of significant properties that
have objective reality in the agent's domain. Therefore, my attention is directed toward understanding
the forms of correlation, coordination, and cooperation among the various components of sign relations
that form the necessary conditions for carrying out coherent inquiries.
1.3.4.3 Semiotic Equivalence Relations A nice property possessed by the sign relations A and B is that their connotative components ASI and BSI
constitute a pair of equivalence relations on their common syntactic domain S = I. It is convenient to refer
to such structures as "semiotic equivalence relations" (SER's) since they equate signs that mean the same
thing to somebody. Each of these semiotic equivalence relations ASI, BSI c SxI = SxS partitions the whole
collection of signs into "semiotic equivalence classes" (SEC's). This constitution makes for a strong form of
representation in that the structure of the participants' common object domain is reflected or reconstructed,
part for part, in the structure of each of their "semiotic partitions" (SEP's) of the syntactic domain.
The main trouble with this notion of semantics in the present situation is that the two semiotic partitions
for A and B are not the same, indeed, they are orthogonal to each other. This makes it difficult to interpret
either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of
objective structure or invariant reality, independent of the individual interpreter's "point of view" (POV).
Information about the different forms of semiotic equivalence induced by the interpreters A and B
is summarized in Tables 3 and 4. The form of these Tables should suffice to explain what is meant
by saying that the SEP's for A and B are orthogonal to each other.
Table 3. Semiotic Partition of Interpreter A
Table 4. Semiotic Partition of Interpreter B
To discuss this situation further, I introduce the square bracket notation "[x]E" for "the equivalence class
of the element x under the equivalence relation E". A statement that the elements x and y are equivalent
under E is called an "equation". When the particular equivalence relation that qualifies an equation needs
to be made explicit, or cannot otherwise be taken for granted, as being implicitly understood, the equation
can be written in either one of two ways, as "[x]E = [y]E" or as "x =E y".
In the application to sign relations I extend this notation in the following ways. When R is a sign relation
whose "syntactic projection" or connotative component RSI is an equivalence relation on S, I write "[s]R"
for "the equivalence class of s under RSI". A statement that the signs x and y are synonymous under
a semiotic equivalence relation RSI is called a "semiotic equation" (SEQ), and can be written in either
of the forms: "[x]R = [y]R" or "x =R y".
In many situations there is one further adaptation of the square bracket notation that can be useful.
Namely, when there is known to exist a particular triple <o, s, i> C R, it is permissible to use "[o]R"
to mean the same thing as "[s]R". These modifications are designed to make the notation for semiotic
equivalence classes harmonize as well as possible with the frequent use of similar devices for the
denotations of signs and expressions.
In these terms, the SER for interpreter A yields the semiotic equations:
["A"]A
|
=
|
["i"]A
|
,
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["B"]A
|
=
|
["u"]A
|
,
|
"A"
|
=A
|
"i"
|
,
|
"B"
|
=A
|
"u"
|
,
|
and the semiotic partition: {{"A", "i"}, {"B", "u"}}.
In contrast, the SER for interpreter B yields the semiotic equations:
["A"]B
|
=
|
["u"]B
|
,
|
["B"]B
|
=
|
["i"]B
|
,
|
"A"
|
=B
|
"u"
|
,
|
"B"
|
=B
|
"i"
|
,
|
and the semiotic partition: {{"A", "u"}, {"B", "i"}}.
1.3.4.4 Graphical Representations The dyadic components of sign relations can be given graph-theoretic representations, as "digraphs"
(or "directed graphs"), that provide concise pictures of their structural and potential dynamic properties.
By way of terminology, a directed edge <x, y> is called an "arc" from point x to point y, and a self-loop
<x, x> is called a "sling" at x.
The denotative components Den (A) and Den (B) can be represented as directed graphs on the six points
of their common world set W = O U S U I = {A, B, "A", "B", "i", "u"}. The arcs of the corresponding
digraphs are given as follows:
1.
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Den (A) has an arc from each point of {"A", "i"} to A and from each point of {"B", "u"} to B.
|
2.
|
Den (B) has an arc from each point of {"A", "u"} to A and from each point of {"B", "i"} to B.
|
Den (A) and Den (B) can be interpreted as "transition digraphs" that chart the succession of steps or
the connection of states in a computational process. Read this way, the denotational arcs summarize
the "upshots" of the computations that are involved when the interpreters A and B evaluate the signs
in S according to their own lights, that is to say, in line with their own respective frames of reference.
The connotative components Con (A) and Con (B) can be represented as digraphs on the four points
of their common syntactic domain S = I = {"A", "B", "i", "u"}. Since Con (A) and Con (B) are SER's,
their digraphs conform to the generic pattern that is manifested by all digraphs of equivalence relations.
In general, a digraph of an equivalence relation falls into connected components that correspond to the
parts of the associated partition, with a "complete digraph" on the points of each part, and no other arcs.
By way of definition, a "complete digraph" is one that has all of the possible arcs on a given point set.
In the present case, the arcs of the digraphs for Con (A) and Con (B) are given as follows:
1.
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Con (A) has the structure of a SER on S, with a sling on each of the points in S,
two-way arcs between the points of the syntactic subset {"A", "i"}, and
two-way arcs between the points of the syntactic subset {"B", "u"}.
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2.
|
Con (B) has the structure of a SER on S, with a sling on each of the points in S,
two-way arcs between the points of the syntactic subset {"A", "u"}, and
two-way arcs between the points of the syntactic subset {"B", "i"}.
|
Taken as transition digraphs, Con (A) and Con (B) highlight the associations that are permitted
between equivalent signs, as this equivalence is judged by the interpreters A and B, respectively.
The theme running through the last two subsections, that associates different interpreters and
different aspects of interpretation with different kinds of relational structures on the same set
of points, heralds a topic that will be developed extensively in the sequel.
So far, my discussion of the discussion between A and B, in the picture it gives of sign relations and their
connection to the imagined processes of interpretation and inquiry, can best be described as fragmentary.
In the story of A and B, as I have presented it up to this point, a sample of typical language use has been
drawn from the context of informal discussion and partially formalized in the guise of two independent
sign relations, but no unified conception of the commonly understood interpretive practices in such
a situation has yet been drafted.
It seems like a good idea to pause at this point and reflect on the state of understanding that has been
reached. In order to motivate further developments it will be useful to inventory two types of shortfall
in the present state of discussion, the first having to do with the defects of my present narration in revealing
the relevant attributes of even so simple an example as the one I used to begin, the second having to do with
the defects that this species of example exhibits within the genus of sign relations it is intended to illustrate.
As a general schema, I describe these respective limitations as the "rhetorical" and the "objective" defects
that a discussion, a meditation, or a narration can have in addressing its intended object. The immediate
concern is to remedy the insufficiencies of the current analysis that affect the treatment of the present case.
The overarching task is to address the atypically simplistic features of this example as it falls within the class
of sign relations that are relevant to actual, pressing, and somewhat more realistic inquiries.
The next few subsections will be concerned with the most problematic features of the A and B dialogue,
especially with the sorts of difficulties that furnish clues to significant deficits in theory and technique,
and that point out directions for future improvements.
1.3.4.6 The "Meta" Question There is one point of common contention that I finessed from play in my handling of the discussion
between A and B, even though it lies in plain view on both of their Tables. This is that troubling business,
recalcitrant to analysis precisely because its operations race on so heedlessly ahead of thought and grind on
so routinely beneath its notice, that concerns the proper placements of object languages within the frame of
a meta-language.
Numerous bars to insight appear to interlock here. Each one is forged with a good aim in mind, if a bit
single-minded in its coverage of the scene, and the whole gang is set to work innocently enough in the
unavoidable circumstances of informal discussion. But a failure to absorb their amalgamated impact
on the figurative representations and the analytic intentions of sign relations can lead to several types
of false impression, both about the true characters of the tables presented here and about the proper
utilities of their graphical equivalents to be implemented as data structures in the computer. The next
few remarks are put forward in hopes of averting these brands of misreading.
The general character of this question can be expressed in the schematic terms that were used earlier
to give a rough sketch of the modeling activity as a whole. How do the isolated SOI's of A and B relate
to the interpretive framework that I am using to present them, and how does this IF operate, not only to
objectify A and B as "models of interpretation" (MOI's), but simultaneously to embrace the present and
the prospective SOI's of the current narrative, the implicit systems of interpretation that embody in turn
the initial conditions and the final intentions of this whole discussion?
One way to see how this issue arises in the discussion of A and B is to recognize that each inscribed table
of a sign relation is a complex sign in itself, each of whose syntactic constituents plays the role of a simpler
sign. In other words, there is nothing but text to be seen on the page. In comparison to what it represents,
the table is like a sign relation that has undergone a step of "semantic ascent". It is as if the entire contents
of the original sign relation have been transposed up a notch on the scale that registers levels of indirectness
in reference, each item passing from a more objective standing to a more symbolic mode of presentation.
Sign relations themselves, like any real objects of discussion, are either too abstract or else too concrete
to reside in the medium of communication, but can only find themselves represented there. The tokens
of tables and graphs that are used to represent sign relations are themselves complex signs, necessarily
involving a step of denotation to reach the sign relation intended. The intricacies of this step demand
interpretive agents who are able, over and above executing all of the rudimentary steps of denotation,
to orchestrate the requisite kinds of concerted steps. This performance in turn requires a whole array
of interpretive techniques to match the connotations of complex signs and to test their alternative styles
of representation for semiotic equivalence. In a fashion that is not coincidentally analogous to the ways
that matrices represent linear transformations and that multiplication tables represent group operations,
a large part of the usefulness of these complex signs comes from the fact that they are not just another
pretty fine mass of conventional symbols for their objects but iconic representations of their structure.
In the pragmatic theory of signs, an "icon" is a sign that accomplishes its representation, including the
projects of denotation and connotation, by virtue of properties that it shares with its object. In the case
of relational tables and graphs, interpreted as iconic representations or analogous expressions of logical
and mathematical objects, the pivotal properties are formal and abstract in character. Since a uniform
translation through any dimension (of sight, of sound, or the imagination) does not affect the abstract
structural properties of a configuration of signs in relation to each other, this may help to explain how
tables and graphs, in spite of all their semantic shiftiness, can succeed in representing sign relations
without essential distortion.
Taking this unsuspecting introduction of iconic signs as a serendipitous lesson in the art of representation,
an important principle is there to be lifted from the style of their peculiar form of representational success.
They bring the search for models of intellectual processes to look for classes of representation that do not
lean too heavily on local idioms for devising labels but rather suspend their abstract formal structures in
qualities of media that can best be preserved through a wide variety of global transformations. In time
these ventures will lead this project to contemplate various forms of graphical abstraction as supplying
possibly the most solid sites for pouring the foundations of formal expression.
What does appear in one of these Tables? It is not the objects that appear under the "Object" heading,
but only the signs of these objects. It is not even the signs and interpretants themselves that appear under
the "Sign" and "Interpretant" headings, but only the remoter signs of these signs that are formed through
the syntactic offices of quotation marks. The unformalized sign relation in which these signs of objects,
signs of signs, and signs of interpretants have their role as such is not the one Tabled, but another one,
a casually causative sign relation that operates behind the scenes to bring the image and intent of the
thus-raised Table, through the facilitations, the interventions, and the obstructions of the medium,
to the eventual reader.
To understand what the Table is meant to convey the reader has to participate in the informal and more
accessory sign relation in order to follow its indications to the intended and more accessible sign relation.
As logical or mathematical objects, the sign relations A and B do not exist in the medium of their Tables
but are represented there by dint of the relevant structural properties that they share with these Tables.
As fictional characters, the interpretive agents A and B do not exist in a uniquely literal sense but serve
as typical literary figures to convey the intended formal account, standing in for concrete experiences
with everyday language use the likes of which are familiar to writer and reader alike.
The successful formalization of a focal sign relation cannot get around its reliance on prior forms
of understanding, like the raw ability to follow indications whose components of competence are
embodied in the vaster and largely unarticulated context of a peripheral sign relation. But the extent
to which the analysis of a formal sign relation depends on a particular context or a particular interpreter
is the extent to which an opportunity for understanding is undermined by a prior petition of the very
principles to be explained. Thus, there is little satisfaction in special pleadings or ad hoc accounts of
interpretive practice that cannot be transported across a multitude of contexts, media, and interpreters.
What does all of this mean, in concrete form, for the proper appreciation of the present example?
And looking beyond that question, what does it mean in terms of the concrete activities that need
to be tackled by this work?
One task is to eliminate several types of formal confound that currently affect this investigation.
Even though there is an essential tension to be maintained down the lines between casual and formal
discussion, the traffic across these realms needs to be monitored carefully. There are identifiable sources
of confusion that devolve from the context of informal discussion and invade the arena of formal study,
subverting its necessary powers of reflection and undermining its overall effectiveness.
One serious form of contamination can be traced to the accidental circumstance that A and B and I
all use the same proper names for A and B. This renders it is impossible to tell, purely from the tokens
that are being tendered, whether it is a formal or a casual transaction that forms the issue of the moment.
It also means that a formalization of the writer's and the reader's accessory sign relations would have
several portions of its abstract mien, its formal countenance or its idealized visage, that look identical
to various pieces of those Tables that are presently placed under formal review. This is tantamount to
having a sort of "mirror" between the formal and the informal domains, one that reflects certain aspects
of the casual circumstances of discourse into the forms of the formalization itself. Although a device of
this kind can be a useful tool, even, on reflection, indispensable at times, so long as the character and the
nature of its operation are understood by its prospective user, it can also become a source of bewildering
confusions and thoroughly distracting nuisances, if the conditions for its effective employment are not met.
1.3.4.8 The Conflict of Interpretations One discrepancy that needs to be documented can be observed in the conflict of interpretations between
A and B, as reflected in the lack of congruity between their semiotic partitions of their syntactic domain.
This is a problematic but realistic feature of the present example. That is, it represents a type of problem
with the interpretation of pronouns (indexical signs or bound variables) that actually arises in practice
whenever one attempts to formalize the semantics of natural, logical, and programming languages.
On this account, the deficiency resides with the present analysis, and the burden remains to clarify
exactly what is going on here.
Notice, however, that I have deliberately avoided dealing with indexical tokens in the usual ways, namely,
by seeking to eliminate all semantic ambiguities from the initial formalization. Instead, I have preserved
this aspect of interpretive discrepancy as one of the essential phenomena or the inescapable facts in the
realm of pragmatic semantics, tantamount to the irreducible nature of perspective diversity. I believe
that the desired competence at this faculty of language will come, not from any strategy of substitution
that constantly replenishes bound variables with their objective referents on every fixed occasion, but from
a pattern of recognition that keeps indexical signs persistently attached to their due interpreters of reference.
In the pragmatic theory of signs, an "index" is a sign that achieves its representation of its object by virtue
of an actual connection with it. Though real and objective, however, the indexical linkage can be purely
incidental and even a bit accidental. Its effectiveness depends only on the fact that an object in actual
existence has many properties, definitive and derivative, any number of which can serve as its signs.
Indices of an object frequently reside among the more tangential varieties of its attributes, typically,
its accessory traces or its accidental traits, which are really the features of some but not all of the
points in the locus, the orbit, the status, or the trajectory of the object's existential actualization.
Pronouns qualify as indices because their objective references cannot be traced without recovering further
information about their actual context, not just their objective and their syntactic contexts but the pragmatic
context that is involved in the actualizing "situation of use" (SOU) or the realizing "instance of use" (IOU).
To fulfill their duty to sense the reading of indices demands to be supplemented by a suitably determinate
indication of their interpreter of reference, the agent that is responsible for putting them into active use
at the moment of interpretation in question.
Typical examples of indexical signs in programming languages are: (1) "variables", signs that need
to be bound to a syntactic context or an instantiation frame in order to have a determinate meaning,
and (2) "pointers", signs that serve particular interpreters, as they find themselves operating relative
to their locally active contexts and temporally dynamic environments, as accessory addresses of
modifiable memory contents. In any case something extra -- some further information about
the objective, syntactic, or interpretive context -- must be added to the index in order to tell
what it does in fact denote, or even if it does indeed denote anything at all.
If a real object can be regarded as a generic and permanent property that is shared by all of its specific
and momentary instantiations, then it is possible to re-characterize indexical signs in the following terms:
An index of an object is a property of an actual instance of that object. It is in this sense that indices are
said to have actual but not essential connections to what they denote.
Saying that an index is a property of an instance of an object almost makes it sound as though the relation
of an index to what it denotes could be defined in purely objective terms, as a relative product of the two
dyadic relations, "property of" and "instance of", and wholly independently of any particular interpreter.
But jumping to this conclusion would only produce an approximation to the truth, or a likely story, and
thus the kind of a shabby pretension to real-life narrative that would deservedly provoke the rejoinders:
"In whose approach?" or "Likely to whom?"
Taking up these challenges provides a clue as to how a sign relation can appear to be "nearly objective",
"moderately independent", or "relatively composite", all with appropriate respect to the intermediary of
an operative interpreter and all within the medium of a particular framework for analysis and interpretation.
Careful inspection of the context of definition reveals that it is not really the supposedly frame-free relations
of properties and instances that suffice to compose the indexical connection. Indeed, it is not nearly enough
that the separate links exist in principle to make something a property of an instance of something. In order
to constitute a genuine sign relation, indexical or otherwise, each link must be recognized to exist by one
and the same interpreter.
From this point of view, the object is considered to be something in the external world and the index is
considered to be something that touches on the interpreter's experience, both of which subsume, though
perhaps in different senses, the "object instance" (OI) that mediates their actual connection. Although the
respective subsumptions, of OI to object and of OI to index, can appear to fall at first glance only within
the reach of divergent senses, both must appeal for their eventual realization to a common sense, one that
rests within the grasp of a single interpreter. Apparently then, the object instance is the sort of entity that
can contribute to generating both the object and the experience, in this way connecting the diverse forms
of abstraction called "objects" and "indices".
If a suitable framework of object instances can be found to rationalize a particular interpreter's experience
with objects, then the actual connection that subsists between an object and its index becomes in this frame
precisely the connection that exists between two properties of the same object instance, or between two sets
intersecting in a common element. Relative to the appropriate framework, the actual connections needed to
explain a global indexing operation can be identified, point for point, with the collective function of those
joint instances or common elements.
At this stage of analysis, what were originally regarded as real objects have become hypostatic abstractions,
extended as generic entities over classes of more transient objects, their instantiating actualizations. In this
setting, a real object is now analogous to an extended property or a generative predicate, whose extension
generates the trajectory of its momentary instances or the locus of its points in actual existence.
Persisting in this form of analysis appears to lead the discussion toward levels of existence that are in one
way or another more real, more determinate, in a word, more objective than its original objects. If only
a particular way of pursuing this form of analysis could be established as reaching a truly fundamental
level of existence, then reason could not object to speaking of objects of objects, nor even to invoking
the ultimate objects of objects, meaning the unique atoms at the base of the hierarchy that is formed
by the descent of objects.
And yet experience leads me to believe that forms of analysis are too peculiar to persons and communities,
times and mores, too dependent on their particular experiences and traditions, and overall too much bound
to interpretive constitutions of learning and culture to ever be justly established as invariants of nature.
In the end, or rather, by way of appeal to the many courts of final opinion, to invoke any particular
form of analysis, no matter whether it is baseless or well-founded, is just another way of referring
judgment to a particular interpreter, a contingent IF or a self-serving SOI. Consequently, every
form of arbitration retains an irreducibly arbitrary element, and the best policy remains what
it has always been, to maintain an honest index of that fact.
Therefore, I consider any supposed form of "ontological descent" to be, more likely, just one among many
possible forms of "semantic descent", each one of which details a particular way to reformulate objects as
signs of more determinate objects, and every one of which forms of devolution operates with respect to its
own implicit assumption of a form of analysis or its own proper, and probably tacit, analytic framework.
There are moments in the development of an analytic discussion when a thing initially described as a single
object under a single sign needs to be reformulated as a congeries extending over more determinate objects.
If the usage of the original singular sign is preserved, as it often is, then the multitude of new instances that
one comes to fathom beneath the old object's superficial appearance gradually serve to reconstitute the
singular sign's denotation in the fashion of a plural reference.
One such moment was reached in the preceding subsection, where the topics opened up by indexical signs
invited the discussion to begin addressing much wider areas of concern. Eventually, to account for the
effective operation of indexical signs I will have to invoke the concept of a "real object" and pursue the
analysis of ostensible objects in terms of still more objective things. These are the extended multitudes
of increasingly determinate objects that I will variously refer to as the actualizations, the instantiations,
the realizations, etc. of objects, and on occasion (and not without reason) the "objects of objects" (OOO's).
Another such moment will arrive when I turn to developing suitable embodiments of sign relations within
dynamically realistic systems. In order to implement interpreters as state transition systems, I will have to
justify the idea that dynamic states are the "real signs" and proceed to reconstitute the customary types of
signs as abstractions from still more significant tokens. These are the immediate occasions of sign-using
transactions that I will tender as "instances of use" (IOU's) or "situations of use" (SOU's), plus the states
and motions, that is, the projectable evolutions, of dynamic systems that solely are able to realize these
uses and discharge the obligations they incur to reality.
In every case, working within the framework of systems theory will lead this discussion toward systems
and conditions of systems as the ultimate objects of investigation, implicated as the ends of both synthetic
and analytic proceedings. Sign relations, initially formulated as relations among three arbitrary sets, will
gradually have their original substrates replaced with three systems, the object system, the sign system,
and the interpretant system -- not just sets, but systems all -- not just set in their several places, but
actively, dynamically, triadically interacting.
Since the roles of a sign relation are formally and pragmatically defined, they do not overly fixedly depend,
to the exclusion of every conceivable transubstantiation, on the material aspects or the entitative attributes
of the initial domains of their consensual definition or the transient elements of their temporal realization.
Therefore, it is conceivable that the very same system could appear in all three roles, and from the open
chance of this possibility arises much of the ensuing complication of the subject, not to mention many
of its most baffling subtleties.
A related source of conceptual turbulence stems from the circumstance that, even though a certain
aesthetic dynamics attracts the mind toward sign relational systems that are capable of reflecting on,
commenting on, and thus "counter-rolling" their own behavior, it is still important to distinguish in
every active instance the part of the system that is doing the discussing from the part of the system
that is being discussed. To do this, the duly observant interpreter needs two things: (1) the senses
to discern the essential tensions that typically prevail between the formal pole and the informal arena,
and (2) the language to articulate, aside from their potential roles, the moment by moment placement
of dynamic elements and systematic components with respect to this compassing field of polarities.
1.3.4.11 Review & Prospect What has been learned from the foregoing study of icons and indices? The import of this examination
can be sized up in two stages, at first, by reflecting on the action of both the formal and the casual signs
that were found to be operating in and around the discussion of A and B, and then, by taking up the
lessons of this circumscribed arena as a paradigm for future investigation.
In order to explain the operation of sign relations corresponding to the iconic and the indexical signs
in the A and B example, it becomes necessary to refer to potential objects of thought that are located,
if they exist at all, outside the realm of the initial object set, in other words, lying beyond the objects
of thought that are present at the outset of the discussion and that one initially recognizes as objects
of formally identified signs. In the process of doing this, it is incumbent on a satisfying explanation
of the initial objects to invoke the abstract properties of objects and the actual instances of objects,
where all of these properties and all of these instances are usually assumed to be "new" objects of
thought, that is, ones that are normally and typically distinct from the objects to which they relate.
In the pragmatic account of things, thoughts are just signs in the mind of their thinker, so every object
of a thought is the object of a sign, though perhaps in a sign relation that has not been fully formalized.
Considered on these grounds, the search for a satisfactory context in which to explain the actions and
the effects of signs turns into a recursive process that potentially calls on ever higher levels of properties
and ever deeper levels of instances that are found to stem from whatever objects instigated the search.
To make it serve as a paradigm for future developments, I repeat the basic pattern that has just been
observed, but with a slightly different emphasis, more suitably adapted for extended and flexible use:
In order to explain the operation of icons and indices in a particular discussion, it is necessary to invoke
the abstract properties of objects and the actual instances of objects, where under the heading of "objects"
one initially comprehends a limited collection of objects of thought under discussion. Now, if these
properties and these instances are themselves regarded as potential objects of thought, and if they are
conceived to be definitively other than the objects whose properties and instances they happen to be,
then every initial collection of objects is forced to expand on further consideration, in this way pointing
to a world of objects of thought that extends in two directions beyond the originating frame of discussion.
Can this manner of recursively searching for explanations of objects be established as well-founded?
In order to organize the expanding circle of thoughts and the growing wealth of objects that can come
to be envisioned within its scheme, it helps to introduce a set of organizing conceptions. Doing this will
be the business of the next four subsections.
1.3.4.12 Objective Plans & Levels In accounting for the special characters of icons and indices that arose in previous discussions,
it was necessary to open the domain of objects coming under formal consideration to include
unspecified numbers of properties and instances of whatever objects were initially set down.
This is a general phenomenon, affecting every motion toward the explanation of objects and
the phenomena affecting them, whether pursued by analytic or by synthetic means. What it
calls for in practice is a systematic way of organizing growing domains of objects, without
having to specify in advance all of the objects that there are, or that may be allowed to be.
This subsection presents the "objective project" (OP) that I plan to take up for investigating the forms
of sign relations. It outlines three "objective levels" (OL's) of formulation that guide the intertwined
analytic and synthetic studies of interpretive structure and that regulate the prospective stages of
implementing this plan in particular cases. The main purpose of these schematic conceptions is
organizational, to provide a conceptual architecture for the burgeoning hierarchies of objects
that arise in the generative processes of inquiry.
