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PLAN OF 0.FIRST AND SECOND ENLIGHTENMENT
0a outline
FIRST ENLIGHTENMENT
0b galilean relativity and newton
0c descartes
0d aether and dogmatic thinking
SECOND ENLIGHTENMENT
0e einstein and extended relativity
0f kant and einstein
Og EPR Paradox
BACK TO SITE PLAN
0F KANT AND EINSTEIN
NOTE: neologies and ambiguous terms clarified in GLOSSARY
are marked "[G]".
Einstein's quotation:
*Concepts and Conceptual Systems get justified exclusively
by their capacity to coordinate events. They cannot be
justified in any other way. Therefore, it is, in my opinion,
one of the most pernicious acts of Philosophers to have
transferred some conceptual bases of Natural Science from
the controllable domain of empiric adequacy into inaccessible
height of the Necessary Apriori. This applies particularly
to our concepts of time and space, which the Physicists
- forced by the facts - had to descend from the Olympus
of Apriori in order to repair them and make them usable[1].*
(He meant Kant, for whom the direct perception space and time
are aprioristic, necessary and universal[2] categories.)
Actually, as we explain below, the apparently contradictory
views of Kant and Einstein are both right, only concern two
different aspects of time/space and Einstein did not reject
Philosophy altogether, but only the Dogmatism, one of
"two Philosophies":
1.olympian apriori Dogmatism,
2.empirically controllable Rationality.
Dogmatism consists of whimsical speculations a priori,
aspiring to absolute truth, and high-handedly snubs science,
know-how and, above all, facts. "If the facts disagree with
me then so much worse for the facts." - this Hegel's
declaration may serve as motto of Dogmatism. It is nothing
else than Naive View (sometimes called "Naive Realism)
dressed up in highbrow verbiage.
Rationality rests upon contemporary scientific and practical
now-how generalizing it into a critical synthesis of
contemporary knowledge. A rational Ontology, in keeping with
science, is rigorous, phenomenological and empirically
controllable.
[1] Subsequently we shall use upper case "SPACE" to designate this
repaired and usable "time and space" abstract construct, in order
to distinguish it from the "space" of the direct perception.
[2] By "universal" we mean "invariant for all observers and
referentials". We prefer it to "absolute" which is charged
with innumerable transcendental and theological implications.
REVIEW OF KANT
We shall review the pertinent ideas of Kant prior to
comparing them with Einstein's view.
Discussing Kant may follow one of two ways:
1.Learn to use his terminology inside of the Universe of
discourse of his time. Only after having accomplished that
would we be able to talk reasonably about "synthetic
judgements a priori" and their role in "transcendental logic,
or aestetic".
2.Express his Weltanschaung in contemporary terms.
We shall follow the second approach.
Any theory is for us, today, axiomatic. What would we see as
axioms and theorems of Kant's Weltanschauung?
Axiom A1: necessary and universal science exists.
Axiom A2: Science is created by inductive inference.
Axiom A3: Only a priori inference is necessary and
universal.
Axiom A4: Induction a priori requires subjective
representations a priori (categories) encompassing space and
time.
Axiom A5: Space and time are subjective representations a
priori. (According to Kant we can imagine "empty space"
without any "objects"[3] but we can only represent objects
in space. The same holds for time.)
Theorem T1, concluded from Axioms: Induction a priori is
possible, necessary and universal.
COMMENTS
A1: At Kant's epoch the First Scientific Revolution had
culminated in Newton's Model, whose rules and concepts were
considered as exact, necessary and universal. Even the 19th
century mechanistic Physics claimed those qualities. Only
the Einstanian Second Scientific Revolution turned to consider
science as fuzzy, relative and restricted, making A1
unacceptable for us.
A2: We nearly agree with it: for us the inductive inference
"verifies" rather than "creates" science.
A3,A4,T1: We accept now only induction a posteriori.
A5: Kant's main objective was to create the
"Transcendental Logic" with induction a priori in its
center. For this purpose A5 was a necessary addition
to A1. Yet, "Empty space" and "objects in space" are
clearly illusions of the "Naive View" (aka "Naive
Realism"). We had to wait for the Extended Relativity
to see the "empty space" abolished and replaced with
P_Equivalence of SPACE and Field. [4]
Transcendental Logic: Kant tried to create what
appears to us as a "prototype" of Propositional
Calculus. He failed due to missing mathematical and
logical tools, mainly the Boole Algebra.
He considered only statements, or, as we would say
"operands", but neglected the operators. His 'Logic"
was in fact just a classification of statements:
-Statements analytical a priori which we would call
deductive,
-Statements synthetical a posteriori which we would
call inductive,
-Statements synthetical a priori supposed to support
the induction a priori, unacceptable for us.
COMPARISON
They are both right, talking however about two different
things: Kant about Event Domain or Imagery and Einstein
about Abstract Symbolism.
Imagery is unique per observer and Theory independent.
Now, a Subject perceives indeed events of his Imagery
exactly as described by Kant: ordered by unique values
of space and time. Mapping this Imagery directly into
a naive Symbolism we obtain a 4 dimensional SPACE
whose time component is affine with respect to the 3D
space sub-SPACE. Time and space have no common measure,
thus the space/time SPACE is affine.
Consequently, scalar product, angle and rotation in planes
x,t are undefined. Transformations are thus limited to
translations, i.e. to Galilean Transformations, or additive
speed cumulation. This direct mapping may be naive,
but it supported Newton's Model, perhaps the greatest
intellectual achievement of all times, which stays till now
a rigorous approximation, adequate for most of mechanics
including space travel.
Kant-Newton affine space/time SPACE could accommodate low
speed mechanics, but not the invariance of C nor the
subluminal phenomena. Einstein's genial idea was to create
a 4D SPACE whose all 4 components have a common measure:
3 space dimensions and one LightTime (not time!!!), Ct
dimension having distance measure. Now, all these distance
dimensions can be structured into metrics: Minkowski metric
for SR, Lobatschevski and Riemann metrics for GR.
[3] The term "object" does not exist in Physics. In the
metalanguage it is multivalued and charged with noxious
metaphysical connotations. We use it here in order not to
diverge too far from Kant's terminology, as synonym
of "event".
[4] Phenomenal Equivalence (P-Equivalence):
Association of Aspects of a Phenomenon (Field Density
and SPACE curvature are P-Equivalent Aspects of the
Phenomenon "Cosmos"). P-Equivalence is often confused
with Causality. