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==Outline==
==Inquiry Driven Systems==
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IDS. Inquiry Driven Systems
1.1.1 Problem
1.1.2 Method
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1.1.2.1 The Paradigmatic & Process-Analytic Phase.
Version : May-Jun 2004
1.1.2.3 Reprise of Methods
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1.1.4 Application
Chapter 1.
1.2.1 A Modulating Prelude
Division 1.1
Section 1.1.1
Subsection 1.1.1.1
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Inquiry Driven Systems: An Inquiry Into Inquiry
1. Introduction
1.1. Outline of the Project: Inquiry Into Inquiry
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.
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1.5 Obstacles to the Project : In the Way of Inquiry
1.1.2. Method
1.5.3.2 Conceptual Extensions
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 that 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?
Accordingly, 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 -- and what those are
is just another 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 give preference to two kinds
of technique, one analytic and one synthetic.
The principal 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 in the study.
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 iterative or even opportunistic
fashions, working on any edge of research that appears to be ready at
a given time. If forced to anticipate the most 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 that 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.
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IDS. Inquiry Driven Systems
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1.1.2.1. The Paradigmatic and Process-Analytic Phase
In this phase I describe the performance and the competence
of intelligent agents in terms of a variety of formal systems:
For aspects of an inquiry process that affect its dynamic or
its temporal performance I will typically use representations
that are modeled on finite automata and differential systems.
For aspects of an inquiry faculty that reflect its formal or
its symbolic competence I will generally use representations
like formal grammars, logical calculi, constraint-based axiom
systems, and rule-based theories, all in connection with many
different "proof styles", for example, equational or illative.
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:
1. Introduction
1. Focus on a problematic phenomenon. This is a general property
or a generic process that attracts one's interest, for example,
intelligence or inquiry.
2. Gather under consideration significant cases of concrete agents
or systems that exhibit the property or the process in question.
3. Reflect on the common properties of these systems in a search for the
less obvious traits that might explain their more surprising features.
4. 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 the 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.
The last option of the last step already overlaps with the synthetic phase of work.
Regarding this phase of procedure within the frame of experimental research, it is
important to recognize that a computer program can fill the role of a hypothesis,
that is to say, a testable (defeasible or falsifiable) construal of how a process
is actually, might be possibly, or ought to be optimally carried out.
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1.1.2. Method
1.1.2.2. The Paraphrastic and 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 for discharging contextual definitions that
is known as "paraphrasis". All of these methods are founded on the idea of
providing meanings for operational specifications, "definitions in use",
alleged descriptions, or "incomplete symbols". No excessive generosity
with the resources of meaning is intended, though. It often happens
in practice that 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, p. 216).
See also (Whitehead & Russell, in Van Heijenoort, pp. 217-223).
Synthesis. Regard computer programs as implementations of hypothetical
or postulated faculties. Within the framework of experimental research,
programs can serve as descriptive, modal, or normative hypotheses, that
is to say, as conjectures about how a process is actually accomplished
in nature, as speculations about how it might be done in principle, or
as explorations of how it might be done better in the medium of
technological extensions.
This is the most concise and comprehensive answer that I know, but
For the purposes of this project, "paraphrastic definition" denotes the
it is likely to sound facetious at this point. On the other hand,
analysis of formal specifications and contextual constraints to derive
effective implementations of a process or its corresponding faculty.
This is carried out by considering what the faculty in question is
required to do in the many contexts that it is required to serve,
and then by analyzing these formal specifications with an eye to
the design of computer programs that can fulfill them, at least,
to whatever extent makes sense with regard to the ends in view.
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1.1.2.3. Reprise of Methods
The methodology that underlies this approach has two components:
The whole array of methods will be typical of the "top-down" strategies
used in artificial intelligence research, involving the conceptual and
operational analysis of higher-order cognitive capacities with an eye
toward the modeling, grounding, and support of these faculties in the
form of effective computer programs. The most critical and toughest
part of this discipline is in making sure that one does "come down",
that is, in finding guarantees that the analytic reagents and the
synthetic apparatus that one applies are actually effective,
reducing the excipients of speculation to arrive at active
ingredients and effective principles.
Finally, I ought to observe a hedge against betting too much on this
the competence of intelligent agents in the medium of various
or any other 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 runners, shoots, and tendrils of research tend to interleave
and intertwine as they will.
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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 provisional model of
inquiry that will guide this project, the criterion of an inquiry's competence
is how well it works 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 advanced:
Successful results of inquiry provide the agent with augmented
powers of (1) control and (2) prediction with respect to how
the object system will behave under the given circumstances.
If a common theme is sought that will cover both of these
goals, even if 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.
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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 two-way bridges 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
linkages among cognitive psychology (the descriptive study of how we think),
artificial intelligence (the prospective study of how we might think), and
logic (the normative study of how we ought to think in order to accomplish
the goals of reasoning).
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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 so
to a strategy for establishing or for discharging contextual definitions that
taken 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
in practice that a larger share of the routine is spent detecting
but never out of necessity afford a sense of direction. One senses
that 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.
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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 their way
through the constellations of contingent, incomplete, and contradictory
indications that they actually find themselves sailing under at present.
In the remainder of this Division (1.2) I will indicate
as briefly as possible the nature of the problem that
must be faced in this particular approach to inquiry,
and try to explain what a large share of the ensuing
effort will be directed toward clearing up.
Toward the end of this discussion I will be using highly concrete
mathematical models, or 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.
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1.1.3. Criterion
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
is how well it works in reducing the uncertainty of its agent about its object.
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
the object system will behave under the given circumstances.
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?
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1.1.4. Application
1.3. Option of the Project: A Way Up To Inquiry
I begin with an informal examination of the concept of inquiry.
In this Division I take as subjects the supposed faculty of
inquiry in general and the present inquiry into inquiry in
particular and I attempt to analyze them in relation to
each other on formal principles alone.
The initial set of concepts that I need to get the discussion
started are relatively few in number. Assuming that a working
set of ideas can be understood on informal grounds at the outset,
to be applied in the furtherance of the other.
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 into components
that amount to simpler types of phenomenal processes, to the extent
that this is seen possible.
In yet another development, computer models of learning and reasoning form
As a phenomenon, a particular way of doing inquiry will here be regarded
as embodied in a faculty of inquiry, as possessed by an agent of inquiry.
As a process, a particular example of inquiry will be regarded as extended
in time through a sequence of states, as experienced by its mediating agent.
In this view of phenomena and processes, it is envisioned that an agent or
a faculty of any generically described phenomenal process, inquiry included,
could be started off from different initial states and would conceivably go
through different trajectories of subsequent states, and yet there would be
a recognizable quality or an abstractable property that justifies invoking
the name of the genus in question, inquiry included.
The steps of this analysis will be annotated below by making use of the
following conventions. Lower case letters denote phenomena, processes,
or faculties under investigation. Upper case letters denote classes of
the same sorts of entities. Special use is made of the following symbols:
Y = genus of inquiry; y = generic inquiry; y_0 = present inquiry.
Compositions of "faculties" are indicated by concatenating their names,
as fg, and are posed in the sense that the right "applies to" the left.
The notation "f >= g" indicates that f is greater than or equal to g in
a decompositional series, in other words, f possesses g as a component.
The coset notation FG indicates a class of "faculties" of the form fg,
with f in F and g in G. Notations like "{?}", "{?, ?}", and so on,
serve as proxies for unknown components and indicate tentative
analyses of faculties in question.