In the immediate context the objective project and the three levels of objective description are presented in
broad terms. In the process of surveying a variety of problems that serve to instigate efforts in this general
direction, I explore the prospects of a particular "organon", or "an instrumental scheme for the analysis and
the synthesis of objects", that is intended to address these issues, and I give an overview of its design.
In interpreting the sense of the word "objective" as it is used in this application, it may help to regard
this objective project in the light of a telescopic analogy, with an "objective" being "a lens or a system
of lenses that forms an image of an object" (Webster's).
In the next three subsections after this one the focus returns to the separate levels of object structure,
starting with the highest level of specification and treating the supporting levels in order of increasing
detail. At each stage, the developing tools are applied to the analysis of concrete problems that arise
in trying to clarify the structures and the functions of sign relations. For the present task, elaborations
of this perspective are kept within the bounds of what is essential to deal with the example of A and B.
At this point, I need to apologize in advance for a introducing a certain difficulty of terminology,
but the underlying issue that it raises can no longer be avoided. To wit, I am forced to use the word
"objective" in a way that conflicts with several traditions of interpretation, going so seriously against
the grain of dominant and prevailing connotations that it will probably sound like a joke to many readers.
Nevertheless, it is a definite "motive of consistency" (MOC) that requires me to do this.
As always, my use of the word "object" derives from the stock of the Greek root "pragma", which captures
all of the senses that are needed to suggest both the stability of concern and the dedication to purpose that
are forever bound up in the constitution of objects and the institution of objectives. What it implies is that
every object, objective, or objectivity is always someone's object, objective, or objectivity.
In other words, objectivity is always a matter of interpretation. It is concerned with and quantified by
the magnitude of the consensus that a matter is bound to have at the end of inquiry, but in no way does
this diminish or dismiss the fact that the fated determination is something on which any particular collection
of current opinions may be granted to differ. In principle, there begins to be a degree of objectivity as soon
as something becomes an object to somebody, and the issue of whether this objective waxes or wanes over
time is bound up with the number of observers that are destined to concur on it.
The critical question is not whether a thing is an object of thought and discussion, but what sort of thought
and discussion it is an object of. How does one determine the character of this thought and this discussion?
And should this query be construed as addressing a task of finding or of making? Whether it appeals to the
art of acquisition, production, or discernment, and however one expects to decide or to decode the conduct
that it requires, the character of the thought and discussion in view can be sized up and riddled out in turn
by looking at the whole domain of objects and the entire pattern of relations among them that it actively
charts and encompasses. This makes what is usually called "subjectivity" a special case of what I must
call "objectivity", since the interpretive and the perspectival elements are ab initio operative and cannot
be eliminated from any conceivable form of discernment, including their own.
Consequently, analyses of objects and syntheses of objects are always analyses and syntheses to somebody.
Both modes of approaching the constitutions of objects lead to the tentative orders of approximation that are
appropriate to particular agents and that are able to be appropriated by whole communities of interpretation.
By way of relief, on occasions when this motive of consistency hobbles the discussion too severely, I will
resort to using fantastic chimeras like "object-analytic" and "object-synthetic", paying the price of biasing
the perceived constitution of objects, along with the preconceived orientation that is projected into objects,
as though it could realistically inhere there, in one direction or the other.
In this project I would like to treat the difference between construction and deconstruction as being more or
less synonymous with the contrast between synthesis and analysis, but doing this without the introduction
of too much distortion requires the intervention of a further distinction. Therefore, let it be recognized that
all orientations to the constitutions of objects can be pursued in both "regimented" and "radical" fashions.
In the weaker senses of the terms, analysis and synthesis work within a preset and limited regime of objects,
construing each object as being composed from a fixed inventory of stock constituents. In stronger senses,
contracting for the application of these terms places a more strenuous demand on the would-be construer.
A radical form of analysis, in order to discern the contrasting intentions that reside in everything construed
as an object, requires interpreters to leave, or at least to re-place, each object within the context of its living
acquaintance, to reflect on their own motives and partial motifs for construing and employing objects in the
ways that they do, and to deconstruct how their own aims and biases enter into the form and use of objects.
A radical form of synthesis, in order to integrate ideas and information devolving from entirely different
"frameworks of interpretation" (FOI's), requires interpreters to reconstruct their initially isolated concepts
and descriptions on a mutually compatible basis and to use a means of composition that can constitute
a medium for common sensibilities.
Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis
that can reflect a measure of light on the initially unstated assumptions of their prospective agents.
The foregoing considerations lead up to the organizing conception of an "objective framework" (OF),
in which objects can be analyzed into sets of constituent objects, perhaps proceeding recursively to some
limiting level where the fundamental objects of thought are thought to rest. If an OF is felt to be completely
unique and uniquely complete, then people tend to regard it as constituting a veritable "ontology", but I will
not be able to go that far. The recognition of plural and fallible perspectives that goes with pragmatic forms
of thinking does not see itself falling into line any time soon with any one or only one ontology.
On the opposite score, there is no reason to deny the possibility that a unique and complete OF exists.
Indeed, the hope that such a standpoint does exist often provides inquiry with a beneficial regulative
principle or a helpful heuristic hypothesis to work on. It merely happens, for the run of our kinds of
"finitely informed creatures" (FIC's) at any rate, that the existence of an ideal framework is something
to be established after the fact, at least nearer toward the end of inquiry than the present time marks.
In this project, an OF embodies one or more "objective genres" (OG's), which may be called in alternation
"forms of analysis" (FOA's) or "forms of synthesis" (FOS's), each one of which delivers its own rendition
of a "great chain of being" for all of the objects under its purview. In effect, each OG can be viewed as
developing its own version of an "ontological hierarchy" (OH), designed independently, in principle,
from the others that are possible to capture an aspect of structure in its objective domain.
For now, the level of an OF operates as a catch-all, giving the projected discussion the elbow room that
it needs to range over an unspecified variety of different OG's and to place the particular OG's of active
interest in a running context of comparative evaluations and developmental options.
Any given OG can appear under the alias of a "form of analysis" (FOA) or a "form of synthesis" (FOS),
depending on the direction of prevailing interest. A notion frequently invoked for the same purpose is
that of an "ontological hierarchy" (OH), but I will use this only provisionally, and only so long as it is
clear that alternative ontologies can always be proposed for the same space of objects.
An OG embodies many "objective motives" or "objective motifs" (OM's). If an OG constitutes a genus,
or a generic pattern of object structure, then the OM's amount to its specific and its individual exemplars.
Thus, an OM can appear in the guise of a particular instance, trial, or "run" of the general form of analytic
or synthetic procedure that accords with the protocols of a given OG.
In order to provide a way of talking about objective points of view in general without having to specify
a particular level, I will use the term "objective concern" (OC) to cover any particular OF, OG, or OM.
An OG, in its general way, or an OM, in its individual way, begins by relating each object in its purview
to a unique set of further objects, called the "components", the "constituents", the "effects", the "ingredients",
or the "instances" of that object with respect to that "objective concern" (OC), namely, the OG or the OM
that one happens to have in mind at the moment in question. As long as the discussion remains fixed to
what is visible within the scope of a particular OC, the collected effects of each object in view constitute
its "active ingredients", supplying it with a unique decomposition that defines it to a degree sufficient
for all practical purposes that are admitted as conceivable within that discussion.
Contemplated from an outside perspective, however, the status of these effects and these instances as the
"defining unique determinants" (DUD's) of each object under examination is something to be questioned.
The supposed constituents of an object that are obvious with respect to one OC can be regarded with some
suspicion from the points of view of alternative OC's, and their apparent status as rock-bottom substantives
can find itself reconstituted in the guise of provisional placeholders (placebos or excipients) that precipitately
index the potential operation of more subtly active ingredients.
If a single OG could be unique and the realization of every object in it could be complete, then there might
be some basis for saying that the elements of objects and the extensions of objects are known, and thus that
the very "objects of objects" (OOO's) are determined by its plan. In practice, however, it takes a diversity
of overlapping and not entirely systematic OG's to make up a moderately useful OF.
What gives an OG a definite constitution is the naming of a space of objects that falls under its purview
and the setting down of a system of axioms that affects its generating relations.
What gives an OM a determinate character from moment to moment within the continuing framing
of a definite discussion is the particular selection of objects and the personal election of linkages from
its governing OG that it can say it has actualized, apprehended, or appropriated, in other words, the portion
of its OG that it can say actually belongs to it, and whether they make up a lot or a little, the roles it can say
it has made its own.
In setting out the preceding characterization, I have reiterated a figure of speech that is likely to seem like
an anthropomorphism, prefacing each requirement of the candidate OM with the qualification "it can say".
This is done in order to emphasize that an OM's command of a share of its OG is partly a function of the
interpretive effability that it can be depicted as bringing to bear on its object domain and partly a matter
of the expressive power that it is able to dictate over its own development.
1.3.4.13 Formalization of OF: Objective Levels The three levels of objective detail to be discussed are referred to as the objective "framework", "genre",
and "motive" that one finds actively involved in organizing, guiding, and regulating a particular inquiry.
1.
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An "objective framework" (OF) consists of one or more "objective genres" (OG's), also called
"forms of analysis" (FOA's), "forms of synthesis" (FOS's), or "ontological hierarchies" (OH's).
Typically, these span a diverse spectrum of formal characteristics and intended interpretations.
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2.
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An OG is made up of one or more "objective motives" or "objective motifs" (OM's), which are
sometimes regarded as particular "instances of analysis" (IOA's) or "instances of synthesis" (IOS's).
All of the OM's that are governed by a particular OG exhibit a kinship of structures and intentions,
and each OM roughly fits the pattern or "follows in the footsteps" of its guiding OG.
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3.
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An OM can be identified with a certain moment of interpretation, one in which a particular
dyadic relation appears to govern all of the objects in its purview. Initially presented as an
abstraction, an individual OM is commonly fleshed out by identifying it with its interpretive
agent. As this practice amounts to a very loose form of personification, it is subject to all of
the dangers of its type and is bound eventually to engender a multitude of misunderstandings.
In contexts where more precision is needed it is best to recognize that the application of an OM
is restricted to special instants and limited intervals of time. This means that the individual OM
must look to the "interpretive moment" (IM) of its immediate activity to find the materials that
are available for both its concrete instantiation and its real implementation. Finally, having
come round to the picture of an objective motive realized in an interpretive moment, this
discussion has made a discrete advance toward the desired forms of dynamically realistic
models, providing itself with what begins to look like the elemental states and dispositions
that are needed to build up the characters of fully self-actualizing systems of interpretation.
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A major theoretical task that remains outstanding for this project is to discover a minimally adequate basis
for defining the state of uncertainty that an interpretive system has with respect to the questions it is able
to formulate about the state of an object system. Achieving this would permit a measure of definiteness
to be brought to the question of inquiry's nature, since it can be grasped intuitively, granted a pluralistic
form of correctable intuition, that the gist of inquiry is to reduce an agent's level of uncertainty about its
object, objective, or objectivity through appropriate changes of state.
Accordingly, one of the roles intended for the desired OF is to provide a set of standard formulations for
describing the moment to moment uncertainty of interpretive systems. In view of these aims, the formally
definable concepts of the MOI (the objective case of a SOI) and the IM (the momentary state of a SOI) are
intended to formalize the intuitive notions of a generic mental constitution and a specific mental disposition
that usually serve in discussing states and directions of mind.
The structures that one finds present at each objective level are formulated by means of converse pairs
of "staging relations", prototypically symbolized by the signs "<" and ">". At the more generic levels of
OF's and OG's the "staging operations" associated with the generators "<" and ">" involve the application
of dyadic relations that are analogous to class membership "C" and its converse, but the increasing amounts
of parametric information that are needed to determine their specific motives and their detailed motifs give
the more determinate OM's the full power of triadic relations. Using the same pair of symbols to designate
staging relations at all objective levels helps to prevent an excessive proliferation of symbols, but it means
that the meaning of these symbols is always heavily dependent on context. In particular, even fundamental
properties like the effective "arity" of the relations signified can vary from level to level.
The staging relations divide into two orientations, "<" versus ">", indicating opposing senses of direction
with respect to the distinction between analytic and synthetic projects:
1.
|
The "standing relations", indicated by "<", are analogous to the "element of" relation, also known as
the "elementhood" or the "membership" relation, and usually denoted by "C". Another interpretation
of "<" is the "instance of" relation. At least with respect to the more generic levels of analysis, any
distinction between these readings is immaterial to the formal interests and the structural objectives
of the present discussion. When it is necessary to refer to a specific standing relation as a collection
of ordered pairs, one may use square brackets around the relation symbol, thus: "[<]".
|
2.
|
The "propping relations", indicated by ">", are analogous to the "class of" relation or the converse
of the membership relation. An alternate meaning for ">" is the "property of" relation. Although
it is possible to maintain a distinction here, the present discussion is mainly concerned with levels
of abstract formal structure to which this difference is largely irrelevant. When it is necessary to
refer to a specific propping relation as a collection of ordered pairs, one may use square brackets
around the relation symbol, thus: "[>]".
|
Although it may be logically redundant, it is useful in practice to introduce efficient symbolic devices
for both directions of relation, "<" and ">", and to maintain a formal calculus that treats analogous pairs
of relations on an equal footing. Extra measures of convenience come into play when the relations are
used as "assignment operations", or as what might metaphorically be described as "field promotions",
in other words, to create titles, to define terms, and to establish offices of objects in the active contexts
of given relations. Thus, I regard these dual relationships as symmetric primitives and use them as
the "generating relations" of all three objective levels.
