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The present chapter and especially its sections "Physical
Bodies" and "Space" is based upon Einstein's "PHYSICS AND
REALITY", which it intends to refine and to complement.
Einstein presents the natural model as interplay of sensations
and abstractions, lacking the IOO essential imagery, necessary
for memorizing, recalling and manipulating Einstein's "physical
bodies" or percepts. Einstein was mainly interested by the
physical reality and restricted the mental input to
sensations or percepts. Imagery, while supporting percepts
deals as well with abstract, emotional and recursive input,
extending the "physical reality" over the entire human
universe of discourse.
Thus extended imagery supports "mental experiments", whose
events are projections of abstract concepts, of emotions
or images brought about recursively by analogy with known
ones. Mental experiments support the main part of human
creativity. Abstract input supports pure mathematics and
- together with the recursive - natural science starting
with fundamental physics. Emotional input supports esthetics,
ethics and a good part of psychology and sociology.
We asserted in "STRUCTURES OF MIND", that sensations,
though stemming arbitrarily from unknown transcendency,
trigger ordered immanent "reality" of images and, that
mind's faculty of cognition guides us through their
labyrinth allowing to survive, to reproduce and to avoid
oncoming buses. Mind can thus be seen as a natural model
developed by evolution to enable and to support the survival
of human species.
While accepting with Einstein that "reality" is merely an
illusion, in every day life one takes it at its face value,
uses mind's natural model instinctively and leaps to the side
to avoid the bus, without cogitating about its epistemological
This instinctive attitude taking the illusion of reality at
its face value is known as "common sense". It guided original
humans in their struggle for survival directly as individuals
and socially by dint of natural languages (see the following
The first step in the setting of the physical reality is the
formation of images of "objects", or, to comply with Einstein's
terms - "physical bodies".
Out of the multitude of his event-images one takes, mentally
and arbitrarily, certain repeatedly occurring patterns of
sensations, and collects them into a secondary image
under a particular symbolic name. One attributes to this name
its originating secondary image as meaning, thus constructing
a meaningful concept of a particular "body".
It's crucial to emphasize that one intuits such secondary
constructs as unshakably certain and "real", unlike their
originating percepts affected by doubt and uncertainty and
that finally, one conceives the "physical world" as populated
SELF, SIGNS AND OTHERS
Associating a body with somatic and kinesthetic sensations
one constructs the particularly important "own body" under
some originally primitive symbolic name, which, with the
development of natural languages becomes "self".
In the wake of kinesthetic sensations one perceives particular
bodies which get associated with one's "self" as its "signs",
"expressions" or "manifestations".
Out of the multitude of his event-images one takes some, which,
while lacking somatic and kinesthetic sensations, are otherwise
homomorphic with one's own body and also, occasionally associated
with signs. One collects them under "others" and considers their
signs as expressions of their otherwise inaccessible but alleged
sensations, images and symbols.
Besides direct sensations, signs provide additional input of
the mentally constructed "reality", enlarging one's own
experience, by that of the others.
The idea of space is based on that of body defined above.
Although the body is a secondary construct of mind, one
coordinates to it unshakable intuition of continuous
"physical existence" in spite of the fact that one perceives
temporal alterations in it. We may distinguish with Poincare
two kinds of alterations of an "object": changes of
state and changes of position. The latter are alterations
which one can reverse by arbitrary motions of his own body.
That there are bodies to which one can ascribe, within a
certain sphere of perception, no alteration of state, but
only alterations of position, has fundamental importance
for the formation of the intuition of space. Let us call
them "rigid". Given a percept encompassing two rigid bodies,
some of its alterations can not be considered as changes
of position of the whole, notwithstanding that this is the
case for each one of the two constituents.
This leads to the intuition of "change of relative position"
of the two bodies and of their "relative position ".
Moreover, among the relative positions, there is one of a
specific kind which we designate as "Contact". Permanent
contact of two bodies in three or more "points" makes them
united as a quasi rigid compound body. It is permissible to
say that the second body forms a (quasi rigid) continuation
of the first body and may, in its turn, be continued quasi
rigidly. The consequence of the imaginary quasi rigid
continuation of a body B0 is the intuition of the infinite
continuum - the "space".
