| Table of Contents |
|---|
|
Unity Duality Trigram Quadrangle Pentagram Hexagram Septuple Octant Ennead To the bottom |
Click here to see the table. Synopses of Chapters
Chapter 1: Unity.
In the system of logic known as geometry, the "point" is the primary componential unit. All geometric spaces are defined by an enclosing boundary or perimeter. The shape of the boundary determines the dimensionality of the space. "Shape" refers to ''configuration of points," hence the point becomes the primary componential unit for all configurations or geometric shapes.In philosophical investigations, unity emerges as a holistic entity, sometimes called "the monad" (e.g., by Leibniz). In the physical and chemical sciences, the holistic unit or monad appears as the "elementary particle." Note that unity implies "discreetness" of particles, whether in the form of atomic or sub-atomic units, or in the form of a label name, title, or code. Thus, the discreet units of discourse in human thought and speech are visible performatively as words or groups or words which we call "orthographs." In any speech community, there is a "pool" of standard orthographs which individuals use and share by virtue of their membership in a community. These standard orthographs form an inventory of available expressions, names, or titles. thus, the ethnosemantic function of "form" is served by the availability of enculturation units held in common by a cultural group, society, or community.
In philosophy, the instantiation of the level of structure is
expressed through the idea of
"duality"
and its derivative, "dialectics." In human speech and thought,
duality manifests itself as "the
dialectics of relationship" which we shall refer to as
"association." When two points are related to
each other through a dialectic association, what might be
referred to as "assertion." An assertion
is thus a structural level phenomenon and translates as the
joining in relationship, of minimally
two
points. When two points are thus joined, they form an
adjacency-pair which manifests a tension
sustained by the line of association. This shard tension will be
called a "contention point."
With three points, the structural configuration yields either
an open figure ("angle") or a close
figure ("triangle"). When the open figure or angle is of a
determinate number, i.e., 900 or a
"right-angle", the structural configuration becomes a ''field
location" known as "the Cartesian
system of
coordinates." Thus, all graph functions and mathematical
expressions derive from the structural
field properties of the coordinate system. Here we can observe
such topological properties as
localization, rank of value, proportionality, and
relative position. The idea of "oppositeness" is another
derivative of the structural level,
namely,
two points joined by a line (or three, points forming a 180
angle). Oppositeness establishes such
further derivative phenomena as "polarity" (positive/negative),
"bi-modality"
(member/not-member), "contrast" (same/different), "aspect" (same
facet/other facet),
"qualification"
(better/worse; more/less), and others.
In discourse (i.e., thought or speech), the concatenation of
form units into structures is
usually
known as the phenomenon of "syntax" (grammar). Thus, standard
orthographs, expression, or
labels, known in linguistics as "morphophonemic units," are
concatenated by the speaker (or
thinker) into structural configurations, which in the minimum
case, is the assertion.
Chapter 2: Duality
In the system of
logic of geometry, the
first level of unity transforms into the second level of
"structure" which comes about minimally through the association
of two points (a "line"). A line
formed by two points now becomes the simplest structural unit.
Adding a third point complicates
the structural configuration but does not alter the level of
structure. No matter how many points
are included in a configuration, the notion of structure remains
the only significant descriptor.
Chapter 3: Trigram.
Level 1, "FORM" metamorphoses into "STRUCTURE" at level 2, which
in turn metamorphoses
into "FUNCTION" at level 3. This third jump establishes the
(FORM/STRUCTURE/FUNCTION) compound which we've named "trigram."
In geometry, the
structural configurations at level 2 yield a horizontal expansion
series as represented by
two-dimensional figures of N sides (e.g., point, line, or angle,
triangle, quadrangle, pentagon,
hexagon,
etc. to the N-sided polygons). The vertical jump from level 2 to
level 3 is accomplished through
the addition of third, fourth, and subsequent dimensions (as in
the cube, the tenerac, and other
multi-dimensional manifolds).
In philosophy, the third level of "function" is discusses as the "dialectic resolution" of contention points manifesting as a new local system. For example, the structural combination of parents as (Father + Mother) yields a dialectic contention point at level 2 which resolves itself at level 3 as children. New the local system (Father + Mother children) raises the level of an assertion to that of a "concept."
"Concepts are therefore third level reifications defining a local semantic field and are always "trigrammatic" since they embody three morphogenetic components (form/structure/ function). In discourse, the forms here, am, and I, are structured into an assertion by various possible configurations (e.g., "I am." and "Am I?"). At this level, the assertion compound lacks functional differentiation or "meaning." Function is added when the structure is elevated through a vertical dimension by the addition of the localizer, here. Now, (I am here.) or (Am I here?) is a trigrammatic component: it survives as an independent or integrated functional field. This is known as a "concept.
