(11) We next take up the discussion on the operational characteristics of the meta-topical element of topic intersection operator. Consider some ethnosemanticgeometric correspondences (see Notes on the Dialectics of Ethnosemantics.] The operation of intersecting lines inside a geometric figure, which is accomplished by inter-connecting the vertices, is resolved into a determined set of constitutive fragments, these being geometric figures themselves. Thus, the quadrangle resolves into four triangles:
There is an exact relationship between the quadrangular domain [1, 2, 3, 4] and the four constitutive triangles in that the area bounded by the quadrangle is identical to the sum of the areas bounded jointly by the four triangles. This is given in the following expression:
(1, 2 ,3 ,4) = [l, 2, 5J + [1, 4, 5] + (2 ,5 ,3) + [3 ,4 ,5]
Thus, computing the area by either of these two operations yields the same value. The two operations for resolving the area bounded by the four points are therefore functionally equivalent.
Note now that a pre-condition for achieving the equivalence between the two operations is the labeling of the intersected point (5). Labeling inter-sections is a mathematical operation that involves the specification of the topological features of the defined arrangements of points. In a topological manifold defined by two-dimensional figures continuously connected (the definition that fits Euclidean or Plane Geometry), the operation of labeling intersections resolves into naming or identifying a point.
In Ethnosemantics, the topological manifold is defined as an ethnosemantic outline. Ethnosemantic outlines are topological arrangements of topic domains. These topic domains thus correspond to topological fields or spaces whose empirically derived dimensionality and interconnectivity characterize exactly the notion of ethnic group or ethnicity. Labeling intersections in ethnosemantic outlines amounts to the operation topic fragmentation. Topic fragmentation re-solves into labeled topical constituents called deictic topic nominals. These are fixed in form and number and correspond to the labels of geometric figures. Deictic topic nominals are natural entities whose defined constitutive structure, like a mathematical postulate system or geometry, characterizes ethnic membership (or more formally, affiliative structure, or universe of sets, or etc.). For instance, the constitutive structure of the deictic topic nominal "American", as derivable through the combinatorial analysis of its paraphrastic equivalence set of neologic topic nominals, would characterize the ethnicity or membership affiliative structure of an informant. Thus:
| (Original Deictic Topic Nominal: American) Paraphrastic Equivalence Set of Neologic Topic Nominals | |
|---|---|
| Informant A | Informant B |
| A man A courageous man The symbol of civilized progress Democratic process A powerful nationality etc. |
A man An arrogant man The most warmongering epithet Imperialistic expansion A dangerous nationality etc. |
It is clear that there exists an exact relationship between deictic topic nominals (as a fixed, closed set) and their derived paraphrastic equivalents in the form of an open set of neologic topic nominals. This correspondence defines the manifold of display repertoire (i.e. ethnic affiliative structure) and, consequently, the paraphrastic equivalence set of neologic topic nominals. The resolution of paraphrastic equivalencies through the operation of membership specified meta-topical elements and operations will now be discussed.
[15] Consider the topic nominal, "I am basking in the air of delightful studies." Its constituent meta-topical elements and intersecting operators can be listed as follows:
| Anchor Concepts | Topic Intersection Operators |
|---|---|
| I am [be] bask air delight study |
[to] -ing in; the of; -ful -ies |
There is an exact relationship between the defined constitutive structure of anchor concepts and that of topic intersection operators which specifies their topological interconnectivity. A dictionary is an arbitrary alphabetical exhaustive arrangement of deictic topic nominals. Dictionaries also provide paraphrastic neological topic nominals in the specialized form of "the definition" (-- which is an independent argument or paragraph). Ethnosemantic Glossaries are empirically derived exhaustive arrangements of deictic topic nominals together with paraphrastic neologic topic nominals.