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1.3.1. Initial Analysis of Inquiry -- Allegro Aperto
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. y_0 = y y = {?}{?}.
If I aim to devise the kind of computational support that can give the
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 >= {discussion, formalization}.
In accord with this plan, the main body of this Division (1.3) is devoted
to a discussion of formalization. y_0 = y y >= {d, f}{d, f} >= {f}{d}.
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1.2.2. A Fugitive Canon
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, and that is the discussion of
discussion itself. y_0 = 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
in relating one human experience to another, that is, in describing and
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".
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1.3. Option of the Project: A Way Up To Inquiry
1.3.3. Discussion of Formalization: General Topics
Because this project makes constant use of formal models
of phenomenal processes, it is incumbent on me 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.
1.3.3.1. A Formal Charge
An introduction to the topic of formalization, if proper,
is obliged to begin informally. But it will be my constant
practice here to keep a formal eye on the whole proceedings.
What this form of observation reveals must be kept silent for
the project gets under way. Inquiry in general will be described
the most part at first, but I see no rule against sharing with
the reader the general order of this watch:
1. Examine every notion of the casual intuition
that enters into the informal discussion and
inquire into its qualifications as a potential
candidate for formalization.
a recognizable quality or an abstractable property that justifies invoking
2. Pay special attention to the nominal operations
that are invoked to substantiate each tentative
explanation of a critically important process.
the same sorts of entities. Special use is made of the following symbols:
Frequently, but not infallibly, operations of
this sort can be detected appearing in the
guise of "-ionized" words, in other words,
terms ending in the suffix "-ion" that
typically connote both a process and
its result.
3. Ask yourself, with regard to each postulant faculty
in the current running 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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1.3.1. Initial Analysis of Inquiry -- Allegro Aperto
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 mere foreshadowing of its character will
have to do for the present. y_0 = y y >= {d, f}{d, f} >= {f}{f}.
To illustrate the formal charge by taking the present matter to task,
I have brought inquiry face to face with itself, inditing it to apply
the word "formalization" is itself exemplary of the "-ionized" terms
its action in pursuing a knowledge of its passion. y_0 = y y = {?}{?}.
that fall under the charge, and so it can be lionized as the nominal
head of a prospectively formal discussion. The reader is entitled 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
have recourse to easier actions and simpler objects. y >= {?, ?}.
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 discussion 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
to a discussion of formalization. y_0 = y y >= {d, f}{d, f} >= {f}{d}.
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.
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1.3.2. Discussion of Discussion
1.3.3.3. A Formalization of Discussion?
The previous Subsection took the concept of "formalization" as an example
an interruption, a topic so easy that I almost omitted it altogether
of a topic that a writer might try to translate from informal discussion
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 monologues with themselves, or
(2) that a writer (speaker) conducts in real or imagined dialogue
with a reader (hearer). In view of this implicitly discursive
mediation, I see no harm in letting the concept of discussion
be stretched to cover all attempted processes of formalization.
This assumption may be annotated as F c D.
In this Subsection, I step back from the example of "formalization"
and consider the general task of clarifying and communicating concepts
by means of a suitably directed discussion. Let this kind of "motivated"
or "measured" discussion be referred to as a "meditation", in other words,
"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, allowing the chain of subsumptions 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? y_0 = y y >= {d, f}{d, f} >= {d}{f}.
is constrained to the envelope of life and required to contribute to the
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 14
IDS. Note 17
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3. Discussion of Formalization: General Topics
1.3.3.3. A Formalization of Discussion? (cont.)
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
that I will use throughout this work and to preview
particular meanings that are intended to be
a concrete example of its application.
the effects of a particular discussion.
In cases where 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 (SOI_1),
and builds a relation from it to another system of interpretation (SOI_2).
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 to highlight the effects of a discussion that "builds a relation"
between SOI's, I will call this aspect of the process "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 indexed or ordered 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 SOI_1 to SOI_2, 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 "considerate discussion" or "polite discourse".
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
the powers for choice in the resulting SOI.
As conditions for the possibility of considerate but significant
narration, there are a few requirements placed on the writer and
the reader. Considerate narration, constructing a relation from
SOI to SOI in a politic fashion, cannot operate in an infectious
or addictive manner, invading a SOI like a virus or trojan horse,
but ultimately must transfer its communication 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 extensible in non-trivial ways.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 18
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.3. A Formalization of Discussion? (concl.)
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.
of limited uncertainty, each attaching a distribution of meanings
On several occasions this discussion of inquiry will arrive at a form
of "aesthetic deduction", in general terms, a piece of reasoning that
results in a design recommendation, and in the immediate case, where
an analysis of the general interests and objectives of inquiry leads
us to conclude 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
of inquiry, and be assured that it is has not often slipped my attention
together into the qualifications of inquiry and a definition
of what exactly is desired in order to constitute knowledge?
in its present state of completion would be far too tedious and tenuous
to escape expurgation.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 16
IDS. Note 19
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.3. A Formalization of Discussion?
1.3.3.4. A Concept of Formalization
The previous Subsection took the concept of "formalization" as an example
The concept of formalization is intended to cover the whole collection
of a topic that a writer might try to translate from informal discussion
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
a functional image that captures an aspect of the casual circumstances.
Relations between casual and formal discussion are often treated in
and consider the general task of clarifying and communicating concepts
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
in contemplation" (Webster's). The motive of a meditation is to mediate a
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.
of measured discussions and the qualifications of a writer so motivated.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 17
IDS. Note 20
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.3. A Formalization of Discussion? (cont.)
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
that are available in ordinary discourse to the
an effective conception of "interpretive frameworks" or "interpretive systems".
This concept encompasses any organized system of interpretive practice, ranging
from those used in everyday speech, to the ones that inform technical discourse,
to the kinds of completely formalized symbol systems that one can safely regard
as mathematical objects. Depending on the degree of objectification that it
possesses from one's point of view, the same system of conduct can variously
be described as an interpretive framework (IF), interpretive system (IS),
interpretive object (IO), or 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
a technical concept that will be increasingly formalized as this project
or a substantive agent of the system. I will often refer to an agent of
this kind as the "interpreter" of the moment. At other times, it may be
necessary to analyze the action of interpretation a bit more carefully.
At these latter 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. Therefore, 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 meantime a sign
that serves to convey an appearance of knowledge in a place where very
little is known about the subject itself.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 21
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.5. A Formal Approach (cont.)
A meta-language corresponds to what I call an "interpretive framework".
Besides a set of descriptions and conceptions, it embodies the whole
of a transformation taking place from SOI_1 to SOI_2, but this is more
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, in other words, as a comprehensive organization
of related activities.
of SOI-building worth having leads me to enumerate a few characteristics
of "considerate discussion" or "polite discourse".
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 an arbitrary nature, but freely to augment the options for meaning and
of compact symbols and isolated instruments. In short, though a framework
the powers for choice in the resulting SOI.
may have pointer dials and portable tools attached to it, it is usually
far too incumbent and cumbersome to be easily moved on its own grounds,
at least, it often 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
or addictive manner, invading a SOI like a virus or trojan horse,
its character to the constituent members of the framework. In some cases,
the rules of the IF in question proscribe against reflecting on its form.
of the receiving SOI. Significant communication, in which the
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 these acts of reflection and critique are permitted in principle.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 18
IDS. Note 22
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.3. A Formalization of Discussion? (concl.)