Chapter 4: Ouadrangle.
The establishment of function at the third level completes the first ring of ethnosemantic morphotopology. This first ring is called "the light trigram" (levels 1, 2, 3) and contrasts with the second ring (levels 4, 5, 6) which is known as "the dark trigram." Between the two rings is a space bounded by a "double line. n This boundary or inter-face will be defined its significance discusses in the sixth chapter on "hexagrams." The jump from levels 3 to 4 is thus not equivalent to the other level switches which are simplex metamorphoses.The Euclidian geometric analogy is no longer applicable to the morphogenetic evolution beyond the third level. The double line separates inanimate and animate systems.
In other words, while the behavior of points in a space or graph is fully exhausted through the first three levels, the behavior of organisms includes these at the lower level, but then goes on to higher level not attained by inanimate entities.
The first of these higher levels is level 4 symbolized by the expansion of the quadrangular system. Here a particular technique we've evolved serves to define the character of this expansion. Begin with four concepts (level 3) arranged at the points of a rectangle or square. Now the four concepts form a local system which they define by titling the four corners: A, B, C, D. Take each of the six dyadic pairs (AB, AC, BD, etc.) one at a time as adjacency-pairs forming a contention point (level 2) and arrive at a resolution through triangulation (see Chapter 3). Title each of the six resolutions. These six titles now are called "conceptualizations." Each of the six conceptualizations is now defined in terms of its own co-ordinate system, the sides of which has associated with it, (i) a domain title ("conceptualization"); (ii) a title for the horizontal and the vertical lines of the coordinate system; and (iii) a name for each of the octants on the ES-coordinates. At this point, having started with four concepts, then having defined six conceptualizations constructed into two coordinate lines having eight directional octants, we've generated a semantic domain containing 6 x 2 x 8 or 96 conceptual elements. The final step consists of constructing an 8 x 8 matrix obtained when the octants of one conceptualization are aligned against the octants of another conceptualization. With six conceptualizations, we can derive 12 dyadic octant matrices. These will contain 12 x 64 or 768 new titles. Thus the total number of conceptual elements defining the quadrangular expansion is 96 + 768 or, 864. We call this procedure the "ethnosemantic probe technique," or "ES-Probe." the conceptual domain constructed with this technique yields a "semantic chart" which we call an ethnosemantic "glossary."
ES-glossaries or glossary-parts constitute a hierarchical semantic system of a fixed mathematical order and geometric shape. The interconnections between the points on the chart are graphic values for what is otherwise known as "argument" in logic and formal theorems. In other words, the argument made in some organized stretch of discourse is to be defined as the connectivity of the elements in the glossary chart. Hence, all discourse derives its argument from the shape of the glossary chart. Hence, all discourse derives its argument from the shape of the glossary in whose domain that stretch of discourse belongs. Argument is thus a fourth-level derivative corresponding to the ethnosemantic value of medium. We can say that names (Form/Level 1) connect into assertions (Structure/Level 2) to yield concepts (Function/Level 3) which are then interconnected through a reference chart (glossary) to create a "medium" for discourse, i.e., argument (Medium/Level 4).
Chapter 5: Pentagram
.
When the medium of argument is constrained by a particular frame,
the fifth level is reached. We
call this the "transactional" level since its constitutive
elements are determined by the rules
governing the ritual exchanges of two or more individuals who are
coparticipants in a social
episode. The minimal transactional system consists of five
interconnected steps, forming a
pentagram. We may illustrate this by using one of Goffman's
examples of "remedial
interchanges":
(i) Deed: A approaches B
(ii) Remedy: A: "Can I sue the phone?"
(iii) Relief: B: "Sure, go ahead."
(iv) Appreciation: A: "That's very good of you."
(v) Minimization: B: "It's okay. n All complex transactions are derivable from this minimal five-step unit.
Chapter 6: Hexagram
.
The sixth level manifests itself under the ethnosemantic function
of "appearance." It also
establishes the second ring, or "dark trigram." The morphogenetic
movement from Form (Level
1) to Appearance (Level 5) completes the hexagrammatic system.
The hexagram is thus an
ordered semantic series that sufficiently defines all the stages
of a social act, i.e., it is a formal
specification of human behavior known as communicative acts. We
might say that human
communication (oral, written, and in thought) comprises six
morphogenetic phases, in this order:
(i) standard names, expressions, and titles (Level 1: form);
(ii) syntactic collocations of these into assertions, two at a time (Level 2: Structure);
(iii) dialectic resolution of assertions into concepts (Level 3: Function);
(iv) interconnectivity of concepts through a reference chart and defining argument (Level 4: Medium);
(v) constriction of argument into a ritually specified procedure of exchange (Level 5: frame):
(vi) visible manifestation of framed argument as a presentational display (Level 6: Appearance).the sixth phase of "appearance" may be taken as an "index" of events. In other words, appearances are "indications" of events as for example, a gesture or utterance is taken as an indication of a person's behavior.