In Einstein's opinion, mind's faculty of putting every body
situated in any arbitrary manner into contact with the quasi
rigid continuation of a chosen body of relation B0 is the
basis of our intuition of space. In pre-scientific thinking,
the solid earth's crust plays the role of B0. The very name
geometry indicates that the idea of space is mentally
connected with the earth considered as the relation body.
We shall find the intuition of space founded by rigid bodies
at the base of Einstein's Covering Principle which requires
physical distance to be measured, also in mental experiments,
with physical rods complying with physical rules, such as
the Lorentz Contraction. The Covering Principle underlies
directly or indirectly the entire Extended Relativity.
For the first time in the history of science an ontological
principle is directly incorporated in mathematical formulation
of physical theorems.
Continuous space, its primacy and the discrete covering
measurement rods are aspects of the fundamental Dichotomy
Continuum/Discreteness (CD) defined in "TIME, AWARENESS
AND EVENTS" as the elementary structure of human Universe.
In mathematical terms geometry symbolizes the basic intuitive
image of continuous space and arithmetic - its discrete
covering measurements. The ultimate foundation of mathematics
is the continuum. Discrete concepts starting with that of
"number" are founded in continuum and symbolize its covering
measurements. Shortly, arithmetic is founded in geometry.
We shall discuss it in more detail in "FOUNDATIONS OF MATHEMATICS".
In "SET THEORY" we shall show that its failure to define during
100 years the very concept of "set" and to ascent from discrete
to continuous is due to the perverted inversion of the natural
order and to founding mathematics in the discrete.
SPACE-TIME and GENERALIZED COVERING PRINCIPLE
We have introduced in "TIME, AWARENESS AND EVENTS" the
eventtual time as indications or ticks of a "clock," i.e.
as recurrences of a periodical event.
Clocks disretize intuitive time as "physical rods" discretize
intuitive space, which allows to formulate the Generalized
EVENTS DISCRETIZE INTUITIVE TIME AND SPACE INTO EVENTTUAL
PERIODS AND DISTANCES.
Associating each point of the intuitive space with a clock
we construct intuitive Space-Time continuum accessible via
rod/clock discretized eventtual bulks. We shall call this
continuum "SPACE", capitalized in order to distinguish it
from its "space" components.
The above described SPACE is structured as the CD (Continuum/
Discreteness) dichotomy, whose intuitive continuous term is
unveiled and locally concretized by discrete percepts acting
as covering rods and clocks.
This passive and static construct is complemented with the
active, dynamic counterpart "Field" set up by such percepts
as force, movement, inertia (resistance to force), action at
distance (terrestrial, magnetic or electric attraction, the
latter originally by amber - "electron" in Greek), sensing
heat of remote sources, etc.
Field and SPACE are conceptually represented by differential
vector calculus. The fact that gravitational, electric etc.
field appears only in presence of corresponding "masses",
which, in turn exist only within their fields, leads to the
principle that apparent "masses" are nothing else than places
of non-disappearing divergency of their associated fields.
INTUITIVE CAUSALITY AND LOGIC
In "STRUCTURES OF MIND" we asserted that sensations trigger
ordered "physical reality" of images and that mind's faculty
of (re)cognition guides us through their labyrinth.
"Physical bodies" have been constructed by collecting some
repeatedly occurring patterns of sensations into
secondary images, apparently more "real" than their
Similarly, one selects some pattern of event-images
apparently always followed by another one and under names
respectively "cause"/"effect" collects them into the
secondary image under the symbolic name "causality".
Like in the case of "physical body", one attributes to
this secondary construct "causality" the unshakable "physical
reality" and certainty, unlike to its "cause/effect" instances.
And, having constructed the "physical world" by populating it
with "physical bodies", one orders it with the principal
A particular type of Reflection ("STRUCTURES OF MIND"), which
we shall call "Inference", maps events ordered by causality
into symbolic structures of expressions related "deductively"
by Implication, shortly "ER structures". Inverse operation
regresses "inductively" expressions to their territory of
Due to intuiting causality as unshakably "real", deduction
appears as "necessary" or "certain".
Induction, on the contrary, retrieving the originating events
of symbolic expressions, gets affected by their uncertainty
and fuzziness (see "FUZZINESS" below).
Causality maps to the primary logical operator "implication".
Other subordinated orderers order particular patterns of
causes and effects. Let's mention a few, with their logical
negation (not), conjunction (and), causal equivalence (or),
"one of" selecting a unique event out of a cause pattern,
becoming "exclusive or" for two-event patterns.