The Operation of intersection of an anchor concept by a topic inter-section operator allows the derivation of the minimal topic nominal (as dis-cussed earlier). The minimal topic nominal corresponds to the intersected figure in geometry. Thus, the quadrangle -- or quadrangular arrangement of four anchor points -- resolves into four constituent triangles -- or four triangular arrangements of three anchor points, two of which are old and one new). Consider what happens in the derivation of the set of topic nominals accomplished by intersecting the six anchor concepts through topical inflection:
| Original Anchor Concepts | Intersected Anchor Concepts Minimal Topic Nominals |
|---|---|
| I | I am; I who; given that I; I alone; me; without me; etc. |
| am | I am; am I; am belatedly; am engaging; etc. |
| bask | basking; basked; to bask; have been basking |
| air | the air; in the air; above the air; without air; air-aplenty; etc. |
| delight | delightful; without delight; plenty of delight; etc. |
| study | studies; delightful studies; tiring studies; studies that inform; etc. |
It is clear that the number of minimal topic nominals that can be derived through intersection is indeterminate. The branch of contemporary linguistics called "generative transformational grammar" concerns in itself centrally with the procedures for the exact derivation of topic nominals through the various intersection operations (called transformations and re-write rules). However, thus far, linguistics has concerned itself with sentences and their derivative utterances, rather than with situated topic nominals (viz. those derivable by ethnosemantic reference to glossary rather than dictionary). I is worth noting here that linguists have traditionally excluded the bulk of encyclopedic knowledge in an ethnic group from their re-write rule operations. One of the apparently compelling rationales given for this is that encyclopedic knowledge correspondences to an open set, hence cannot form the basis of a grammar (which is a finite set of re-write rules).
And, indeed, we have seen above that the number of derivable minimal topic nominals is indeterminately large (these correspond to the ethnic knowledge that the linguist excludes from the finite set of grammar rules). Therefore, the grammars linguists define are in independent of topicalization dynamics in situated talk. For the analysis of the latter, it is necessary to work with a different set of postulates, such that the natural character of openness of topic nominal sets is not a criterion of exclusion. Such a postulate system, viz., one that deals centrally with topic as a natural phenomenon, is called an ethnosemantic system. Thus, linguistics and ethnosemantics are different postulate systems in a series whose other members include the various geometries of manifold or conceptual universes.
Postulate systems are varied on pragmatic grounds. Thus, the postulate system of Euclidean Geometry is used in engineering for drafting. The postulate system of generative linguistics is as yet undefined in totality though it has stable characteristics that have been used in applied linguistics to derive rationales for language teaching materials. The N-Dimensional topological geometries are defined postulate systems whose derivations are used in common industrial applications. The postulate system of ethnosemantics (called ESNOSYS --see Notes on Ethnosemantics) allows the derivation of topic glossaries which are used in the characterization of cultural behavior.
[[[section]] 16.] 'We have been discussing the meta-topical elements of topic intersection operator, and the various problems that might be involved in the projected analysis of topic fragmentation. The discussion has dealt with the need for
developing a formal rationale for dealing with open sets of topic fragments, this being the natural constitutive character of the phenomenon of topicalization dynamics. We now present such a rationale by introducing the notion function of topic or topic function.
The function of topic nominals is expressed by the situated assertion or comment. Situated assertions are display resolutions to contention points (i.e. they are remedies, transactionally ) that arise in exchanges of situated discourse. Situated assertions belong to a pragmatic set. In other words, though they are derivationally productive (i.e., leading to open classes of nominals), they are arbitrarily contracted. The analysis of the structure and dynamics of contracted pragmatic sets of situated assertions is called transactional engineering and will be discussed fully in connection with the nature of constitutive exchanges (see Notes on Constitutive Exchanges).
It is seen now the way in which we propose to specify a formal rationale for the derivation of topic glossaries, namely, in terms of topic focus contraction operations that are functionally contingent upon the pragmatics of situated assertions. Such an ethnosemantic manifold system is called register. Thus, The First Ethnosemantic Topic Glossary presents the pragmatics of situated assertions in the North American register. Register is the organizing derivation for argument.
To Chapter 3: Dialectics of Ethnosemantics