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BAB.REFLECTION SPIRAL
NOTE: neologies and ambiguous terms clarified in GLOSSARY
are marked "[G]".
In BAA.STRUCTURE OF MIND we defined Reflection as follows:
Faculty of "Reflection", aka "Lateral Thinking" consists of
reciprocal, two-way mapping between Imagery (or Phenomenon
#Space (PS)) and Symbolics (or Abstract #Space (AS)):
1."Symbolizing" or Mapping Patterns into Symbolic, (or
"Abstract") Entity/Relation (ER) Network structures.
2."Understanding", or regressing symbolic Structures to
Patterns of Imagery, which embody their "Meaning" and that
of their Implication Relations.
In BAA.STRUCTURE OF MIND we defined Phenomenon
as an understood Entity coupled with the Imagery Pattern
which embodies its Meaning. We may denote an Entity by a
shortcut as "Phenomenon" when it's meant as "understood".
PS Orderers , Causality and "Encompassment" are imaginary
representations of abstract Implications. In the terms
of Reflection we may say that abstract Implication may be
imagined (ie. understood) as phenomenal Causality or
Encompassment.
We prefer the term "Reflection" to "Lateral Thinking"
because "Lateral" and "Thinking" are overcharged with
traditional, often misleading denotations. "Reflection",
less overloaded, has the advantage of evoking Imagery and
Symbolics as reciprocally "reflecting" one another.
We shall see Mind's activity as incessant dynamic circle
of Reflections elongated along the time dimension into
a spiral. (Fig.1)
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Details and modes of Reflection
Structures of Fig 1 are illustrated in some detail in Fig 2.
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Comments
Considering in the ER Network a related couple of Entities,
we shall call "Aggregate" the more general one, which implies
(meaning "causes" or "encompasses") the other, the "Part".
In terms defined in the STRUCTURE OF MIND , Part is an Aspect
of its Aggregate.
Relation is represented in Fig. 2 by an arrow pointing from
Aggregate to "Part", eg. "colour" pointing to "black" and
"white".
Relation supports the function of "Inference" or "Logic"
scanning the ER Network in two directions:
1.Deduction scans it in the "Top-down", Aggregate/Part
direction. Aggregates are deductive premises of their Parts.
Top Entities have no Aggregates and are therefore deductively
(intensionally) undefined Presumptions. Deductively consistent
ER instance is a "Theory".
2.Induction scans it in the "Bottom-up", Part/Aggregate
direction. Parts are inductive premises of their Aggregates.
Inductive scan sets at Aggregates a fuzzy certainty value
in function of certainties of their Parts. Bottom Entities
have no Parts and are therefore inductively (extensionally)
undefined, unless having their certainty set by extralogical
Events aka empirical Facts. A Theory bottomed with potential
Facts is a "Model".
NOTE: fuzzy "certainty" ranging continuously from 0 to 1
replaces the binary "truth/falsity" of corrupted Boole
Algebra illegitimately dragged to Logic.
(see INTRODUCTION TO PROPOSITIONAL CALCULUS ).
Entities have 3 Modes:
1.Hypothetical Entity or "Class" represented graphically as
red.
2.Concrete Entity or "Set" represented graphically as black.
3.Factual Entity or "Fact" represented graphically as green.
Within Deductive structure all Entities are hypothetical
Classes.
Within Inductive structure an Entity may be "concretized"
and become a Set when it implies a Fact or, recurrently,
a Set.
Linguistic context
As we said in OUTLINE OF THE SECOND ENLIGHTENMENT ,
Naive Common Sense guided original Humans in their struggle
for survival. It was assisted by natural languages which
came forth and developed to express Naive View (NV) and to
support human groups in this struggle.
The principal linguistic construct supporting the NV is
the assignment expression assigning Attribute to Entity;
"[Entity] is [Attribute]", eg. "my car is green", or
"[Entity] has [Attribute]", eg. "my car has greenness".
Taken at the face value, assignment expression presents Entity
as a naive "Container of Attributes" existing "in itself",
also in their absence, as a "Ding an sich", briefly, as
a Noumenon.
Rationality starts by escaping from the linguistic enslavement
to emancipated Reflection and to phenomenal interpretation
of the assignment expression. We shall now briefly review
the phenomenal and the noumenal interpretation.