Next, I present several different ways of formalizing OG's and OM's. The reason for employing multiple
descriptions is to capture the various ways that these patterns of organization actually appear in practice.
One way to approach the formalization of an objective genre G is through an indexed collection
of dyadic relations:
G = {Gj} = {Gj : j C J}, with Gj c PjxQj for all j C J.
Here, J is a set of actual (not formal) parameters that are used to index the OG, while Pj and Qj
are domains of objects (initially in the informal sense) that enter into the dyadic relations Gj.
Aside from their indices, any of the Gj in G are permitted to be abstractly identical to each other.
This would earn G the designation of a "multi-family" or a "multi-set" according to some usages,
but I prefer to treat the index j as a concrete part of the indexed relation Gj, in this way, at least,
distinguishing each dyadic relation Gj c PjxQj from all other members of the indexed family G.
Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains,
Pj and Qj for all j C J. Common strategies for getting around this trouble involve the introduction
of additional domains, designed to encompass all of the objects that are needed in given contexts.
Toward this end, an adequate supply of intermediate domains or moderating environments, called
the "rudiments of universal mediation" (RUM's), can be defined as follows:
Xj = Pj U Qj ,
|
P = Uj Pj ,
|
Q = Uj Qj .
|
Ultimately, all of these "totalitarian" strategies end the same way, at first, by envisioning a domain X
that is ostensibly big enough to encompass all of the objects of thought that might conceivably demand
entry into a given discussion, and then, by invoking one of the following conventions:
Rubric of Universal Inclusion (RUI):
|
X = Uj (Pj U Qj).
|
Rubric of Universal Equality (RUE):
|
X = Pj = Qj for all j C J.
|
Working under either of these assumptions, G can be provided with a simplified form of presentation:
G = {Gj} = {Gj : j C J}, with Gj c XxX for all j C J.
Nevertheless, it serves certain purposes of this project to preserve the individual indexing of relational
domains for a little while longer, or at least to keep this usage available as an alternative formulation.
Generally speaking, it is always possible in principle to form the union required by the RUI, or else,
without loss of generality, to assume the equality imposed by the RUE. The problem is that the
unions and the equalities that are invoked by these rubrics may not be effectively definable or
efficiently testable in a computational context. Further, even when these sets or tests can be
constructed or certified by some computational agent or another, the pertinent question at
any interpretive moment is whether each collection or constraint is actively apprehended
or warranted by the particular interpreter that is charged with responsibility for it by the
indicated assignment of domains.
But an overall purpose of this formalism is to represent the objects and the constituencies that are
"known to" specific interpreters at definite moments of their interpretive proceedings, in other words,
to depict the information about objective existence and constituent structure that is possessed, recognized,
responded to, acted on, and followed up by concrete agents as they move through their immediate contexts
of activity. Accordingly, keeping individual tabs on the relational domains Pj and Qj, though it does not
solve this array of problems, does serve to mark the concern with particularity and to keep before the
mind the issues of individual attention and responsibility that are appropriate to interpretive agents.
In short, whether or not relational domains appear with explicit subscripts in a given presentation,
one should always be prepared to answer the question: "Who subscribes to these domains?"
It is important to emphasize that the index set J and the particular attachments of indices to dyadic relations
are part and parcel to G, befitting the concrete character that is intended for the concept of an OG, which is,
after all, expected to realistically embody in the character of each Gj both "a local habitation and a name".
For this reason, among others, the Gj can safely be referred to as "individual dyadic relations" (IDR's).
Since the classical notion of an "individual" as a "perfectly determinate entity" has, strictly speaking,
no application in the sorts of finite information contexts that I am treating here, it is safe to recycle
this term to distinguish the "terminally informative particulars" (TIP's) that a concrete index j adds
to its thematic object Gj, whether this addition is made parenthetically or more paraphatically.
Depending on the prevailing direction of interest in the genre G, "<" or ">", the same symbol is used
equivocally for any of the relations Gj. The Gj can be regarded as formalizing the OM's that make up
the genre G, provided it is understood that the information corresponding to the parameter j constitutes
an integral part of the "motive" or the "motif" that is associated with the dyadic relation Gj.
In this formulation, G constitutes an "ontological hierarchy" (OH) of a plenary and a potentiating type,
one that determines the complete array of objects and relationships that are conceivably available and
describably "effable" within a given discussion. Operating with regard to the global field of possibilities
presented by G, each Gj corresponds to the specialized competence of a particular agent, selecting out the
objects and the links of the generic hierarchy that are known to, owing to, or owned by a given interpreter.
Another way to formalize the structure of an OG can be posed in terms of a "relative membership relation"
or a notion of "relative elementhood". The constitutional structure or the formal definition of a given OG
can be set up in a moderately flexible manner by taking its construction in two stages, starting from the
level of the finer details and working up to the big picture:
1.
|
Each OM is constituted by what it means to be an object within it.
What constitutes an object in a given OM can be fixed as follows:
|
|
a.
|
In absolute terms, by specifying the domain of the objects that fall under its purview.
For the present, I assume that each OM inherits one and the same object domain X
from its governing OG.
|
|
b.
|
In relative terms, by specifying a converse pair of dyadic relations that determine,
if a bit redundantly, two sets of facts:
|
|
|
i.
|
What is an instance, example, member, or element of what,
relative to the OM in question.
|
|
|
ii.
|
What is a property, quality, class, or set of what,
relative to the OM in question.
|
2.
|
The various OM's of a particular OG can be unified under its overall aegis by means
of a single triadic relation, one that names an OM and a pair of objects and holds
when one object belongs to the other in the sense identified by the relevant OM.
If it becomes absolutely essential to emphasize the relativity of elements, one
may resort to calling them "relements", in this way jostling the mind to ask:
"Relement to what?"
|
The last and likely the best way one can choose to follow in order to form an objective genre G
is to present it as a triadic relation, usually given in either one of two ways:
G = {<j, p, q>} c JxPxQ,
G = {<j, x, y>} c JxXxX.
For some reason the ultimately obvious method seldom presents itself exactly in this wise without a lot
diligent work on the part of the inquirer, or on the part of anyone who would arrogate the roles of both
its former and its follower. Perhaps this has to do with the problematic role of "synthetic a priori" truths
in constructive mathematics. Perhaps the mystery lies encrypted still, no doubt buried in some obscure
dead letter office, due to the obliterate indicia on the letters "P", "Q", and "X" that are inscribed above.
No matter -- at the moment there are far more pressing rounds to make.
Given a genre G whose OM's are indexed by a set J and whose objects form a set X, there is determined
a triadic relation that exists among an OM and a pair of objects just in case the first object belongs to the
second object according to that OM. This is called the "standing relation" of the OG, and it can be taken
as one way of defining and establishing the genre. In the way that triadic relations usually give rise to
dyadic operations, the associated "standing operation" of the OG can be thought of as a brand of
assignment operation that makes one object belong to another in a certain sense, namely, in the
precise sense that is indicated by the designated OM.
There is a "partial converse" of the standing relation that transposes the order in which
the two object domains are mentioned. This is called the "propping relation" of the OG,
and it can be taken as an alternate way of defining the genre. Once again, there are two
ways that one usually sees the converse genre G^ being presented and defined in terms
of the given genre G:
G^ = {<j, q, p> C JxQxP : <j, p, q> C G},
G^ = {<j, y, x> C JxXxX : <j, x, y> C G}.
The following conventions are useful for discussing the set-theoretic extensions of the staging relations
and staging operations of an OG:
1.
|
The full triadic standing relation of an OG is denoted by the symbol ":<", pronounced "set-in",
so that one may write "[:<] c JxPxQ" or "[:<] c JxXxX".
|
2.
|
The full triadic propping relation of an OG is denoted by the symbol ":>", pronounced "set-on",
so that one may write "[:>] c JxQxP" or "[:>] c JxXxX".
|
Often one's level of interest in a genre is "purely generic". When the relevant genre is regarded
as an indexed family of dyadic relations, G = {Gj}, then this generic interest is tantamount
to having one's concern rest with the union over all of the dyadic relations in the genre.
UJG = Uj Gj = {<x, y> C XxX : <x, y> C Gj for some j C J}.
When the relevant genre is contemplated as a triadic relation, G c JxXxX, then one is dealing with
the projection of G on the object dyad XxX.
GXX = ProjXX(G) = {<x, y> C XxX : <j, x, y> C G for some j C J}.
On these occasions, the assertion that <x, y> C UJG = GXX can be indicated by any one
of the following equivalent expressions:
G : x < y,
|
x <G y,
|
x < y : G,
|
G : y > x,
|
y >G x,
|
y > x : G.
|
At other times more explicit mention needs to be made of the interpretive perspective,
as formalized by the "individual dyadic relation" (IDR) that links each pair of objects.
To indicate that a triple consisting of an OM j and two objects x and y belongs to the
standing relation of the OG, otherwise written as "<j, x, y> C [:< ]", or equivalently,
to indicate that a triple consisting of an OM j and two objects y and x belongs to the
propping relation of the OG, otherwise written as "<j, y, x> C [:>]", all of the
following notations are equivalent:
j : x < y,
|
x <j y,
|
x < y : j,
|
j : y > x,
|
y >j x,
|
y > x : j.
|
In actual, concrete, live, and particular contexts, assertions falling under the abstract forms of these relations
may find themselves being fleshed out, interpreted, read, and taken in a multitude of ways, for example:
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j sets x in y.
j makes x an instance of y.
j thinks x an instance of y.
j attests x an instance of y.
j appoints x an instance of y.
j witnesses x an instance of y.
j interprets x an instance of y.
j contributes x to y.
j determines x an example of y.
j evaluates x an example of y.
j proposes x an example of y.
j musters x under y.
j indites x among y.
j imputes x among y.
j judges x beneath y.
j finds x preceding y.
j poses x before y.
j forms x below y.
|
|
j sets y on x.
j makes y a property of x.
j thinks y a property of x.
j attests y a property of x.
j appoints y a property of x.
j witnesses y a property of x.
j interprets y a property of x.
j attributes y to x.
j determines y a quality of x.
j evaluates y a quality of x.
j proposes y a quality of x.
j marshals y over x.
j ascribes y about x.
j imputes y about x.
j judges y beyond x.
j finds y succeeding x.
j poses y after x.
j forms y above x.
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In making these sorts of free interpretations of genres and motifs, one needs to read them in
a "logical" rather than a "cognitive" sense. Thus, a statement like "j thinks x an instance of y"
should be taken to mean that "j is a thought with the logical import that x is an instance of y",
and a statement like "j proposes y a property of x" should be implicitly understood as saying
that "j is a proposition to the effect that y is a property of x".
These cautions are necessary to forestall the problems of intentional attitudes and intentional contexts,
topics that I intend to clarify later on in this project. At present, I regard the well-known opacities of this
subject as arising from the circumstance that cognitive glosses tend to impute an unspecified order of extra
reflection to each construal of the basic predicates. The way that I plan to approach this issue is through
a detailed analysis of the cognitive capacity for reflective thought, to be developed to the extent possible
in formal terms by using sign relational models.
By way of anticipating the nature of the intentional problem, consider the following examples,
that will serve well enough for now to illustrate the contrast between logical and cognitive senses:
1.
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In a cognitive context:
If j is a considered opinion that S is true, and j is a considered opinion that T is true,
then it does not automatically follow that j is a considered opinion that S and T are true,
since an extra measure of consideration might conceivably be involved in cognizing
the conjunction of S and T.
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2.
|
In a logical context:
If j is a piece of evidence that S is true, and j is a piece of evidence that T is true,
then it follows by these very facts alone that j is a piece of evidence that S and T are true.
This is analogous to a situation where, if a person j draws a set of three lines AB, BC, CA,
then j has drawn a triangle ABC, whether j recognizes the fact on immediate reflection,
on further consideration, or not.
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Some readings of staging relations are tantamount to statements of (a possibly higher order) model theory.
For example, the predicate P : J -> B = {0, 1} that is defined by P(j) <=> "j proposes x an instance of y",
is a proposition that applies to a domain of propositions, or elements with the evidentiary import
of propositions, and its models are therefore conceived to be certain propositional entities in J.
And yet, all of these expressions are just elaborate ways of stating the underlying assertion
which says that there exists a triple <j, x, y> in the genre G(:<).
1.3.4.14 Application of OF: Generic Level Given an ontological framework that can provide multiple perspectives and moving platforms for dealing
with object structure, in other words, that can organize diverse hierarchies and developing orders of objects,
attention can now return to the discussion of sign relations as models of intellectual processes.