1.3.3.5. A Formal Approach (cont.)
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,
of aspects, throughout this work. In recognition of this circumstance,
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
of "aesthetic deduction", in general terms, a piece of reasoning that
between object language and meta-language ordinarily goes unexamined.
This means that the assumption of a distinction between the two
languages is de facto a part of the meta-language and not even
an object of discussion in the object language. A slippery
slope begins at this step. A failure to build reflective
capacities into an interpretive framework can let go
unchallenged the spurious opinion that presumes that
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 to "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.
1.3.3.4. A Concept of Formalization
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 23
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.5. A Formal Approach (concl.)
The grounds of discussion that I'm raking over here constellate a rather
striking scene, especially for a setting that is intended to function as
a neutral backdrop. Departing from the rule that we seek and often find
in 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 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 tend to derive from the prefix "meta",
leading them to search for higher and higher levels of meaning and truth,
on beyond language, on beyond every conceivable system of signs, thus on
beyond the realm of sense. Prolonged use of the affix "meta" after this
fashion leads people to act as if the meta-language were step outside of
ordinary language, or an artificial platform built above and beyond our
natural languages, then they forget that formal models are developments
that are internal to the informal context. For this reason and others,
I recommend replacing allusions to rigidly stratified object languages
and meta-languages with indices of contingent interpretive frameworks.
To avoid the types of cul-de-sac that are outlined above, I am taking 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 own 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.
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
of formalization are addressed by postulating a distinction between the
between objective and instrumental languages then it
must be possible to describe it within the frame
and technical discourse that can be used without being formalized, and
of this informally discursive universe.
the object language, the domain of structures and processes that can be
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 20
IDS. Note 24
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.5. A Formal Approach
1.3.3.6. A Formal Development
I plan to approach the issue of formalization from a slightly different angle,
The point of view 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 discloses the active
ingredients of its source materials in a critically reflective recapitulation
or an analytically representative recipe, or (3) whether it instead insistently
obscures what portion of its domain it manages to cover.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 21
IDS. Note 25
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.5. A Formal Approach (cont.)
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
that are trusted by agents at a given moment to make its employment
only to entertain different points of view on the use of symbols. One of
the chief design considerations for an interpretive system is that it must
never function as a virus or addiction. Its suggestions must always be,
initially and finally, purely optional adjunctions to the interpretive
framework that was already in place before it installed itself on the
scene. Interpretive systems are 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 beliefs that one actually
has at each given moment.
In use, an interpretive framework operates to contain activity and constrain
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
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 every
interpretive framework is likely to support
at any foreseeable moment in its field of
view. Of course, each interpreter enters
discussion initially operating as if its
own perspective were "meta" in relation
the requisite forms and taking part in the step by step routines of the IF,
to all the others, but a well-developed
interpretive system is likely to have
acquired the notion and taken notice
of the fact that this is not likely
to be a universally shared opinion.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 22
IDS. Note 26
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.5. A Formal Approach (cont.)
1.3.4. Discussion of Formalization: Concrete Examples
Section 1.3.3 outlined a variety of general issues surrounding the concept
of formalization. Section 1.3.5 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.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 27
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.1. Formal Models: A Sketch
To sketch as briefly as possible the features of the modeling activity
that are most relevant to our present purpose: The modeler begins with
a "phenomenon of interest" or a "process of interest" (POI) and relates
it to a formal "model of interest" (MOI), the whole while working within
a given "interpretive framework" (IF) and relating the results from one
"system of interpretation" (SOI) to another, or to a later development
of the same SOI.
The POI's that define the intents and the 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 interpretive systems and all of the process models
that are being 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. The typical POI comes from natural sources or from 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.
and meta-languages with indices of contingent interpretive frameworks.
2. Beyond the initial stages of investigation, the MOI is postulated as a
to ensure a reflective capacity for the interpretive frameworks I develop
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 that
is 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 get a handle on these directions is
the opportune mathematical circumstance that there can be well-defined
finite relations between entities that are infinite and even indefinite
in themselves. Indeed, exploiting this handle on infinity is the main
the ordinary universe.
trick of all computational models and effective procedures. It is how
a finitely informed creature can "make infinite use of finite means".
In sum, the MOI is pivotal or cardinal in that it constitutes a model
in two senses, (a) loosely analogical and (b) more strictly logical,
integrating twin roles of the model concept in a single focus.
3. Finally, the IF's and the SOI's always remain partly out of sight, caught up
of drawing distinctions between various levels of formalization
in various stages of explicit notice between casual informality and partial
formalization, with no guarantee or even much likelihood of a completely
articulate formulation being forthcoming. Still, it is usually worth
the effort to try lifting one or another edge of these frameworks
and backdrops into the light, at least for a time.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 24
IDS. Note 28
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.6. A Formal Development
1.3.4.2. Sign Relations: A Primer
To the extent that their structures and functions can be discussed at all,
it appears likely at this point that all of the formal entities destined
in the context of informal activity, until gradually the most relevant
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 easily converted to or ultimately grounded in
sign relations. This class of triadic relations constitutes
the main study of the "pragmatic theory of signs", a branch
of logical philosophy devoted to understanding all types
of symbolic representation and communication.
There is a close relationship between the pragmatic theory of signs and the
of informal discussion, the questions that become important to ask of
pragmatic theory of inquiry. In fact, the correspondence between the two
a prospective formal model are: (1) whether it highlights the structure
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.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 25
IDS. Note 29
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.3.7. A Formal Persuasion
1.3.4.2. Sign Relations: A Primer (cont.)
Because the examples in this Section (1.3.4) have been artificially
constructed to be as simple as possible, their detailed elaboration
can run the risk of trivializing the whole theory of sign relations.
Despite their simplicity, however, these examples have subtleties of
their own, and their careful treatment will serve to illustrate many
important issues in the general theory of signs.
Example 1. The Story of A and B
and independent perspective, with no objective
Imagine a discussion between two people, Ann and Bob, and attend only
to that aspect of their 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 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 that 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 L
is a subset of a cartesian product O x S x I. Here, O, S, I are three
sets that are known as the "object domain", the "sign domain", and the
"interpretant domain", respectively, of the sign relation L c O x S x I.
Broadly speaking, the three domains of a sign relation can be
any sets whatsoever, but the kinds of sign relations that are
typically contemplated in a computational setting are usually
constrained to having I c S. In this case, interpretants are
just a special variety of signs, and this makes it convenient
to lump signs and interpretants together into a single class
called the "syntactic domain". In the forthcoming examples,
S and I are identical as sets, so the same elements manifest
I have in mind using as formal models.
themselves in two different roles of the sign relations in
question. When it is necessary to refer to the whole set
of objects and signs in the union of the domains O, S, I
for a given sign relation L, one may call this set the
"world of L" and write W = W(L) = O |_| S |_| I.