Hexagrams are the genes of intellect. They combine with each other in units of two (the "double hexagram") and eight (the "electric couple"). These genes form the basis for subsequent levels of discourse phenomena such as topicalization (Level 7), thematic domains (Level 8), and biographic accounts (Level 9).
Chapter 7: Septuple
.
Level 7 introduces "morphotopology" that is, the forms of topic.
The six pre-topical phases
(Levels 1-6) achieve a level of behavior that characterizes the
community life of prehuman
societies. The six pre-topical levels of communicative acts
culminate in the indexical function it
displays during social transactions. Territoriality exchanges
among the birds in an aviary
demonstrate that a bird's particular situated display, has an
indexical function. For example, an
unattached adult female parakeet is chased from the general
region around occupied nest boxes.
If
the aviary is narrow (say three feet or less), the single female
will be prevented from any physical
contact with the mothers when the latter are in the public areas.
However, if a chicken wire
barrier is erected between the two walls, the single female and a
mother will occupy adjacent
positions on the wire barrier and through the holes would
exchange close physical
contact
("beaking",eyeballing", and "synchronized twitching"). This
phenomenon shows that the
exchanges among the birds are not merely transactional (as in the
ordinary territoriality behavior
of chasing the other away --level 5). The chicken wire
"barrier" is not merely a physical
barrier
since under different circumstances a bird can be observed to
continue chasing successfully
another bird directly on the other side of a chicken wire barrier
(up to dislodging the opponent
from contact with the barrier). Therefore, the barrier in this
case, has an indexical
function -- it
indicates a new, novel situation for the transactants, a new
event in their relationship and
behavioral milieu; in effect, a new ritual comes into being.
Yet this sixth level of communicative exchange is locked to the stage of "appearance." The chicken wire barrier is a necessary emblem; its proximal visibility is necessary for the advent of the new ritual. Many human interactions similarly operate at the level where indicative emblems (called "access rituals") are necessary components of the exchange. However, some do not.
The ascension of humans to the seventh level of communicative exchange is manifested most visibly in the phenomena of literacy (oral, written, and in thought). Literacy encompasses the third ring (Levels 7, 8, 9), the first stage of which is seen in the phenomenon of topic or topicalization.
Topicalization rests on the ethnosemantic function of predication. This may be defined as a situated comment, i.e., a verbal statement made by a person and referring to something in particular. Topicalization is a two-channeled information device. It contains content units separated by frame units. For example, an utterance contains reference and intonation; a sentence or paragraph contains words and punctuation marks. The magic number "7" (plus or minus 2) represents the information limits of human processing. All coding and recoding systems reach their highest application at level 7.
Chapter 8: Octant
.
The referential function in topicalization achieved at level 7 is
non-reflexive. Children can easily
predicate, refer, and topicalize, but they have difficulty with
the thematic significance of topics.
Their topicalization is associative, conceptual, and
transactional, i.e., they model
paradigmatically
on adult behavior. But, when it comes to making a speech or
writing a composition, they act
"lost" and inept. They are unable to sustain thinking at the
eighth level. This is because they lack
a
sufficiently developed "metalanguage" which serves adults to
"annotate" events, i.e., to realize
their acts at level 8 by taking into account thematic cycles and
their natural evolution in
relationship. "Annotations" are footnotes to others communicative
acts and operate according to
standard interpretation rules. These shared ways of annotating
and keeping track are called
"reciprocally ratified recognitions" (or "RRR"s). They form the
basis of the generational
character
of communities "traditions," "mores").
Chapter 9: Ennead
.
The third ring culminates in the highest form of literacy at
level 9 thinking, namely "biography. "
This may be defined as the integrating or unifying phenomenon of
self-consciousness.
The
possibility of biography rests on what we may call the "ordinary
social competence" of people.
Biography gives a justifying context or "rationale" for the
coherent evolution of personality. The
phenomenon of personality are already manifest in the second ring
(level 4, 5, 6) but they are not
fully elaborated even at the stages of referential predication
(level 7) and annotation (level 8)
since
there is lacking an organizing device for accumulating their
effects. Biographic channels are
provided for the individual as "sociomaps" to locate oneself on
(e.g., reputation, age, stature in
the community, seniority). Using these cognitive/normative maps,
the individual keeps
track of the
self's progression in time. These shared accounting methods are
called "community
cataloguing-practices" (or "CCP"s).
To account for these phenomena of biography and ordinary social competence of humans a minimal and sufficient model of the order of 9 is needed. The enneadic model of social competence is such an attempt and consists of three rings identified as Territoriality, Variability, and Biography.