A principal aim of using sign relations as formal models is to be capable of analyzing the complex activities
that are observed to arise in nature and especially in human domains. Proceeding by an opportunistic mode
of "analysis by synthesis" (ABS), one generates likely constructions from a stock of familiar, favorite, and
well-understood sign relations, the supply of which hopefully grows with time, continually matching their
formal properties against the structures encountered in the "wilds" of natural phenomena and in the realms
of human conduct. When the salient traits of both the freely generated products and the widely gathered
phenomena coincide in enough significant points, then the details of the model constructions that one has
built for oneself can help in articulating a plausible hypothesis as to how the observable appearances might
be explained.
A principal difficulty of using sign relations for this purpose arises from the very power of productivity
that they bring to bear in the process, the capacity of triadic relations to generate a welter of what are
bound to be mostly arbitrary structures, with only a scattered few hoping to show any promise, but
the massive profusion of which exceeds from the outset any reason's ability to sort them out and
test them in practice. And yet, as the phenomena of interest become more complex, the chances
grow slimmer that adequate explanations will be found in any of the thinner haystacks of models.
In this respect, sign relations inherit the basic proclivities of set theory, which can be so successful
and succinct in presenting and clarifying the properties of already found materials and hard won
formal insights, and yet so overwhelming to use as a tool of random exploration and discovery.
The sign relations of A and B, though natural in themselves as far as they go, were nevertheless introduced
in an artificial fashion and presented by means of arbitrary stipulations. Sign relations that arise in more
natural settings usually have a rationale, a reason for being as they are, and therefore become amenable
to classification on the basis of the distinctive characters that make them what they are.
Consequently, naturally occurring sign relations can be expected to fall into species or natural kinds,
and to have special properties that make them keep on occurring in nature. Moreover, cultivated varieties
of sign relations, the kinds that have been converted to social purposes and found to be useful and viable
in actual practice, will have identifiable and especially effective properties by virtue of which their signs
are rendered not just significant but reliably so.
In the pragmatic theory of sign relations, three natural kinds of signs are recognized, under the names
of "icons", "indices", and "symbols". Examples of indexical or accessional signs figured significantly
in the discussion of A and B, as illustrated by the pronouns "i" and "u" in the syntactic domain S = I.
Examples of iconic or analogical signs were also present, though keeping to the background, in the
shapes of the sign relation Tables that were used to schematize the whole activity of each interpreter.
Examples of symbolic or conventional signs are rife, of course, in the text, abiding even more deeply
in the background, pervading the entire context, and going to make up the very fabric of this discussion.
In order to deal with the array of issues presented so far in this subsection, all of which have to do with
controlling the generative power of sign relations to serve the specific purposes of understanding, I apply
the previously introduced concept of an "objective genre" (OG). This is intended to be a definite purpose
or a deliberate pattern of analysis and synthesis that one can identify as being active at given moments in
a discussion and that affects what one regards as the relevant structural properties of its objects.
In the remainder of this subsection the concept of an OG is used informally, and only to the extent needed
for a pressing application, namely, to rationalize the natural kinds that are claimed for signs and to clarify
an important contrast that exists between icons and indices.
The OG that I apply here is called the genre of "properties and instances". One moves in general through
its space, higher and lower in a particular ontology, by means of two dyadic relations, upward by taking
a "property of" and downward by taking an "instance of" whatever object initially enters one's focus of
attention. Each object of this OG is reckoned to be the unique common property of the set of objects
that lie one step below it, objects that are in turn reckoned to be the instances of the object in focus.
Pretty much the same relational structures could be found to form the genre or the paradigm of
"qualities and examples", but the use of "examples" here is polymorphous enough to include
experiential, exegetic, and executable examples (EXE's). This points the way to a series of
related genres, for example, the OG's of "principles and illustrations", "laws and existents",
"precedents and exercises", and on to "lessons and experiences". All in all, in their turn,
these modulations of the basic OG show a way to shift the foundations of ontological
hierarchies toward bases that rest in individual and systematic experience, and thus
to put existentially dynamic rollers under the blocks of what are all too frequently
presented or presumed to be essentially invariant pyramids.
Any object of these OG's can be contemplated in the light of two potential relationships, namely, with
respect to its chances of being an "object quality" (OQ) or an "object example" (OE) of something else.
In future references, abbreviated notations like "OG (Prop, Inst)" or "OG = áProp, Instñ" will be used
to specify particular genres, giving the intended interpretations of their generating relations { < , > }.
With respect to this OG, I can now give a generic characterization icons and indices as kinds of signs:
|
Icons are signs by virtue of being instances of properties of objects.
|
|
Indices are signs by virtue of being properties of instances of objects.
|
Because the initial discussion seems to flow more smoothly if I apply dyadic relations on the left,
I formulate these definitions as follows:
|
For Icons:
|
Sign (Obj)
|
=
|
Inst (Prop (Obj)).
|
|
For Indices:
|
Sign (Obj)
|
=
|
Prop (Inst (Obj)).
|
Imagine starting from the sign and retracing steps to reach the object, in this way finding
the converses of these relations to be as follows:
|
For Icons:
|
Obj (Sign)
|
=
|
Inst (Prop (Obj)).
|
|
For Indices:
|
Obj (Sign)
|
=
|
Prop (Inst (Obj)).
|
In spite of the apparent duality between these patterns of composition, there is a significant asymmetry to be
observed in the way that the insistent theme of realism interrupts the underlying genre. To understand what
this means, it is necessary to note that the strain of pragmatic thinking I am using here takes its definition of
"reality" from the word's original Scholastic sources, where the adjective "real" means "having properties".
Taken in this sense, "reality" is necessary but not sufficient to "actuality", where the word "actual" means
"existing in act and not merely potentially" (Webster's). To reiterate the same thing from the converse
direction, actuality is sufficient but not necessary to reality. The distinction between the two ideas is
further pointed up by the fact that a potential can be real, and that its reality can be independent of
any particular moment in which the power acts.
These "angelic doctrines" would probably remain distant from the present concern,
were it not for two points of connection:
1.
|
Relative to the present genre, the distinction of reality, that can be granted to certain objects
of thought and not to others, fulfills an analogous role to the distinction that singles out "sets"
among "classes" in modern versions of set theory. Taking the membership relation "C" as a
predecessor relation in a pre-designated hierarchy of classes, a class attains the status of a set,
and by dint of this becomes an object of determinate discussion, simply if it has successors.
Pragmatic reality is distinguished from both the medieval and the modern versions, however,
by the fact that its reality is always a reality to someone. This is due to the circumstance that
it takes both an abstract property and a concrete interpreter to establish the practical reality
of an object.
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2.
|
This project seeks articulations and implementations of intelligent activity within dynamically
realistic systems. The individual stresses that are placed on articulation, implementation, actuality,
dynamics, and reality by this desideratum collectively reinforce the importance of several issues:
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a.
|
Systems theory, consistently pursued, eventually demands for its rationalization a distinct ontology,
one in which states of being and modes of action form the principal objects of thought, and out of
which the ordinary sorts of stably extended objects must be constructed. In the "grammar" of
process philosophy, verbs and pronouns are more basic than nouns. In its affect on the course
of this discussion, the emphasis that is placed on systematic action is tantamount to the influence
of an objective genre that makes dynamic systems, their momentary states and their passing actions,
become the ultimate objects of synthesis and analysis. Consequently, the drift of this inquiry will be
turned toward conceiving actions, as traced out in the trajectories of systems, to be the primitive
elements of construction, more fundamental in this objective genre than stationary objects as
extended in space. As a corollary, this inqury expects to find that physical objects of the
static variety have a derivative status in relation to the activities that orient agents, both
organisms and organizations, toward purposeful objectives.
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b.
|
At root, the notion of "dynamics" is concerned with "power" in the sense of "potential".
The brand of pragmatic thinking that I use in this work permits potential entities to be
analyzed as real objects and conceptual objects to be constituted by the conception of
their actual effects in practical instances. In the attempt to unify dynamic and symbolic
approaches to intelligent systems (Lower and Upper Kingdoms?), there remains an insistent
need to build conceptual bridges. A facility for relating objects to their actualizing instances
and their instantiating actions lends many useful tools to an effort of this nature, in which
the search for understanding cannot rest until each object and each phenomenon has
been reconstructed in terms of active occurrences and dynamic ways of being.
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c.
|
In prospect of form, it does not matter whether one takes this project as a task of analyzing and
articulating the actualizations of intelligence that already exist in nature, or whether one views it
as a goal of synthesizing and artificing the potentials for intelligence that have yet to be conceived
in living practice. From a formal perspective, the analysis and the synthesis are just reciprocal ways
of tracing and retracing the very same generic patterns of potential structure that determine actual form.
|
Returning to the examination of icons and indices, and keeping the criterion of reality in mind,
notice the radical difference that comes into play in recursive settings between the two types
of contemplated moves that are needed to trace the respective signs back to their objects,
that is, to discover their denotations:
1.
|
Icon -> Object. Taking the iconic sign as an initial instance, try to go up to a property and
then down to a different or perhaps the same instance. This form of ascent does not require
a distinct object, since reality of the sign is sufficient to itself. In other words, if the sign has
any properties at all, then it is an icon of a real object, even if that object is only itself.
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2.
|
Index -> Object. Taking the indexical sign as an initial property, try to go down to an instance and
then up to a different or perhaps the same property. This form of descent requires a real instance
to substantiate it, but not necessarily a distinct object. Consequently, the index always has
a real connection to its object, even if that object is only itself.
|
In sum: For icons a separate reality is optional, for indices a separate reality is obligatory.
As often happens with a form of analysis, each term under the indicated sum appears
to verge on indefinite expansion:
1.
|
"For icons, the existence of a separate reality is optional."
This means that the question of reality in the sign relation can depend on nothing more than
the reality of each sign itself, on whether it has any property with respect to the OG in question.
In effect, icons can rely on their own reality to faithfully provide a real object.
|
2.
|
"For indices, the existence of a separate reality is obligatory."
And yet this reality need not affect the object of the sign. In essence, indices are satisfied
with a basis in reality that need only reside in an actual object instance, one that establishes
a real connection between the object and its index with regard to the OG in question.
|
Finally, suppose that M and N are a couple of hypothetical sign relations that are designed to capture,
however completely or partially, aspects of the iconic sign relations and the indexical sign relations,
respectively, that a typical object x enjoys within its genre G. A sign relation in which every sign
has the same kind of relation to its object under an assumed form of analysis is appropriately called
a "homogeneous sign relation". In particular, if H is a homogeneous sign relation in which every sign
has either an iconic or an indexical relation to its object, then it is convenient to apply the corresponding
adjective to the whole of H.
Typical sign relations of the iconic or indexical kind generate especially simple and remarkably stable sorts
of interpretive processes. In arity, they could almost be classified as "approximately dyadic", since most
of their interesting structure is wrapped up in their denotative aspects, while their connotative functions
are relegated to the tangential role of preserving the directions of their denotative axes. In a metaphorical
but true sense, iconic and indexical sign relations equip objective frameworks with "gyroscopes", helping
them to maintain their interpretive perspectives in a persistent orientation toward their objective world.
Of course, every form of sign relation still depends on the agency of a proper interpreter to bring it to life,
and every species of sign process stays forever relative to the interpreters that actually bring it to term.
But it is a rather special circumstance by means of which the actions of icons and indices are able to
turn on the existence of independently meaningful properties and instances, as recognized within
an objective framework, and this means that the interpretive associations of these signs are not
always as idiosyncratic as they might otherwise be.
The dispensation of consensual bonds in a common medium leaves room for many individual interpreters
to inhabit a shared frame of reference, and for a diversity of transient interpretive moments to take up and
consolidate a continuing perspective on a world of mutual interests. This further increases the likelihood
that developing and differing interpreters, isolated in origin and divergent in aim, will be able to address
a common world, to build a common wealth of meaning, to participate in compatible views and coherent
values in relation to the aggregate of things, to collate information from a variety of sources, and to bring
their concerted actions to bear on an appreciable distribution of extended realities and intended objectives.
Instead of the disparities due to parallax leading to disorder and paralysis, this way of accounting for and
reconciling the distinctive points of view that lie behind the discrepancies can give rise to a stereoscopic
perspective. In a community of interpretation and inquiry that has all of these virtues, each individual
"try at objectivity" (TAO) is a venture that all of the interpreters are nonetheless able to call their own.
Is this prospect a utopian vision? Perhaps it is exactly that, "a view from nowhere in particular", just yet.
But it is the hope that inquiry discovers resting first and last within itself, quietly but persistently guiding
every other aim and motive of inquiry.
Turning to the language of "objective concerns" (OC's), what can now be said about the compositional
structures of the iconic sign relation M and the indexical sign relation N? In preparation for this topic,
a few additional steps must be taken to continue formalizing the concept of an objective genre and
to begin developing a calculus for composing objective motifs.