To facilitate an interest in the abstract structures of sign relations,
and to keep the notations as brief as possible as the examples become
more complicated, I introduce the following general notations:
O = Object Domain
S = Sign Domain
I = Interpretant Domain
Introducing a few abbreviations for use in considering
the present Example, we have the following set of data:
O = {Ann, Bob} = {A, B}
S = {"Ann", "Bob", "I", "You"} = {"A", "B", "i", "u"}
I = {"Ann", "Bob", "I", "You"} = {"A", "B", "i", "u"}
In the present Example, 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 of the form <o, s, i> that make up the
corresponding sign relations: L(A), L(B) c O x S x I. It is often tempting
to use the same names for objects and for relations involving these objects,
but I will avoid this here, taking up the issues that this practice raises
after the less problematic features of these relations have been treated.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Table 1. Sign Relation of Interpreter A
o---------------o---------------o---------------o
| Object | Sign | Interpretant |
o---------------o---------------o---------------o
| A | "A" | "A" |
| A | "A" | "i" |
| A | "i" | "A" |
| A | "i" | "i" |
| B | "B" | "B" |
| B | "B" | "u" |
| B | "u" | "B" |
| B | "u" | "u" |
o---------------o---------------o---------------o
Table 2. Sign Relation of Interpreter B
o---------------o---------------o---------------o
| Object | Sign | Interpretant |
o---------------o---------------o---------------o
| A | "A" | "A" |
| A | "A" | "u" |
| A | "u" | "A" |
| A | "u" | "u" |
| B | "B" | "B" |
| B | "B" | "i" |
| B | "i" | "B" |
| B | "i" | "i" |
o---------------o---------------o---------------o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
These Tables codify a rudimentary level of interpretive practice for the
agents A and B, and provide a basis for formalizing the initial semantics
that is appropriate to their common syntactic domain. Each row of a Table
names an object and two co-referent signs, making up an ordered triple of
the form <o, s, i> that is 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.
the main study of the "pragmatic theory of signs", a branch
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 29
IDS. Note 30
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.2. Sign Relations: A Primer (cont.)
1.3.4.2. Sign Relations: A Primer (cont.)
One aspect of the meaning of a sign is concerned with the reference
that a sign has to its objects, which objects are collectively known
as the "denotation" of the sign.
There is a difficulty that needs to be mentioned at this point, though
for the sake of a first approach to the general theory of sign relations
I will need to sidestep detailed discussion of it until later in the game.
The problem is this: Generally speaking, when it comes to things that are
being contemplated as ostensible or potential signs, neither the existence
nor the uniqueness of any objects in their denotations is guaranteed. Thus,
the denotation of a putative sign can refer to a singular, a plural, or even
a vacuous number of objects. A proper treatment of this complication calls
for the conception of something slightly more general than a sign relation
proper, namely, a construct called a "sign relational complex". In effect,
expressed in the roughest practical terms, this allows for "missing data"
in the columns of the relational database table for the sign relation in
question. Until this concept can be properly developed, let us operate
on the default assumption that signs actually have objects, but remain
wary enough of the exceptions to deal with them on an ad hoc basis.
In the pragmatic theory of sign relations, denotative references are
formalized as certain types of dyadic relations that are obtained by
projection from the triadic sign relations.
The "object domain" of this discussion fragment is the
The dyadic relation that constitutes the "denotative component" of
a sign relation L will here be notated as Den(L). Information about
the denotative component of meaning can be obtained from L by taking
its "dyadic projection" on the object-sign plane, in other words, on
the 2-dimensional space that is generated by the object domain O and
the sign domain S. This denotative aspect or semantic projection of
a sign relation L will here be notated in any one of the following
equivalent forms, Proj_OS (L), Proj_12 (L), L_OS, or L_12, and it
is defined as follows:
Den(L) = Proj_OS (L) = {<o, s> in O x S : <o, s, i> in L for some i in 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
"interpretant domain", respectively, of the sign relation L c O x S x I.
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.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 31
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.2. Sign Relations: A Primer (cont.)
The other dyadic aspects of meaning 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 empty, unique, or multiple in its collection of
terminal points, and both can be formalized as different types
of dyadic relations that are obtained as planar projections
of the triadic sign relations.
The connection that a sign makes to an interpretant will here be referred to
as its "connotation". In the general theory of sign relations, this aspect
of meaning includes the references that a sign has to affects, concepts,
impressions, intentions, mental ideas, and the whole realm of an agent's
mental states and allied activities, broadly encompassing intellectual
associations, emotional impressions, motivational impulses, and real
conduct. This complex system 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 sign relation L,
the dyadic relation that forms the "connotative component"
of L will here be denoted as Con(L).
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 neglects
the mediational character of the whole transaction in which this occurs.
In view of the service that interpretants supply in furnishing a locus
for critical, explanatory, and reflective glosses, both with regard to
the objective scenes and also with respect to their descriptive themes,
it is possible to regard interpretant signs as providing "annotations"
for both objects and signs, but this function points in the opposite
direction of the arrow from interpretants to objects that is needed
in the present connection. What does one call the inverse of the
annotation function? More generally asked, what does one call
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 meaning. On a trial basis,
I will describe it as the "ideational", "intentional", or "canonical" aspect
of the sign relation, and I will see how it works in the long run to call the
reference of an interpretant sign to its object by the name of its "ideation",
"intention", or "conation". For the time being, then, the dyadic relation that
constitutes the "intentional component" of a given sign relation L will here be
notated as Int(L).
A full consideration of the connotative and intentional aspects of meaning
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.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 32
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o---------------o---------------o---------------o
o---------------o---------------o---------------o
1.3.4.2. Sign Relations: A Primer (concl.)
o---------------o---------------o---------------o
Formally speaking, the connotative and intentional
o---------------o---------------o---------------o
aspects of meaning present no additional difficulty.
The connotative component of a sign relation L can be formulated
as a dyadic projection on the plane of the sign and interpretant
domains, and thus defined as follows:
Con(L) = Proj_SI (L) = {<s, i> in S x I : <o, s, i> in L for some o in O}.
The intentional component of meaning for a sign relation L, or its
"second moment of denotation", is adequately captured as a dyadic
projection on the plane of the object and interpretant domains,
and thus defined as follows:
Int(L) = Proj_OI (L) = {<o, i> in O x I : <o, s, i> in L for some s in S}.
As it happens, the sign relations L(A) and L(B) in the present Example
are fully symmetric with respect to exchanging signs and interpretants,
so all of the data of Proj_OS L(A) is echoed unchanged in Proj_OI L(A)
and all of the data of Proj_OS L(B) is echoed unchanged in Proj_OI L(B).
The principal concern of this project is not with every conceivable
sign relation but chiefly with those that are capable of supporting
inquiry processes. In these species of sign relation, the relation
between the connotational and the denotational aspects of meaning
is not wholly arbitrary. Instead, this relationship is naturally
constrained or deliberately designed in such a way that it can
achieve the following aims:
1. Represent the embodiment of significant properties
that have objective reality in the agent's domain.
2. Support the achievement of particular purposes
that have intentional value for the agent.
Therefore, my attention is directed chiefly toward understanding the forms
of correlation, coordination, and cooperation among the various components
of discussing these alternatives, I will introduce a few terms that are
of sign relations that form the necessary conditions for achieving these
aims and thus for being able to conduct coherently directed inquiries.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 30
IDS. Note 33
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.2. Sign Relations: A Primer (cont.)
1.3.4.3. Semiotic Equivalence Relations
If one examines the sign relations L(A) and L(B) that are associated with
that a sign has to its objects, which objects are collectively known
the interpreters A and B, respectively, one observes that they have many
contingent properties that are not possessed by sign relations in general.