It has to be emphasized that there is an illimited,
innumerable amount of secondary orderers symbolized as
Common sense taking the illusory "reality" at its face value,
considers the intuitive causality/logic as an evident rule
of practical behavior, applying it instinctively to the
day-to-day practice. One knows intuitively that hitting a nail
with a hammer will drive it into the wall and that standing
in the way of the oncoming bus will cause not a little misery.
In the social praxis people tending to stand in the way of
oncoming buses are isolated in lunatic asylums with others
who cast similar doubts on causality and logic.
However, extended over intellection, the common sense unveils
the prejudices it has gathered through the daily practice,
and rigorous rationality starts by overcoming it. We shall
present a rigorous view of causality in the chapter
"CAUSALITY AND IMPLICATION".
The natural faculty of inferring, also called "Logical
Reflection" or "Logic" is rather inefficient, due to mind's
restricted capacity of simultaneously recalling numerous
expressions and executing numerous operations.
Humans attempt to enhance their limited natural capacities by
creating tools. Thus hammer enhances the striking capacity of
human hand and extrinsic logic enhances the limited capacity
of human intrinsic, natural inference. Being an enhancement
of the natural faculty, extrinsic logical systems may only be
justified by extending and simulating the ER structures of
the natural Logic, by accounting for the illimited number of
logical operators as well as for the fuzziness of the
Extrinsic purely deductive logical systems will be called
"Theories" and complete, deductive-inductive ones - "Models".
Extrinsic ERN (Expression-Relation-Network) logic rigorously
extending the ER structures of the natural Logic is presented
in the chapter "ERN LOGIC".
TRANSCENDENCY AND IMMANENCY
In "STRUCTURES OF MIND" we saw that "reality" defined as all
what's experiential, is entirely mental and immanent,
encompassed by sensations and by percepts of Imagery.
However, Sensorium maps Imagery as a map of some hypothetical
territory - "Transcendency". And, Imagery appearing as an
ordered reality, temptation arises to regress it to its
transcendental territory and to posit thus called forth
transcendency as the "real world out there". Yet, no matter
how tenacious and persistent this temptation may be, the
transcendental "reality" of regressed mental constructs
is nothing, but a "transcendental illusion".
We saw above that one attributes to the secondary constructs,
viz. "physical bodies" a more unshakable "reality" than to
the percepts which gave rise to them and that finally, one
constructs the "physical world" by populating it with them.
We are now in position to precise it further:
One may give in to the temptation and fall prey to the
transcendental illusion by regressing mental secondary
constructs - the "physical bodies" to "real objects"
of transcendency. To use the fashionable philosophical term,
the transcendental illusion is tantamount to reification.
Once reified, the transcendental "real object" maintains
the illusory speculative reality independently of its
originating percepts and sensations, as a "container"
which may, but does not have to contain them i.e. functions
as autonomous "thing in itself" aka "noumenon".
Contrariwise, the bodies of imagery are indissociable from
their originating percepts and sensations, i.e.
function as phenomena.
We may conclude:
IMMANENCY IF PHENOMENAL AND TRANSCENDENCY - NOUMENAL.
The transcendental illusion applies also to logic. The
transcendental "world out there" being populated with
noumenal "real objects", their interrelations and associations
with "contained" sensations fall into the province of
the reified, noumenal, absolute logic.
While the ER structures of the immanent logic represent the
relative causal order of events, the transcendental logic
posits absolute structures of transcendental "real objects"
related by the reified "deterministic" causality.
All imagery constructs are affected by fuzziness stemming
from two principal sources:
1.Time approximation by discrete tick intervals of involved
clocks ("TIME, AWARENESS AND EVENTS").
2.Arbitrariness of bodies constructed by collecting similar
patterns of sensations. It affects, of course, the
bodies themselves, via bodies - the space, and, together
with time - the space-time.
The general, ontological fuzziness of the physical reality
should not be confused with particular uncertainty cases
stemming from detectors affecting the detected, from
statistic procedures, or from singularity areas of continua.
The Natural Model described in the present chapter represents
our view - based upon that of Einstein - of mental processes
constructing the "Physical Reality", such as underlies the
physical theories. It's a purely factual description, in no
way attempting to judge the Natural Model, which would be
tantamount to judging gravity. The Natural Model is not based
upon any established philosophical system and eventual
similitude with some of them would be coincidental.