I recall the OG of "properties and instances" and re-introduce the symbols "<" and ">" for the converse pair
of dyadic relations, "property of" and "instance of", that generate it. Using the "generator bracket" notation,
where "áA, B, Cñ" signifies the space of relationships that is generated by the "generating relations" A, B, C,
all of this can now be summed up by invoking the name of the genre as G = OG (Prop, Inst) = á< , >ñ.
Now and for the rest of this discussion, I will frequently revert to the convention that I prefer to employ
in more formal discussions, namely, the custom of applying the symbols for relational operators on the
right side of an ongoing chain of syntactic applications. In accord with this "right-thinking" practice,
it becomes convenient to express the relative terms "property of x" and "instance of x" by means of
a case inflection on the argument x, that is to say, as "x's property" and "x's instance", respectively.
Described in this way, OG (Prop, Inst) = á< , >ñ, where the following interpretations and relations
are in force:
|
"x <"
|
=
|
"x's Property"
|
=
|
"Property of x"
|
=
|
"Object above x".
|
|
"x >"
|
=
|
"x's Instance"
|
=
|
"Instance of x"
|
=
|
"Object below x".
|
A symbol like "x <" or "x >", with extra spaces or raised dots "." being used as optional separators,
is called a "catenation", where "x" is the "catenand" and "<" or ">" is the "catenator". Due to the fact
that "<" and ">" indicate dyadic relations, the significance of these so-called "unsaturated" catenations
can be rationalized as follows:
|
"x <"
|
=
|
"x is the Instance of what?"
|
=
|
"x's Property".
|
|
"x >"
|
=
|
"x is the Property of what?"
|
=
|
"x's Instance".
|
In this fashion, the definitions of icons and indices can be reformulated as follows:
|
x's Icon
|
=
|
x's Property's Instance
|
=
|
x . <>
|
|
x's Index
|
=
|
x's Instance's Property
|
=
|
x . ><
|
According to the definitions of the homogeneous sign relations M and N, we have:
|
x's Icon
|
=
|
x . ProjOS(M)
|
=
|
x . MOS
|
|
x's Index
|
=
|
x . ProjOS(N)
|
=
|
x . NOS
|
Equating the results of these equations yields the analysis of M and N as forms of composition
within the genre of properties and instances:
|
x's Icon
|
=
|
x . MOS
|
=
|
x . <>
|
|
x's Index
|
=
|
x . NOS
|
=
|
x . ><
|
On the assumption (to be examined more closely later) that any object x can be taken as a sign,
the converse relations appear to be manifestly identical to the originals:
|
For Icons:
|
x's Object
|
=
|
x . MSO
|
=
|
x . <>
|
|
For Indices:
|
x's Object
|
=
|
x . NSO
|
=
|
x . ><
|
Abstracting the forms of these applications from the appearance of an otiose argument x delivers the results:
|
For Icons:
|
MOS
|
=
|
MSO
|
=
|
<>
|
|
For Indices:
|
NOS
|
=
|
NSO
|
=
|
><
|
This appears to suggest that icons and their objects are icons of each other, and that indices and their objects
are indices of each other. Are the putative results, or the mere suggestions, of these symbolic manipulations
really to be trusted on this score? Given that there is no mention yet of the interpretive agent to whom these
sign relations are supposed to appear, one might well suspect that these computations, or these imputations,
can amount only to approximate truths or potential verities, tentative results that need to be checked out,
then certified, corrected, hedged, qualified appropriately, or rejected absolutely, as the case may require.
1.3.4.15 Application of OF: Motive Level Now that an adequate variety of formal tools have been set in order and the workspace afforded by
an objective framework has been rendered reasonably clear, the structural theory of sign relations
can be pursued with greater precision. In support of this aim, the concept of an objective genre
and the particular case provided by OG (Prop, Inst) have served to rough out the basic shapes
of the more refined analytic instruments to be developed in this subsection.
The notion of an "objective motive" or "objective motif" (OM) is intended to specialize or personalize
the application of objective genres to take particular interpreters into account. For example, pursuing
the pattern of OG (Prop, Inst), a prospective OM of this genre does not merely tell about the properties
and the instances that objects can have in general, it recognizes a particular arrangement of objects and
supplies them with its own ontology, giving "a local habitation and a name" to the bunch. What matters
to an OM is a particular collection of objects (of thought) and a personal selection of links that go from
each object (of thought) to higher and lower objects (of thought), all things being relative to a subjective
ontology or a live "hierarchy of thought" (HOT), one that is currently known to and actively pursued by
a designated interpreter of those thoughts.
The cautionary details ("of thought") interspersed at critical points in the preceding paragraph are intended
to keep this inquiry vigilant against a constant danger of using ontological language, namely, the insidious
illusion that one can analyze the being of any real object simply by articulating the grammar of one's own
thoughts, in effect, sheerly by parsing signs in the mind. As always, it is best to regard OG's and OM's as
"filters" and "reticles", as transparent templates that are slid into place in order to view a space, constituting
the structures of objects in a limited number of respects at a time, but never with any assurance of totality.
With these refinements, the use of dyadic projections to investigate sign relations can be combined with
the perspective of objective motives to "factor the facets" or "decompose the components" of sign relations
in a more systematic fashion. Given a homogeneous sign relation H of iconic or indexical type, the dyadic
projections HOS and HOI can be analyzed as compound relations over the basis supplied by the relations Gj
in the relevant genre G = OG (Prop, Inst). As an application that is sufficiently important in its own right,
the investigation of icons and indices continues to provide a useful testing ground for breaking in likely
proposals of concepts and notation.
To pursue the analysis of icons and indices at the next stage of formalization, fix the OG of this discussion
to have the type G = OG (Prop, Inst) = áProp, Instñ = á< , >ñ, and let each sign relation under discussion be
articulated in terms of an objective motif that tells what signs and objects, plus what mediating linkages by
way of properties and instances, are assumed to be recognized by its interpreter. Under these conditions,
one will quite naturally, if still informally, identify the interpreter with the motive. At least, it will usually
be safe to regard the OM as capturing an aspect of the interpreter's semiotic competence, that which the
interpreter may express to different degrees of virtuosity within the conduct of any semiotic performance.
Let X collect the objects of thought that fall within a particular OM, and let X include the whole world W
of a sign relation R plus everything else that is needed to contain and to support it. That is, X collects all
of the types of things that go into a sign relation R, so that W(R) = O U S U I = W c X, plus whatever
else in the way of distinct "object qualities" (OQ's) and distinct "object exemplars" (OE's) happens to be
discovered or established as being generated out of this initial basis by the relations of the relevant OM.
In order to keep the set X simple enough to contemplate on a single pass, but still make it deep enough
to cover all of the issues of interest in this part of the discussion, I limit X to having just three disjoint
layers of things to worry about, to be described as follows:
|
The upper layer Q is the relevant collection of object properties:
|
Q
|
=
|
X0 . <
|
=
|
W . <
|
|
The middle layer K is the initial collection of objects and signs:
|
K
|
=
|
X0
|
=
|
W
|
|
The lower layer E is the relevant collection of object instances:
|
E
|
=
|
X0 . >
|
=
|
W . >
|
Recall the reading of the staging relations:
|
"h : x < m"
|
=
|
"h regards x as an instance of m",
|
|
"h : m > y"
|
=
|
"h regards m as a property of y".
|
|
|
|
|
|
"h : x > n"
|
=
|
"h regards x as a property of n",
|
|
"h : n < y"
|
=
|
"h regards n as an instance of y".
|
Express the analysis of icons and indices as follows:
|
For Icons:
|
MOS : x <> <x's Sign>.
|
|
For Indices:
|
NOS : x >< <x's Sign>.
|
Let j and k be hypothetical interpreters that do the jobs of M and N, respectively:
|
For Icons:
|
<x's Sign>
|
=
|
x . MOS
|
=
|
x . <j . >j
|
|
For Indices:
|
<x's Sign>
|
=
|
x . NOS
|
=
|
x . >k . <k
|
Factor out the names of the interpreters j and k to serve as identifiers of objective motifs:
|
For Icons:
|
j : x <> <x's Sign>.
|
|
For Indices:
|
k : x >< <x's Sign>.
|
Finally, the constant motif names j and k can either be collected to one side of a composition expression
or else distributed in subscription form across its individual links. The choice between the corresponding
expressions, "collected" or "distributed", affords a certain stylistic variation, but the logical meaning of the
thus expressed theme is precisely the same in either case:
|
j : x <> y
|
Û
|
j : x < m
|
&
|
j : m > y,
|
for some m C Q.
|
|
k : x >< y
|
Û
|
k : x > n
|
&
|
k : n < y,
|
for some n C E.
|
These statements can be read to say:
1.
|
j thinks x an icon of y if and only if there is an m such that
j thinks x an instance of m and j thinks m a property of y.
|
2.
|
k thinks x an index of y if and only if there is an n such that
k thinks x a property of n and k thinks n an instance of y.
|
Readers who object to the anthropomorphism or the approximation of these statements can replace every
appearance or occurrence of the verb "thinks" with the phrase "interprets ... as", or even the circumlocution
"acts in every formally relevant way as if", changing what must be changed elsewhere. For the moment,
I am not concerned with the exact order of reflective sensitivity that goes into these interpretive linkages,
but only with the roughest outlines of the "pragmatic equivalence classes" (PEC's) that are afforded by
the potential conduct and exercised in the actual conduct of their agents.
In the discussion of the dialogue between A and B, it was allowed that the same signs "A" and "B" could
reference the different categories of things they name with a deliberate duality and a systematic ambiguity.
Used informally as parts of the peripheral discussion, they indicate the entirety of the sign relations A and B.
Used formally within the focal dialogue, they denote the objects of two particular sign relations. In just this
way, or an elaboration of it, the signs "j" and "k" can have their meanings extended to encompass both the
"objective motifs" (OM's) that inform and regulate experience and the "object experiences" (OE's) that
fill out and substantiate their forms.
1.3.4.16 The Integration of Frameworks A large number of the problems arising in this work have to do with the integration of different
interpretive frameworks over a common objective basis, or the prospective bases provided by
shared objectives. The main concern of this project continues to be the integration of dynamic
and symbolic frameworks for understanding intelligent systems, concentrating on the kinds of
interpretive agents that are capable of being involved in inquiry.
The job of integrating divergent IF's and reconciling their sundry and seemingly "cut and dried"
objectifications is, generally speaking, a very difficult maneuver to carry out successfully, and
it is far from the trivial business -- that it may initially appear to the isolated observer to be --
to bring it through to any kind of a satisfactory conclusion. Two factors that contribute to the
awesome tedium and the near intractability of the task can be addressed and analyzed as follows:
1.
|
The trouble is partly due to the obligatory tactics and the ossified taxonomies that come through time
and training to inhabit the conceptual landscapes of agents, especially if they have spent the majority
of their time operating according to a single IF. The IF informs their activity in ways they no longer
have to think about, and thus rarely find a reason to modify. But it also inhibits their interpretive and
their practical conduct to the customary ways of seeing and doing things that are granted by its frame
of contingencies, and it restricts them to "forms of intuition" (FOI's) that are suggested and sanctioned
by the operative IF. Without critical reflection, however, or a mechanism to make amendments to its
own constitution, an IF tends to operate behind the scenes of overt observation and public notice in
such a way as to obliterate any inkling of flexibility in thought or in practice and to obstruct every
hint or threat (so perceived) of conceptual revision.
|
2.
|
Apparently it is so much easier to devise techniques for taking things apart than it is to find ways of
putting them back together that there seem to be only a few heuristic strategies of general application
that are available to guide the work of integration. A few of the tools and the materials needed for the
work of integrative construction have been illustrated in concrete form throughout the presentation
of examples in this section. An overall survey of their principles can be summed up as follows:
|
a.
|
One integration heuristic is the "lattice" metaphor. This is also described as the "partial order"
or the "common denominator" paradigm. When IF's can be objectified as OF's that are organized
according to the principles of suitable orderings, then it is often possible to "lift" or to extend these
order properties to the space of the frameworks themselves, the space in which the frameworks
reside like so many points in a geometry, and thereby to enable the construction of the desired
kinds of integrative frameworks as upper and lower bounds in the appropriate ordering.
|
b.
|
Another integration heuristic is the "mosaic" metaphor. This is also described as the "stereoscopic"
or the "inverse projection" paradigm. This technique has been illustrated in an especially graphic
and visual manner by the methods used throughout this section to analyze the three-dimensional
structures of sign relations. In fact, the picture of any particular sign relation offers a paradigm
in microcosm for the macroscopic work of integration, showing how reductive aspects of structure
can be projected from a shared but irreducible reality. The extent to which the "full-bodied" structure
of a triadic sign relation can be reconstructed from its dyadic projections, although a limited extent
in general, presents a near perfect epitome of the larger task in this situation, namely, to find an
integrated framework that embodies the diverse facets of reality that are there to be severally
observed in the object domain from inside the individual frameworks. Acting as gnomonic
recipes for the higher order processes they limn and delimit, sign relations keep before the
mind's eye the ways in which a higher dimensional structure determines its fragmentary
aspects but is not in general determined by them.
|
To express the nature of this integration task in logical terms, it combines elements of both proof theory
and model theory, interweaving in their turns the following two phases of work:
1.
|
A phase that develops theories about the symbolic competence or "knowledge" of intelligent agents,
using abstract formal systems to represent the theories and phenomenological data to constrain them.
|
2.
|
A phase that seeks concrete models of these theories, looking to the kinds of mathematical structures
that have a dynamic or a system-theoretic interpretation, and compiling the constraints that a recursive
conceptual analysis imposes on both the intermediate and the ultimate elements of their construction.
|
The set of sign relations {A, B} is an example of an extremely simple formal system, encapsulating
aspects of the symbolic competence and the pragmatic performance that might be exhibited by a pair
of prospectively intelligent interpretive agents, however abstractly and partially given at this stage of
description. The symbols of a formal system like {A, B} can be held subject to abstract constraints,
having their meanings in relation to each other determined by definitions and axioms (for example,
the laws defining an equivalence relation), making it possible to manipulate the resulting information
by means of the inference rules in a proof system. This illustrates the "proof-theoretic" aspect of such
a symbol system.