One of the nicest properties possessed by the sign relations L(A) and L(B)
is that their connotative components L(A)_SI and L(B)_SI constitute a pair
of equivalence relations on their common syntactic domain S = I. There is
reason to call such constructions "semiotic equivalence relations" (SER's),
since they equate signs that mean the same thing to somebody. Each of the
SER's L(A)_SI and L(B)_SI c S x I = S x S, partitions the whole collection
the denotation of a putative sign can refer to a singular, a plural, or even
of signs into "semiotic equivalence classes" (SEC's). These constructions
make for an especially strong form of representational relationship between
objects and signs in that the structure of the participants' common object
domain is reflected or reconstructed, part for part, in the structure of
each one's "semiotic partition" (SEP) of their shared syntactic domain.
in the columns of the relational database table for the sign relation in
The main trouble with this notion of shared meaning in the present Example
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 that are
induced by the interpreters A and B is summarized in Tables 3 and 4.
the denotative component of meaning can be obtained from L by taking
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. A's Semiotic Partition
o-------------------------------o
| "A" "i" |
o-------------------------------o
| "u" "B" |
o-------------------------------o
Table 4. B's Semiotic Partition
o---------------o---------------o
| "A" | "i" |
| | |
| "u" | "B" |
o---------------o---------------o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 31
IDS. Note 34
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.2. Sign Relations: A Primer (cont.)
1.3.4.3. Semiotic Equivalence Relations (concl.)
In order to discuss this type of situation further,
the reference that a sign has to its interpretant and the reference
I introduce the square bracket notation "[x]_E" to
mean "the equivalence class of the element x under
the equivalence relation E". A statement that two
elements x and y are equivalent under E is called
of dyadic relations that are obtained as planar projections
an "equation", and it can be expressed in either
of two ways, [x]_E = [y]_E, or x =_E y.
In application to sign relations, I extend the use
of the square bracket notation in the following ways.
of meaning includes the references that a sign has to affects, concepts,
When L is a sign relation whose "syntactic projection"
or connotative component L_SI is an equivalence relation
on S, then I write "[s]_L" for "the equivalence class of s
under the equivalence relation L_SI". A statement that the
two signs x and y are synonymous under a semiotic equivalence
relation L_SI is called a "semiotic equation" (SEQ), and can be
expressed in either one of the forms, [x]_L = [y]_L, or x =_L y.
of L will here be denoted as Con(L).
In many situations there is one further adaptation of the
square bracket notation that is very useful. Namely, when
a sign in its own right, then its independent reference to an object can
there is known to exist a particular triple <o, s, i> in L,
it is permissible to use "[o]_L" to mean the same thing as
the mediational character of the whole transaction in which this occurs.
"[s]_L". This modification is 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 view of the service that interpretants supply in furnishing a locus
In the case of our present Example
we have the following information.
The SER for interpreter A yields
the following semiotic equations:
A full consideration of the connotative and intentional aspects of meaning
["A"]_L(A) = ["i"]_L(A)
["B"]_L(A) = ["u"]_L(A)
Otherwise expressed:
"A" =_L(A) "i"
"B" =_L(A) "u"
This amounts to the semiotic partition:
{{"A", "i"}, {"B", "u"}}.
The SER for interpreter B yields
the following semiotic equations:
["A"]_L(B) = ["u"]_L(B)
"second moment of denotation", is adequately captured as a dyadic
["B"]_L(B) = ["i"]_L(B)
Otherwise expressed:
"A" =_L(B) "u"
"B" =_L(B) "i"
This amounts to the semiotic partition:
{{"A", "u"}, {"B", "i"}}.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 33
IDS. Note 35
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.3. Semiotic Equivalence Relations
1.3.4.4. Graphical Representations
The dyadic components of sign relations can be given graph-theoretic
representations as "directed graphs", or "digraphs" for short, that
provide concise pictures of their structural and potential dynamic
properties. In graph-theoretic terminology, an ordered pair <x, y>
is called an "arc" or a directed edge from point x to point y, and
in the case that x = y, an arc from x to itself is called a "sling"
or a self-loop at the point x.
The denotative components Den L(A) and Den L(B) can be
pictured as digraphs on the six points of their common
of equivalence relations on their common syntactic domain S = I. There is
world set W = O |_| S |_| I = {A, B, "A", "B", "i", "u"}.
The main trouble with this notion of shared meaning in the present Example
The arcs are given as follows:
Den L(A) has an arc
from each point of {"A", "i"} to A and
from each point of {"B", "u"} to B.
Den L(B) has an arc
from each point of {"A", "u"} to A and
from each point of {"B", "i"} to B.
Den L(A) and Den L(B) can be interpreted as "transition digraphs"
that chart the succession of steps or the connection of states in
a computational process. If the graph is read this way, then 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 frames of reference.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 34
IDS. Note 36
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.3. Semiotic Equivalence Relations (concl.)
1.3.4.4. Graphical Representations (concl.)
The connotative components Con L(A) and Con L(B) can be represented
I introduce the square bracket notation "[x]_E" to
as digraphs on the four points of their common syntactic domain
S = I = {"A", "B", "i", "u"}. Con L(A) and Con L(B) are SER's,
and so their digraphs conform to the pattern that is shown by
all digraphs of equivalence relations. In general, a digraph
an "equation", and it can be expressed in either
of an equivalence relation falls into connected components
of two ways, [x]_E = [y]_E, or x =_E y.
that correspond to the parts of the associated partition,
with a complete digraph on the points of each part, and
no arcs between the parts. In the present Example,
the arcs are given as follows:
Con L(A) has the structure of a SER on S, that is,
of the square bracket notation in the following ways.
the digraph has a sling at each of the points in S,
two-way arcs between the points of {"A", "i"}, and
two-way arcs between the points of {"B", "u"}.
on S, then I write "[s]_L" for "the equivalence class of s
Con L(B) has the structure of a SER on S, that is,
the digraph has a sling at each of the points in S,
two-way arcs between the points of {"A", "u"}, and
two-way arcs between the points of {"B", "i"}.
"[s]_L". This modification is designed to make the notation
Taken as transition digraphs, Con L(A) and Con L(B) highlight the
associations that are permitted between equivalent signs, as this
equivalence is judged by the interpreters A and B, respectively.
The SER for interpreter A yields
The theme running through the last three Subsections, that associates
the following semiotic equations:
different interpreters and different aspects of interpretation with
different sorts of relational structures on the same set of points,
heralds a topic that will be developed extensively in the sequel.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 37
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.5. Taking Stock
So far, my discussion of the discussion between A and B, in the picture that
it gives of sign relations and their connection to the imagined processes of
interpretation and inquiry, can best be described as fragmentary. By way of
telling the story of A and B, a sample of typical language use was 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 or even attempted.
It seems like a good idea to pause at this point and to 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 discussion
in revealing the relevant attributes of even so simple an example as the one
that I am taking as a nominal beginning, the second having to do with the
defects that this species of example exhibits within the broader genus
of sign relations that it is meant, however nascently, to exemplify.
As a general schema, I describe these respective types of limitations as
the "rhetorical defects" and the "objective defects" that any discussion
can have in addressing its intended object. My immediate concern is to
remedy the insufficiencies of analysis that affect my treatment of the
present example. The overarching task is to address the atypically
simplistic features of this example as it falls within the class
of sign relations that may be found relevant to realistic cases
of inquiry.
