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PLAN OF 1 RELATIVISTIC_PHENOMENOLOGY
   1a introduction 
   1b information processing 
   1c mind and brain 
   1d mapping and modeling 
   1e causality or implication 

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1D.MAPPING AND MODELING


We have seen that Mind appears essentially as a Mapping device. Symbolic Maps are 
projected from the fundamental Territory Imagery. PS (Phenomenon #Space) or 
Imagery is mapped into AS (Abstract #Space) in Symbolics. In particular, AS
is a covariant transform of PS via specific Model's transformation. 
("Model", a rigorous type of Map is discussed below).

Imagery, the deepest, fundamental territory of conscious perception and cognition
is itself a map of some extrinsic territory, transcending human perception and 
cognition, which we consequently call "Transcendency".

Now, this Transcendency is regarded by Noumenalism as "Reality", perceptible and 
cognizable by speculations a priori. Phenomenology bans such speculations from
human Universe of Discource, considering them as neither right nor wrong, but 
empty and meaningless. 

We assert that Transcendency is beyond Cognition, that nothing can be known or 
stated about it, including its denial, as we reaffirm in the closing note of this 
essay with the help of a famous Newton's allegory.

Symbolic Maps fall into two basic types: Set Theoretical Encompass structures and 
Logical Implication structures, the latter subdivided into Theories and Models. 
Encompass structure has been presented in the previous chapter. Here we shall 
explain the transformation of Encompass to Imply Relation and the distinction 
between Theory and Model, illustrating them with the diagnostic example of Site-2:

1 diagnostics first
  2 diagnosis_1_3 oof mid
    3 syndrome_1 and mid
      4 symptom_a and last
      4 symptom_c and last
      4 symptom_f and last
    3 syndrome_3 and mid
      4 symptom_b and last
      4 symptom_g and last
      4 symptom_h and last
  2 diagnosis_2_4 oof mid
...
  2 diagnosis_3_4 oof mid
...

Terms: 
-"first" denotes Top "pure" premise or Axiom. Here we postulate that 3 illnesses
 may be diagnosticated with diagnosis_1_3, diagnosis_2_4, diagnosis_3_4. They are
 related to diagnostics with the Fuzzy Operator "oof" (one of), replacing the 
 Exact Operator "orr", (either or, exclusive or). Logical expression "diagnostics
 implies one of diagnosis... ..." is a direct transformation of the Set 
 Theoretical: "diagnostics encompasses 3 disjoint classes: diagnosis... ..." .
-"mid" denotes Theorems, premises of lower and conclusions of higher neighbors: 
 syndrome_1 implies symptoms a,c,f and is implied by diagnosis_1_3. Symptoms are 
 necessarily implied by syndromes, thus related with Logical Operator "and". Again, 
 it's a direct transformation of the Set Theoretical: "syndrome_1 encompasses the 
 union of 3 classes: symptoms a,c,f".
-"last" denotes Bottom "pure" conclusions or Predictions. They are necessarily 
 implied by the structure: such diagnosis necessarily implies such syndromes, which
 necessarily imply such symptoms. 

This deductive Implication structure is called Theory. A Logical structure is a 
Theory when its conformly derived from and reducible to a Set Theoretical one, as
in our case. The structure is logically evaluated by setting the Fuzzy variable
"Certainty" which replaces the "truth/falsity of the Exact Calculus. Evaluation
happens inductively starting with "last" Vertices which cannot be evaluated 
logically, as they have no lower neighbors to be induced from. They can only
be evaluated by Observation, like in our case the symptoms have to be Observed
and evaluated by a doctor.

A Theory bottomed by Observable Vertices will be called a Model and the Structure 
supporting it - the Cognitive Network (CN). Thus, our simple example illustrates 
the concept of Model. 

Let's note that Edges of CN are Logical Operators, so that Logic, according to 
our Phenomenology, abandons its  Noumenalistic Olympus and becomes an intrinsic 
"customized" component of Models (Site-2). 

To resume the essential characteristics of "Model": 

-Abstract #Space (AS) has to be a  covariant transform of PS via specific Model's 
 transformation. Example: Due to earth motion a star may get hidden by the sun.
 However, in PS it does not disappear, but appears to change position, to be 
 "pushed away" from the sun. This PS displacement transfers covariantly to GR's
 #Space curved by gravity, resulting in geodesics, thus light trajectories being 
 significantly curved in vicinity of significantly large masses.
-It has to admit to be structuralized as CN. 
-Its deductive Aspect or Theory has to be conformly reducible to the Encompass
 structure of ER Theory (replacement of the naive Set Theory, see CCB.ER THEORY).
-Bottom Vertices of its CN structure have to be Observable, thus supplying roots 
 for inductive verification / falsification of the Model. 
-In order to truly map the Subject/Object Dialectic of Universe, it has to be 
 based in "Subjective" Continuity and symbolize "Objective" Discreteness as its 
 Singularities. We saw in "BAA. Structure of Mind" that ** Symbolic Structures 
 get meaning only by reduction to Continuum of Imagery, which justifies our basic 
 requirement for Models to be founded in Continuum **.

Only Models, i.e. constructs satisfying above requirements, may pretend to have 
phenomenal meaning. Otherwise, they can at best represent recipes of formulas 
void of phenomenal sense.

Due to Learning Feedback, described in the preceding chapter, Models may be 
refined recursively, as maps of Imagery enriched with previous Models via 
Reflection Spiral and Feedback. We shall review in 1G APPENDIX some of the 
most important Theories and Models with respect to our criteria.

References:
Site : http://evans-experientialism.freewebspace.com/metanomskiindex.htm
Site-2: Site, "Fuzzy Inferencing".