Suppose that a formal system like {A, B} is initially approached from a theoretical direction,
in other words, by listing the abstract properties that one thinks the system ought to have.
Then the existence of an extensional model that satisfies these constraints, as exhibited
by the sign relation tables, demonstrates that one's theoretical description is logically
consistent, even if the models that first come to mind are still a bit too abstractly
symbolic and do not have all of the dynamic concreteness that is demanded of
system-theoretic interpretations. This amounts to the other side of the ledger,
the "model-theoretic" aspect of a symbol system, at least insofar as the present
account has dealt with it.
More is required of the modeler, however, in order to find the desired kinds of system-theoretic models
(for example, state transition systems), and this brings the search for realizations of formal systems down
to the toughest part of the exercise. Some of the problems that emerge were highlighted in the example
of A and B. Although it is ordinarily possible to construct state transition systems in which the states of
interpreters correspond relatively directly to the acceptations of the primitive signs given, the conflict of
interpretations that develops between different interpreters from these prima facie implementations
is a sign that there is something superficial about this approach.
The integration of model-theoretic and proof-theoretic aspects of "physical symbol systems", besides being
closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant
to the job of integrating dynamic and symbolic frameworks for intelligent systems. This is so because the
search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where
the mathematical materials that are made available for modeling are further constrained by system-theoretic
principles, like being able to say what the states are and how the transitions are determined.
1.3.4.17 Recapitulation: A Brush with Symbols A common goal of work in artificial intelligence and cognitive simulation is to understand how is it possible
for intelligent life to evolve from elements available in the primordial sea. Most simply put, the question is:
"What's in the brine that ink may character?"
Pursuant to this particular way of setting out on the long-term quest, a more immediate goal of the current
project is to understand the action of full-fledged symbols, insofar as they conduct themselves through the
media of minds and quasi-minds. At this very point the quest is joined by the pragmatic investigations of
signs and inquiry, which share this interest in chasing down symbols to their precursive lairs.
In the pragmatic theory of signs a "symbol" is a strangely insistent yet a curiously indirect type of sign,
one whose accordance with its object depends sheerly on the real possibility that it will be so interpreted.
Taking on the nature of a bet, a symbol's prospective value trades on nothing more than the chance of
acquiring the desired interpretant, and thus it can capitalize on the simple fact that what it proposes is
not impossible. In this way it is possible to see that a formal principle is involved in the success of
symbols. The elementary conceivability of a particular sign relation, the pure circumstance that
renders it logically or mathematically possible, means that the formal constraint it places on its
domains is always really and potentially there, awaiting its discovery and exploitation for the
purposes of representation and communication.
In this question about the symbol's capacity for meaning, then, is found yet another contact point
between the theory of signs and the logic of inquiry. As Charles Sanders Peirce aptly expressed it:
Now, I ask, how is it that anything can be done with a symbol, without reflecting upon
the conception, much less imagining the object that belongs to it? It is simply because
the symbol has acquired a nature, which may be described thus, that when it is brought
before the mind certain principles of its use -- whether reflected on or not -- by association
immediately regulate the action of the mind; and these may be regarded as laws of the symbol
itself which it cannot as a symbol transgress. (Peirce, CE 1, 173).
Inference in general obviously supposes symbolization; and all symbolization is inference.
For every symbol as we have seen contains information. And ... all kinds of information
involve inference. Inference, then, is symbolization. They are the same notions. Now
we have already analyzed the notion of a symbol, and we have found that it depends
upon the possibility of representations acquiring a nature, that is to say an immediate
representative power. This principle is therefore the ground of inference in general.
(Peirce, CE 1, 280).
A symbol which has connotation and denotation contains information. Whatever
symbol contains information contains more connotation than is necessary to limit
its possible denotation to those things which it may denote. That is, every symbol
contains more than is sufficient for a principle of selection. (Peirce, CE 1, 282).
The information of a term is the measure of its superfluous comprehension.
That is to say that the proper office of the comprehension is to determine the
extension of the term. ...
Every addition to the comprehension of a term, lessens its extension up to
a certain point, after that further additions increase the information instead. ...
And therefore as every term must have information, every term has superfluous
comprehension. And, hence, whenever we make a symbol to express any thing
or any attribute we cannot make it so empty that it shall have no superfluous
comprehension.
I am going, next, to show that inference is symbolization and that the puzzle
of the validity of scientific inference lies merely in this superfluous comprehension
and is therefore entirely removed by a consideration of the laws of information.
(Peirce, CE 1, 467).
A full explanation of these statements, linking scientific inference, symbolization, and information together
in such an integral fashion, would require an excursion into the pragmatic theory of information that Peirce
was already presenting in lectures at Harvard as early as 1865. For now, let it suffice to say that this early
anticipation of the information concept, fully recognizing the reality of its dimension, would not sound
too remote from the varieties of "law abiding constraint exploitation" that have become increasingly
familiar to our ears since the dawn of cybernetics.
But more than this, Peirce's notion of information supplies an array of missing links that joins together
in one scheme the logical roles of terms, propositions, and arguments, the semantic functions of denotation
and connotation, and the practical methodology needed to address and measure the quantitative dimensions
of information. This is precisely the kind of linkage that I need in this project to integrate the dynamic and
the symbolic aspects of inquiry.
Not by sheer coincidence, the task of understanding symbolic action, working up gradually through
icons and indices to the point of tackling symbols, is also one of the ultimate aims that the building
of interpretive and objective frameworks, as being proposed in this work, is intended to subserve.
An OF is a convenient stage for those works that have progressed far enough to make use of it,
but in times of flux it must be remembered that an OF is only a hypostatic projection, that is,
the virtual image, reified concept, or "phantom limb" of the IF that tentatively extends it.
When the IF and the OF sketched here have been developed far enough, I hope to tell
wherein and whereof a sign is able, by its very character, to address itself to a purpose,
one determined by its objective nature and determining, in a measure, that of its intended
interpreter, to the extent that it makes the other wiser than the other would otherwise be.
From the emblem unfurled on a tapestry to tease out the working of its loom and spindle, a charge to bind
these frameworks together is drawn by necessity from a single request: "To whom is the sign addressed?"
The easy, all too easy answer comes "To whom it may concern", but this works more to put off the question
than it acts as a genuine response. To say that a sign relation is intended for the use of its interpreter, unless
one has ready an independent account of that agent's conduct, only rephrases the initial question about the
end of interpretation.
The interpreter is an agency depicted over and above the sign relation, but in a very real sense it is simply
identical with the whole of it. And so one is led to examine the relationship between the interpreter and the
interpretant, the element falling within the sign relation to which the sign in actuality tends. The catch is that
the whole of the intended sign relation is seldom known from the beginning of inquiry, and so the aimed for
interpretant is often just as unknown as the rest.
These eventualities call for the elaboration of interpretive and objective frameworks in which not just the
specious but the speculative purpose of a sign can be contemplated, permitting extensions of the initial data,
through error and retrial, to satisfy emergent and recurring questions.
At last, even with the needed frameworks only partly shored up, I can finally ravel up and tighten one thread
of this rambling investigation. All this time, steadily rising to answer the challenge about the identity of the
interpreter, "Who's there?", and the role of the interpretant, "Stand and unfold yourself", has been the ready
and the abiding state of a certain system of interpretation, developing its character and gradually evolving its
meaning through a series of imputations and extensions. Namely, the MOI (the SOI experienced as object)
can answer for the interpreter, to whatever extent that the called for conduct can be formalized, and the IM
(the SOI experienced in act, in statu nascendi) can serve as a proxy for the momentary thrust of interpretive
dynamics, to whatever degree that the called for process can be explicated.
To put a finer point on this result I can do no better at this stage of discussion than to recount
the "metaphorical argument" that Peirce persistently uses to illustrate the same conclusion.
I think we need to reflect upon the circumstance that every word implies some proposition
or, what is the same thing, every word, concept, symbol has an equivalent term -- or one
which has become identified with it, -- in short, has an interpretant.
Consider, what a word or symbol is; it is a sort of representation. Now a representation
is something which stands for something. ... A thing cannot stand for something without
standing to something for that something. Now, what is this that a word stands to?
Is it a person?
We usually say that the word homme stands to a Frenchman for man. It would be
a little more precise to say that it stands to the Frenchman's mind -- to his memory.
It is still more accurate to say that it addresses a particular remembrance or image
in that memory. And what image, what remembrance? Plainly, the one which is
the mental equivalent of the word homme -- in short, its interpretant. Whatever
a word addresses then or stands to, is its interpretant or identified symbol. ...
The interpretant of a term, then, and that which it stands to are identical. Hence,
since it is of the very essence of a symbol that it should stand to something, every
symbol -- every word and every conception -- must have an interpretant -- or what is
the same thing, must have information or implication. (Peirce, CE 1, 466-467).
It will take a while to develop the wealth of information that a suitably perspicacious and persistent IF
would find implicit in this unassuming homily. The main innovations that this project can hope to add
to the story are as follows:
1.
|
To prescribe a "context of effective systems theory" (C'EST), one that
can provide for the computational formalization of each intuitively given
interpreter as a determinate "model of interpretation" (MOI). An optimal array
of concepts and methods would deal with the generic constitutions of interpreters,
converting paraphrastic and periphrastic descriptions of their interpretive practice into
relatively complete specifications of concrete, implementable, and reliable sign relations.
|
2.
|
To prepare a fully dynamic basis for actualizing interpretants. This means that an interpretant
addressed by the interpretation of a sign would not be left in the form of a detached token or
an abstract memory image to be processed by a hypothetical but largely nondescript interpreter,
but realized as a definite brand of state configuration in a qualitatively explicit dynamic system.
To fathom what should be the symbolic analogue of a "state with momentum" has presented this
project with difficulties both conceptual and terminological. So far in this project, I have attempted
to approach the character of an active sign-theoretic state in terms of an "interpretive moment" (IM),
"information state" (IS), "attended token" (AT), "situation of use" (SOU), or "instance of use" (IOU).
A successful concept would capture the transient dispositions that drive interpreters to engage in
specific forms of inquiry, defining their ongoing state of uncertainty with regard to the practical
objects and the topical questions of their immediate concern.
|
Have I pointed at this problem from enough different directions to convey an idea of its location and extent?
Here is one more variation on the theme. I believe that our theoretical empire is bare in spots. There does
not exist yet in the field a suitably comprehensive concept of a dynamic system moving through a variable
state of information. This conceptual gap apparently forces investigators to focus on one aspect or the other,
on the dynamic bearing or the information borne, but leaves their studies unable to integrate their several
perspectives into a full-dimensioned picture of the evolving knowledge system.
It is always possible that the dual aspects of transformation and information are conceptually complementary
and even non-orientable. That is, there may be no way to arrange our mental apparatus to grasp both sides
at the same time, and the whole appearance that there are two sides may be an illusion of overly local and
myopic perspectives. However, none of this should be taken for granted without proof.
Whatever the case, to constantly focus on the restricted aspects of dynamics adequately covered by
currently available concepts leads one to ignore the growing body of symbolic knowledge that the states
of systems potentially carry. Conversely, to leap from the relatively secure grounds of physically based
dynamics into the briar patch of formally defined symbol systems often marks the last time that one has
sufficient footing on the dynamic landscape to contemplate any form of overarching law, or any rule to
prospectively govern the evolution of reflective knowledge. This is one of the reasons why I continue
to strive after the key ideas here. If straw is all that one has in reach, then ships and shelters will have
to be built from straw.
Author's Note: The preceding excerpt represents the introduction to a larger work,
the chapters of which are currently at various stages of development and revison.
What follows is a tenative outline of the prospective work already in progress.