The SER for interpreter B yields
The next few Subsections will be concerned with the most problematic features
the following semiotic equations:
of the A and B dialogue, especially with the sorts of difficulties that are
clues to significant deficits in theory and technique, and that can serve
to point out directions for future improvements.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 35
IDS. Note 38
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.4. Graphical Representations
1.3.4.6. The "Meta" Question
There is one point of common contention that I finessed from play
in my handling of the transaction between A and B, even though it
lies in plain view on both of their sign relational Tables. This
is that troubling business, recalcitrant to analysis precisely on
is called an "arc" or a directed edge from point x to point y, and
account of the fact that its dealings race on so heedlessly ahead
of thought and grind on so routinely beneath its notice, in short,
it concerns the placement 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 on behalf of
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 numerous types of false
impression, both about the true characters of the Tables that are presented
here and about the proper utilities of their graphical equivalents that are
designed to be implemented as data structures in the computer. The next few
remarks are put forth in hopes of averting the ordinary brands of misreading.
The arcs are given as follows:
The general character of this question can be expressed in the schematic terms
that I used earlier to give a rough sketch of the modeling activity as a whole.
How do the isolated "systems of interpretation" (SOI's) of the agents A and B
relate to the "interpretive framework" (IF) that I am using to present them,
and how does this IF operate, not only to objectify A and B in the guise of
the coordinated "models of interpretation" (MOI's), but simultaneously to
embrace the present and the prospective SOI's of the current narrative,
namely, 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 Table of a sign relation is a complex sign in itself,
each of whose syntactic constituents is assigned a smaller part and plays
the role of a simpler sign in its makeup. To put it succinctly, there is
nothing but text to be seen on the page. Viewed 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 are transposed up a notch on the scale that registers
levels of indirectness in reference, with each item passing from
a more objective to a more symbolic mode of presentation.
Sign relations themselves, like any real objects of discussion,
are either too abstract or too concrete to reside in the medium
of communication, but can only find themselves represented there.
The tables and graphs that are used to represent sign relations
are themselves complex signs, involving a step of denotation to
reach the sign relation intended. The intricacies of this step
require an order of interpretive performers who are able, over
and above executing all of the rudimentary steps of denotation,
to orchestrate these steps in concerted coordination with each
other. This performance in its turn requires a whole array of
techniques to match the connotations of complex signs and to
test their alternative styles of representation for semiotic
equivalence. Analogous to the ways that matrices represent
linear transformations and multiplication tables represent
group operations, a large part of the usefulness of these
complex signs comes from the fact that they are not just
conventional symbols for their objects but fully iconic
representations of their objective operative structure.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 36
IDS. Note 39
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.4. Graphical Representations (concl.)
1.3.4.7. Iconic Signs
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
and so their digraphs conform to the pattern that is shown by
relational tabels and graphs, interpreted as iconic representations or
analogous expressions of logical and mathematical objects, the pivotal
of an equivalence relation falls into connected components
properties are formal and abstract in their character. Since a uniform
translation through any dimension -- of sight, of sound, or imagination --
does not affect the structural properties of a configuration of signs in
relation to one another, this may help to explain how tables and graphs,
in spite of their semantic shiftiness, can succeed in representing the
forms of sign relations without essential loss or radical distortion.
Taking this unsuspecting introduction of iconic signs as a serendipitous
lesson, an important principle can be lifted from their style of 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 what are
possibly the most solid sites for pouring the foundations of formal expression.
What does appear in one of these sign relational Tables? It is clearly
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 them that are formed by quotation or
by other devices that effect a similar function. 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 that operates behind the scenes to bring its image and
its intent to the reader.
To understand what the Table is meant to convey the reader is called 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 L(A) and L(B) do
not exist in the literal medium of their Tables but are only represented
there by dint of the formal configurational properties that they happen
to 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 experience with language the likes
of which is familiar to writer and reader alike.
The successful formalization of a focal sign relation cannot get by
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 severity to
which an opportunity for understanding is undermined by prior petitions
of the very principles to be explained. Consequently, 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, what does it mean in terms of
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 this range of 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 casual or a formal transaction that constitutes the issue of the moment.
And it means that a formalization of the writer's and the reader's accessory
sign relations would have several portions that look identical to pieces of
the very sign relational Tables that are being placed under formal review.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 40
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.8. The Conflict of Interpretations
One discrepancy that needs to be documented at this point
the "rhetorical defects" and the "objective defects" that any discussion
can be observed in the conflict of interpretations between
A and B, as reflected in the lack of congruity between their
separate semiotic partitions of their shared syntactic domain.
This is a problematic feature of the present Example but also
one its more realistic characters. That is, it exemplifies
a type of problem with the interpretation of pronouns, more
of inquiry.
generally considered, all indexical signs and bound variables,
that actually arises in practice when attempting to formalize
the semantics of natural, logical, and programming languages.
On this account, the deficiency is with the present analysis,
and the burden remains to clarify precisely what is going on
with indexical signs of all kinds.
Notice, however, that I have deliberately avoided trying to deal with
of the A and B dialogue, especially with the sorts of difficulties that are
these types of indexical tokens in all of the more usual ways, namely,
by trying to eliminate all of the incipient semantic ambiguities from
to point out directions for future improvements.
the canonical formalization of the working textual material. Instead,
I have sought to preserve this quality of interpretive discrepancy as
one of the essential phenomena and one of the inevitable facts in the
realm of pragmatic semantics, tantamount to the irreducible nature of
perspective diversity. I believe that the desired competence in this
faculty of language must develop, not from a strategy of substitution
that replaces bound variables with their objective referents on every
fixed occasion, but from a pattern of recognizing interpretive context
that keeps indexical signs persistently attached to their interpreters
of reference.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 38
IDS. Note 41
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.6. The "Meta" Question
1.3.4.9. Indexical Signs
In the pragmatic theory of signs, an "index" is a sign that achieves its
representation of an object by virtue of an actual connection with it.
Though real and objective, the indexical connection can nevertheless
be purely incidental and even a bit accidental. Its effectiveness
depends only on the fact that any object in actual existence has
a multitude of properties, definitive and derivative, any number
of which are able to serve as its signs. Indices of an object
reside among its more tangential varieties of attributes, its
accidental or its accessory features, which are really the
properties of some but not all points in the locus of its
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 syntactic contexts but the pragmatic context
that is involved in their actualizing "situation of use" (SOU) or their
realizing "instance of use" (IOU). To fulfill its proper duty to sense
of thought and grind on so routinely beneath its notice, in short,
the reading of an indexical sign demands to be supplemented by a still
it concerns the placement of object languages within the frame of
more determinate indication of its interpreter of reference, the agent
that is duly responsible for putting it into active use at the moment
in question.
Typical examples of indexical signs in programming languages are:
1. Variables, signs that need to be bound to a syntactic context or
that I used earlier to give a rough sketch of the modeling activity as a whole.
to an instantiation frame in order to have a determinate meaning.
2. Pointers, signs that serve particular interpreters operating
relative to locally active environments as accessory addresses
the coordinated "models of interpretation" (MOI's), but simultaneously to
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 denotes.
If a real object can be regarded as a generic and permanent property
that is shared by all of its momentary and specific 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.
of "semantic ascent". It is as if the entire contents of the original
It is in this sense that indices are properly
said to have "actual connections" but not of
necessity "essential connections" to whatever
objects they do in fact denote.
to orchestrate these steps in concerted coordination with each
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 39
IDS. Note 42
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.7. Iconic Signs
1.3.4.9. Indexical Signs (cont.)
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 product of the two
dyadic relations, "property of" and "instance of", and independently
of any particular interpreter. But jumping to this conclusion would
only produce an approximation to the truth, or a likely story, one that
duly provokes the rejoinders: "In whose approach?" or "Likely to whom?"