Phenomenology
-Phenomenology sees Entity merely as a structure of
Attributes, a single Attribute being already a full fledged
Entity and an Entity void of Attributes being a nonsense.
Thus, in our example "green" is on the one hand an Entity
and, on the other hand, a more inclusive Entity than "my car",
which it implies among trillions of other green Entities.
In the terms of our Model, "green" is the Aggregate of the
Part "my car". To generalize, in the ontological perspective
Aggregates are Phenomena having Parts as Aspects and in the
linguistic phenomenal perspective - Attributes implying
their Entities as Parts.
One may object that certainty of bottom Entities, having no
Parts, cannot be set inductively. However, phenomenal ER
Network defines necessarily bottom Entities as explicit or
implicit outlines of experiments having extralogical, Events
or Facts as potential Aggregates. Thus, certainty of bottom
Entities is "factual", or set deductively by Facts.
Inductive scan spreads certainties recurrently over the whole
Network, setting also certainties of top Presumptions, which
confirm or falsify them. We define factually falsifiable
Presumptions as "Axioms".
NOTE: Pre-Galilean Naive View considered Axiom as a "self-
evident Truth". It's a glaring nonsense for the contemporary
View which considers "self-evidence" and "Truth" as meaningless
empty noise, "evidence" exclusively as "factual control" and
"Axiom" as factually falsifiable founding Presumption of a
Theory. Indeed, considering the three Axioms of Geometry
(1.One parallel, 2.No parallels and 3.any greater than 1 number
of parallels, passing through a point not on a reference line),
one does not see which should be "self-evidenter" than the
others, nor why any should be "self-evident" at all.
Due to certainties spreading inductively bottom-up, Aggregate-
Phenomena are determined or "given" by their Part-Aspects.
Aspects of a Phenomenon are "Phenomenally Equivalent"
(P-Equivalent).
P-Equivalence is the fundamental fabric of the Universe
as defined by contemporary Ontology derived from the
Second Scientific Revolution of Extended Relativity.
Two examples:
-#Space[G] and Field are P-Equivalent Aspects of the
Phenomenon "Cosmos".
-Continuous wave and discrete photons are P-Equivalent
Aspects of the Phenomenon "Light".
Noumenalism
Noumenalism is based on the assignment expression taken at
the face value, considering Entity as a "Container of
Attributes" existing "in itself", also in their absence, as
a "Ding an sich", briefly, as a Noumenon. Noumenal Theory
consists exclusively of noumenal Entities. Attributes are
strictly an internal matter of Entities and don't pertain
to the ER structure. Thus, bottom Entities don't have
factual Attribute-Aggregates and are, with the whole
structure logically indeterminate. This includes of course
the top Presumptions which are purely speculative, empirically
uncontrollable "Dogma". Noumenal Theory is thus necessarily
founded in Dogma, or "dogmatic" and Noumenalism is a strict
synonym of purely speculative, irrational "Dogmatism".
Facing the irrationality of Noumenalism, Phenomenology
appears as the necessary foundation of Rationality.
Entering the Spiral
Our description of structures and faculties of Mind may give
the impression of a mandatory path: extraneous physical Event,
Sensation, (Morphogenesis), Image Pattern, (Symbolizing), ER
Network, (Understanding), Image Pattern, etc. It would be
misleading: we may enter at any component of the path and
move in any direction. Quite often we enter via an abstract
word or phrase. We may stay at the abstract side and perform
deductive or inductive inference, or we may concentrate on
the Meaning, get the involved Imagery Pattern and, perhaps,
other Patterns associated by causality or encompassment.
In the meantime we may perceive other Events and start a new
reasoning chain.
Certainty, Existence and Reality
Considering the ER variable "Certainty", one may ask "certainty
of what?". We shall answer "of Existence or of being Real".
Certainty appears as measure or Existence or, synonymously,
of Reality of a Phenomenon. Our mix of extraneous Events with
the structures and faculties of perception and inference is
in our opinion necessary and sufficient to determine human
Reality with all its facets and restrictions.
It is a more rigorous version of Einstein's idea of an Entity
being real when it's on one hand well defined and, on the
other hand, empirically confirmed.