Inquiry Driven Systems: An Inquiry Into Inquiry
1. Research Proposal
1.1 Outline of the Project: Inquiry Driven Systems
1.1.1 Problem
1.1.2 Method
1.1.2.1 The Paradigmatic &
Process-Analytic Phase. 1.1.2.2 The Paraphrastic &
Faculty-Synthetic Phase. 1.1.2.3 Reprise of Methods 1.1.3 Criterion
1.1.4 Application
1.2 Onus of the Project: No Way But Inquiry
1.2.1 A Modulating Prelude
1.2.2 A Fugitive Canon
1.3 Option of the Project: A Way Up To Inquiry
1.3.1 Initial Analysis of Inquiry
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1.3.2 Discussion of Discussion
1.3.3 Discussion of Formalization: General Topics
1.3.3.2 A Formalization of Formalization? 1.3.3.3 A Formalization of Discussion? 1.3.3.4 A Concept of Formalization 1.3.3.5 A Formal Approach 1.3.3.6 A Formal Development 1.3.3.7 A Formal Persuasion 1.3.4 Discussion of Formalization: Concrete Examples
1.3.4.1 Formal Models: A Sketch 1.3.4.2 Sign Relations: A Primer 1.3.4.3 Semiotic Equivalence Relations 1.3.4.4 Graphical Representations 1.3.4.6 The "Meta" Question 1.3.4.8 The Conflict of Interpretations 1.3.4.11 Review & Prospect 1.3.4.12 Objective Plans & Levels 1.3.4.13 Formalization of OF: Objective Levels 1.3.4.14 Application of OF: Generic Level 1.3.4.15 Application of OF: Motive Level 1.3.4.16 The Integration of Frameworks 1.3.4.17 Recapitulation: A Brush with Symbols 1.3.5 Discussion of Formalization: Specific Objects
1.3.5.2 Models, Analogs, Images, Icons 1.3.5.3 Steps & Tests of Formalization 1.3.5.5 Partial Formalizations 1.3.5.7 A Formal Aesthetic 1.3.5.9 A Formal Suspicion 1.3.7 The Double Aspect of Concepts
1.3.8 Reconnaissance
1.3.8.1 The Informal Context 1.3.8.3 The Formative Tension 1.3.9 Recurring Themes
1.3.9.1 Preliminary Notions 1.3.9.2 Intermediary Notions 1.3.9.3 Propositions & Sentences 1.3.9.4 Empirical Types & Rational Types 1.3.9.5 Articulate Sentences 1.3.9.6 Stretching Principles 1.3.9.7 Stretching Operations 1.3.9.9 The Cactus Language: Syntax 1.3.9.10 The Cactus Language: Stylistics 1.3.9.11 The Cactus Language: Mechanics 1.3.9.12 The Cactus Language: Semantics 1.3.9.13 Stretching Exercises 1.3.9.14 Syntactic Transformations 1.3.9.15 Derived Equivalence Relations 1.3.9.16 Digression on Derived Relations 1.4 Outlook of the Project: All Ways Lead to Inquiry
1.4.1 The Matrix of Inquiry
1.4.1.1 Inquiry as Conduct 1.4.1.3 Perils of Inquiry 1.4.1.4 Forms of Relations 1.4.1.5 Models of Inquiry 1.4.2 The Moment of Inquiry
1.4.3 The Modes of Inquiry
1.4.3.1 Deductive Reasoning 1.4.3.2 Inductive Reasoning 1.4.3.3 Abductive Reasoning 1.4.3.4 Analogical Reasoning 1.5 Obstacles to the Project: In the Way of Inquiry
1.5.1 The Initial Unpleasantness
1.5.2 The Justification Trap
1.5.3 A Formal Apology
1.5.3.1 Category Double-Takes 1.5.3.2 Conceptual Extensions 1.5.3.3 Explosional Recombinations 1.5.3.4 Interpretive Frameworks 1.5.4 A Material Exigency
1.5.5 A Reconciliation of Accounts
1.5.6 Objections to Reflexive Inquiry
1.5.7 Empirical Considerations
1.5.8 Computational Considerations
1.5.8.1 A Form of Recursion 1.5.8.2 A Power of Abstraction 1.6 Orientation of the Project: A Way Into Inquiry
1.6.1 Initial Description of Inquiry
1.6.2 Terms of Analysis
1.6.2.1 Digression on Signs 1.6.2.2 Empirical Status of ID 1.6.3 Expansion of Terms
1.6.4 Anchoring Terms in Phenomena
1.6.4.2 Phenomenology of Doubt 1.6.4.3 Modalities of Knowledge 1.6.5 Sets, Systems, & Substantive Agents
1.6.6 Interpretive Systems
1.6.6.1 Syntactic Systems 1.6.6.3 Pragmatic Systems 1.6.7 Inquiry Driven Systems
1.6.7.1 A Definition of Inquiry 1.6.7.2 The Faculty of Inquiry 1.6.7.3 A Definition of Determination 1.6.7.4 A Definition of Definition 1.7 Organization of the Project: A Way Through Inquiry
1.7.1 The Problem: Inquiry Found as an Object of Study
1.7.2 The Method: Inquiry Found as a Means of Study
1.7.2.1 Conditions for the Possibility
of Inquiry into Inquiry 1.7.2.2 Conditions for the Success
of Inquiry into Inquiry 1.7.3 The Criterion: Inquiry in Search of a Sensible End
1.7.3.1 The Irritation of Doubt,
& The Scratch Test. 1.7.3.2 Enabling Provision 1:
The Scenes & Context of Inquiry. 1.7.3.3 Enabling Provision 2:
The Stages & Content of Inquiry. 1.8 Objectives of the Project: Inquiry All the Way
1.8.1 Substantial Objective
1.8.1.1 Objective 1a:
The Propositions as Types Analogy. 1.8.1.2 Objective 1b:
The Styles of Proof Development. 1.8.1.3 Objective 1c:
The Analysis of Interpreters,
A Problem with Authority. 1.8.2 Instrumental Objective
1.8.3 Coordination of Objectives
1.8.4 Recapitulation
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Da Capo Al Segno
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2. Discussion of Inquiry
2.1 Approaches to Inquiry
2.1.1 The Classical Framework: Syllogistic Approaches
2.1.2 The Pragmatic Framework: Sign-Theoretic Approaches
2.1.3 The Dynamical Framework: System-Theoretic Approaches
2.1.3.1 Inquiry & Computation 2.1.3.2 Inquiry Driven Systems 2.2 The Context of Inquiry
2.2.1 The Field of Observation
2.2.2 The Problem of Reflection
2.2.3 The Problem of Reconstruction
2.2.4 The Trivializing of Integration
2.2.5 Tensions in the Field of Observation
2.2.6 Problems of Representation & Communication
2.3 The Conduct of Inquiry
2.3.1 Introduction
2.3.2 The Types of Reasoning
2.3.3 Hybrid Types of Inference
2.3.4 Details of Induction
2.3.5 The Stages of Inquiry
3. The Medium & Its Message
3.1 Reflective Expression
3.1.1 Casual Reflection
3.1.1.1 Ostensibly Recursive Texts 3.1.1.2 Analogical Recursion 3.1.2 Conscious Reflection
3.1.2.1 The Signal Moment 3.1.2.2 The Symbolic Object 3.1.2.3 The Endeavor to Communicate 3.1.2.4 The Medium of Communication 3.1.2.5 The Ark of Types:
The Order of Things to Come. 3.1.2.7 The Context of Interpretation 3.1.2.8 The Formative Tension 3.1.2.9 The Vehicle of Communication:
Reflection on the Scene,
Reflection on the Self. 3.1.2.12 Recursions: Possible, Actual, Necessary 3.1.2.13 Ostensibly Recursive Texts 3.1.2.15 The Freedom of Interpretation 3.1.2.16 The Eternal Return 3.1.2.18 Information in Formation 3.1.2.19 Reflectively Indexical Texts 3.1.2.25 The Discursive Universe 3.2 Reflective Inquiry
3.2.1 Integrity & Unity of Inquiry
3.2.2 Apparitions & Allegations
3.2.3 A Reflective Heuristic
3.2.4 Either/Or: A Sense of Absence
3.2.5 Necessity: Apparent, Occasional, Practical
3.2.6 Approaches, Aspects, Exposures, Fronts
3.2.7 Synthetic A Priori Truths
3.2.8 Priorisms of Normative Sciences
3.2.9 A Principle of Rationality
3.2.10 The Pragmatic Cosmos
3.2.11 Reflective Interpretive Frameworks
3.2.11.1 Principals versus Principles 3.2.11.2 The Initial Description of Inquiry 3.2.11.3 An Early Description of Interpretation 3.2.11.4 Descriptions of the Mind 3.2.11.5 Of Signs & The Mind 3.2.11.6 Questions of Justification 3.2.11.7 The Experience of Satisfaction 3.2.11.8 An Organizational Difficulty 3.2.11.9 Pragmatic Certainties 3.2.11.10 Problems & Methods 3.3 Reflection on Reflection
3.4 Reflective Interpretive Frameworks
3.4.1 The Phenomenology of Reflection
3.4.2 A Candid Point of View
3.4.3 A Projective Point of View
3.4.4 A Formal Point of View
3.4.5 Three Styles of Linguistic Usage
3.4.6 Basic Notions of Group Theory
3.4.7 Basic Notions of Formal Language Theory
3.4.8 A Perspective on Computation
3.4.9 Higher Order Sign Relations: Introduction
3.4.10 Higher Order Sign Relations: Examples
3.4.11 Higher Order Sign Relations: Application
3.4.12 Issue 1: The Status of Signs
3.4.13 Issue 2: The Status of Sets
3.4.14 Issue 3: The Status of Variables
3.4.15 Propositional Calculus
3.4.16 Recursive Aspects
3.4.17 Patterns of Self-Reference
3.4.18 Practical Intuitions
3.4.19 Examples of Self-Reference
3.4.20 Three Views of Systems
3.4.21 Building Bridges Between Representations
3.4.22 Extensional Representations of Sign Relations
3.4.23 Intensional Representations of Sign Relations
3.4.24 Literal Intensional Representations
3.4.25 Analytic Intensional Representations
3.4.26 Differential Logic & Directed Graphs
3.4.27 Differential Logic & Group Operations
3.4.28 The Bridge: From Obstruction to Opportunity
3.4.29 Projects of Representation
3.4.30 Connected, Integrated, Reflective Symbols
3.4.31 Generic Orders of Relations
3.4.32 Partiality: Selective Operations
3.4.33 Sign Relational Complexes
3.4.34 Set-Theoretic Constructions
3.4.35 Reducibility of Sign Relations
3.4.36 Irreducibly Triadic Relations
3.4.37 Propositional Types
3.4.38 Considering the Source
3.4.39 Prospective Indices: Pointers to Future Work
3.4.40 Dynamic & Evaluative Frameworks
3.4.41 Elective & Motive Forces
3.4.42 Sign Processes: A Start
3.4.43 Reflective Extensions
3.4.44 Reflections on Closure
3.4.45 Intelligence => Critical Reflection
3.4.46 Looking Ahead
3.4.47 Mutually Intelligible Codes
3.4.48 Discourse Analysis: Ways & Means
3.4.49 Combinations of Sign Relations
3.4.50 Revisiting the Source
3.5 Divertimento:
Eternity in Love with the Creatures of Time
3.5.1 Reflections on the Presentation of Examples
3.5.2 Searching for Parameters
3.5.3 Defect Analysis
3.5.4 The Pragmatic Critique
3.5.5 Pragmatic Operating Notions
3.5.6 Defects of Presentation
3.5.7 Dues to Process
3.5.8 Duties to Purpose
3.6 Computational Design Philosophy
3.6.1 Intentional Objects & Attitudes
3.6.2 Imperfect Design & Persistent Error
3.6.3 Propositional Reasoning About Relations
3.6.4 Dynamic & Evaluative Frameworks
3.6.5 Discussion of Examples
3.6.6 Information & Inquiry
4. Overview of the Domain: Interpretive Inquiry
4.1 Interpretive Bearings: Conceptual & Descriptive Frameworks
4.1.1 Catwalks: Flexible Frameworks & Peripatetic Categories
4.1.1.1 Eponymous Ancestors:
The Precursors of Abstraction? 4.1.1.2 Reticles:
Interpretive Flexibility as a Design Issue. 4.1.2 Heuristic Inclinations & Regulative Principles
4.2 Features of Inquiry Driven Systems
4.2.1 The Pragmatic Theory of Signs
4.2.2 The Pragmatic Theory of Inquiry
4.3 Examples of Inquiry Driven Systems
4.3.1 "Index": A Program for Learning Formal Languages
4.3.2 "Study": A Program for Reasoning with Propositions
5. Discussion & Development of Objectives
5.1 Objective 1a: Propositions as Types
5.2 Objective 1b: Proof Styles & Developments
5.3 Objective 1c: Interpretation & Authority
Document History:
Contact: <jawbrey@oakland.edu>
Version: Draft 8.2
Created: 23 Jun 1996
Revised: 30 Jun 2000
Advisor: M.A. Zohdy
Setting: Oakland University, Rochester, Michigan, USA
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