Taking this unsuspecting introduction of iconic signs as a serendipitous
Taking up these challenges provides a clue as to how a sign relation can appear
to be "moderately independent", "nearly objective", or "relatively composite",
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. It is not enough that the separate links
exist in principle to make something a property of an instance of something.
to contemplate various forms of graphical abstraction as supplying what are
In order to constitute a genuine sign relation, indexical or otherwise, each
of these links 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,
although 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
kind of entity that can contribute to generating both the object and
the experience, in this way connecting the diverse abstractions that
are called "objects" and "indices", respectively.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 43
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.9. Indexical Signs (concl.)
If a suitable framework of object instances can be found to rationalize
an interpreter's experience with objects, then the actual connection that
subsists between an object and its index becomes in this framework precisely
the connection that exists between two properties of the same object instance,
or between two sets that happen to intersect in a common element. Relative to
the appropriate framework, the actual connections that are needed to explain
the very sign relational Tables that are being placed under formal review.
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 to
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 would not object to speaking of objects of objects,
and 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.
However, experience leads me to believe that forms of analysis are too
peculiar to persons and communities, 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 special 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 operates
with respect to its own presumptuous form of analysis and all of
the circular viscosities of its "tacit analytic framework" (TAF).
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 41
IDS. Note 44
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.9. Indexical Signs
1.3.4.10. Sundry Problems
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.
be purely incidental and even a bit accidental. Its effectiveness
If the usage of the original singular sign is preserved, as it tends to be,
then the multitude of new instances that one comes to fathom beneath the
old object's superficial appearance gradually serve to reconstitute the
of which are able to serve as its signs. Indices of an object
singular sign's denotation in the form of a generic 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 to pursue the analysis of ostensible
the reading of an indexical sign demands to be supplemented by a still
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, instantiations,
realizations, and so on, of objects, and on occasion, and not
without sufficient 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 coordination with implementing interpreters as state transition
systems, I will be obliged to justify the idea that dynamic states
of dynamical systems are the "real signs" of concern to us and then
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 tender as "situations of use" (SOU's)
or as "instances of use" (IOU's), plus the states and motions of dynamic
systems that solely are able to realize these uses and to discharge the
obligations that 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, sign, and interpretant systems.
Since the roles of a sign relation are formally and pragmatically defined,
they do not depend on the material aspects or the essential attributes
of elements or domains. Therefore, it is conceivable that the very
same system could appear in all three pragmatic roles, and from
this possibility arises many of the ensuing complications of
the subject.
A related source of conceptual turbulence stems from the circumstance
that, even though a certain aesthetic dynamics attracts the mind toward
the index in order to tell what it denotes.
sign relational systems that are capable of reflecting on, commenting on,
and thus controlling ("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. In order to do this, interpretive agents need two things:
1. The senses to discern the essential tensions that typically prevail
between the formal pole and the informal arena of each discussion.
2. The language to articulate, over and above their potential roles,
the moment to moment placement of dynamic elements and systematic
components with regard to this underlying field of polarities.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 45
IDS. Note 42
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.9. Indexical Signs (cont.)
1.3.4.11. Review and Prospect
What has been learned from the foregoing study of icons and indices?
The impact of this examination can be sized up in a couple of stages:
in the first instance, by reflecting on the action of both the formal
and the formative signs that were found to be operating in and around
of any particular interpreter. But jumping to this conclusion would
the discussion of A and B, and next, by taking up the lessons of this
radically circumscribed arena as a paradigm for further investigation.
In order to explain the operation of sign relations corresponding to the
to be "moderately independent", "nearly objective", or "relatively composite",
iconic signs and the indexical signs in the A and B example, it becomes
all within the medium of a particular framework for analysis and interpretation.
necessary to refer to potential objects of thought that are located,
if they exist at all, outside the realm of the initial object set,
the supposedly frame-free relations of properties and instances that suffice
that is, 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 particular, it is
incumbent on a satisfying explanation to invoke the abstract
properties of objects and the actual instances of objects,
where these properties and instances are normally assumed
to be new objects of thought that are distinct from the
objects to which they refer.
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 yet to be fully formalized.
Considered on these grounds, the search for a satisfactory context
wherein 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 initially instigated the search.
of a single interpreter. Apparently then, the object instance is the
To make it serve as a paradigm for future developments,
I will reiterate the basic pattern that has just been
observed, but with a slightly different emphasis:
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 by this mention of "objects"
one initially comprehends a limited collection of objects of thought
under discussion. If these properties and instances are themselves
regarded as potential objects of thought, and if they are conceived
to be distinct from 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 initial
frame of discussion.
Can this manner of recursively searching for explanation be established
as well-founded? In order to organize the expanding circle of thoughts
and the growing wealth of objects that are envisioned within its scheme,
it helps to introduce a set of organizing conceptions. Doing this will
be the business of the next four Subsections.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 46
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.12. Objective Plans and Levels
In accounting for the special characteristics of icons and indices
that arose in previous discussions, it became necessary to open up
the domain of objects coming under formal consideration to include
unforeseen numbers of properties and instances of whatever objects
were originally set down. This is a general phenomenon, affecting
every motion toward toward explanation whether pursued by analytic
or by synthetic means. What it calls for in practice is a way of
organizing growing domains of objects, without having to specify
in advance all the objects there are.
This Subsection presents the "objective project" (OP) that I plan to
take up for investigating the forms of sign relations, and it outlines
three "objective levels" (OL's) of formulation that guide the analytic
and the 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
to be reformulated as a congeries extending over more determinate objects.
surveying a variety of problems that serve to instigate efforts in this
general direction, I explore the prospects of a particular "organon", or
"instrumental scheme for the analysis and 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
the effective operation of indexical signs I will have to invoke the
detail. At each stage, the developing tools are applied to the analysis
of concrete problems that arise in trying to clarify the structure and
function 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.
of sign-using transactions that I tender as "situations of use" (SOU's)
of elements or domains. Therefore, it is conceivable that the very
this possibility arises many of the ensuing complications of
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 45
IDS. Note 47
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.11. Review and Prospect
1.3.4.12. Objective Plans and Levels (cont.)
At this point in the work, I will need to apologize in advance
for introducing a certain idiosyncrasy of terminology, but the
underlying issue that I can see no other way to address except
by means of it can no longer be avoided. To be specific, I am
forced to use the word "objective" in a sense that will appear
to conflict with several traditions of interpretation, running
so seriously against the grain of some prevailing connotations
that it may sound like a pun or a joke to many readers. Still,
it's a definite "motive of consistency" (MOC) that requires me
to do this, as I will try to justify in the end.
As always, my use of the word "object" derives from the stock of the
Greek root "pragma", which captures all of the senses needed to suggest
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
the outset of the discussion and that one initially recognizes
somebody's object, objective, or objectivity.
In the pragmatic account of things, thoughts are just signs in the mind
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 are 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
to stem from whatever objects initially instigated the search.
or wanes in 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 discussion
and thought, but what kind of discussion and thought it is an object of.
How does one determine the character of this discussion or this thought?
Should this query be construed as a task of finding or a task of making?
Whether it appeals to arts of acquisition, production, or discernment,
and however one expects to decide or decode the conduct it requires,
the character of the discussion and thought in view is sized up and
riddled out in turn by looking at the whole domain of objects and
the 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 of these modes of approaching
and the actual instances of objects, where by this mention of "objects"
the constitutions of objects lead to the sorts 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 discussion too severely, I will resort
to be distinct from the objects whose properties and instances they
to using chimeras like "object-analytic" and "object-synthetic", paying the
price of biasing the constitution of objects in one direction or the other.
objects of thought that extends in two directions beyond the initial
In this work I would like to treat the two-way street of construction
as well-founded? In order to organize the expanding circle of thoughts
and deconstruction as parallel to the difference of direction between
and the growing wealth of objects that are envisioned within its scheme,
synthesis and analysis, respectively. However, being able to do this
without the introduction of too much distortion demands the mediation
of a further distinction. Accordingly, let it be recognized that all
orientations to the constitutions of objects can be pursued in either
"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 the 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 in everything construed as an object, obliges agents
to leave or at least to re-place objects within the contexts of
their live acquaintance, to reflect on their prevailing motives
or their underlying 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 the 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 isolated concepts and descriptions
on a mutually compatible basis and to use means of composition that can
constitute a medium for common sensibilities.
In sum, the radical project in all of these directions demands
forms of interpretation, analysis, synthesis that can reflect
In accounting for the special characteristics of icons and indices
a measure of light on the initially unstated assumptions of
their prospective agents.
the domain of objects coming under formal consideration to include
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 47
IDS. Note 48
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.12. Objective Plans and Levels (cont.)
1.3.4.12. Objective Plans and Levels (cont.)
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 -- or not. 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 complete and unique OF exists. Indeed, the hope that such
the stability of concern and the dedication to purpose that are forever
a "place to stand" does exist, somehow, somewhere, somewhen, often
serves to provide inquiry with a beneficial regulative principle or
a heuristic hypothesis to work on. But it just so happens, for the
run of "finitely informed creatures" (FIC's) at any rate, that the
existence of an ideal framework is a contingency to be established
after the fact, at least, somewhat nearer toward the ultimate end
of inquiry than the present time is apt to mark.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
IDS. Note 49
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
1.3.4.12. Objective Plans and Levels (concl.)
In the project developed here, an "objective framework" (OF)
embodies one or more "objective genres" (OG's), also called
"forms of analysis" (FOA's) or "forms of synthesis" (FOS's),
each of which genres delivers its own rendition of a great
chain of being for all of the objects that happen to fall
under its purview. In effect, each OG develops its own
In the project developed here, an "objective framework" (OF)
embodies one or more "objective genres" (OG's), also called
"forms of analysis" (FOA's) or "forms of synthesis" (FOS's),
each of which genres delivers its own rendition of a great
chain of being for all of the objects that happen to fall
under its purview. In effect, each OG develops its own
version of an "ontological hierarchy" (OH), designed
version of an "ontological hierarchy" (OH), designed
independently of the conceivable others to capture
independently of the conceivable others to capture
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
</pre>
==Outline==
<pre>
Inquiry Driven Systems (07 Apr 2003)
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 : Allegro Aperto
1.3.2 Discussion of Discussion
1.3.3 Discussion of Formalization : General Topics
1.3.3.1 A Formal Charge
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
1.3.4.5 Taking Stock
1.3.4.6 The "Meta" Question
1.3.4.7 Iconic Signs
1.3.4.8 The Conflict of Interpretations
1.3.4.9 Indexical Signs
1.3.4.10 Sundry Problems
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
1.3.4.18 C'est Moi
1.3.4.19 Entr'acte
1.3.5 Discussion of Formalization : Specific Objects
1.3.5.1 The Will to Form
1.3.5.2 The Forms of Reasoning
1.3.5.3 A Fork in the Road
1.3.5.4 A Forged Bond
1.3.5.5 A Formal Account
1.3.5.6 Analogs, Icons, Models, Surrogates
1.3.5.7 Steps & Tests of Formalization
1.3.5.8 Puck, the Ref
1.3.5.9 Partial Formalizations
1.3.5.10 A Formal Utility
1.3.5.11 A Formal Aesthetic
1.3.5.12 A Formal Apology
1.3.5.13 A Formal Suspicion
1.3.5.14 The Double Aspect of Concepts
1.3.5.15 A Formal Permission
1.3.5.16 A Formal Invention
1.3.6 Recursion in Perpetuity
1.3.7 Processus, Regressus, Progressus
1.3.8 Rondeau : Tempo di Menuetto
1.3.9 Reconnaissance
1.3.9.1 The Informal Context
1.3.9.2 The Epitext
1.3.9.3 The Formative Tension
1.3.10 Recurring Themes
1.3.10.1 Preliminary Notions
1.3.10.2 Intermediary Notions
1.3.10.3 Propositions & Sentences
1.3.10.4 Empirical Types & Rational Types
1.3.10.5 Articulate Sentences
1.3.10.6 Stretching Principles
1.3.10.7 Stretching Operations
1.3.10.8 The Cactus Patch
1.3.10.9 The Cactus Language : Syntax
1.3.10.10 The Cactus Language : Stylistics
1.3.10.11 The Cactus Language : Mechanics
1.3.10.12 The Cactus Language : Semantics
1.3.10.13 Stretching Exercises
1.3.10.14 Syntactic Transformations
1.3.10.15 Derived Equivalence Relations
1.3.10.16 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
1.4.1.2 Types of 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
1.6.3.1 Agency
1.6.3.2 Abstraction
1.6.3.3 Analogy
1.6.3.4 Accuracy
1.6.3.5 Authenticity
1.6.4 Anchoring Terms in Phenomena
1.6.4.1 A Mistaken ID
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
1.6.6.2 Semantic 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, and 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, or A Problem with Authority.
1.8.2 Instrumental Objective
1.8.3 Coordination of Objectives
1.8.4 Recapitulation : Da Capo, Al Segno
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
2.3.2.1 Deduction
2.3.2.2 Induction
2.3.2.3 Abduction
2.3.3 Hybrid Types of Inference
2.3.3.1 Analogy
2.3.3.2 Inquiry
2.3.4 Details of Induction
2.3.4.1 Learning
2.3.4.2 Transfer
2.3.4.3 Testing
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.
3.1.2.6 The Epitext
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.
3.1.2.10 (7)
3.1.2.11 (6)
3.1.2.12 Recursions : Possible, Actual, Necessary
3.1.2.13 Ostensibly Recursive Texts
3.1.2.14 (3)
3.1.2.15 The Freedom of Interpretation
3.1.2.16 The Eternal Return
3.1.2.17 (1)
3.1.2.18 Information in Formation
3.1.2.19 Reflectively Indexical Texts
3.1.2.20 (4)
3.1.2.21 (5)
3.1.2.22 (6)
3.1.2.23 (7)
3.1.2.24 (8)
3.1.2.25 The Discursive Universe
3.1.2.26 (7)
3.1.2.27 (6)
3.1.2.28 (5)
3.1.2.29 (4)
3.1.2.30 (3)
3.1.2.31 (2)
3.1.2.32 (1)
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 Apparent, Occasional, & Practical Necessity
3.2.6 Approaches, Aspects, Exposures, Fronts
3.2.7 Synthetic A Priori Truths
3.2.8 Priorisms of Normative Sciences
3.2.9 Principle of Rational Action
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
4.2.1.1 Sign Relations
4.2.1.2 Types of Signs
4.2.2 The Pragmatic Theory of Inquiry
4.2.2.1 Abduction
4.2.2.2 Deduction
4.2.2.3 Induction
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
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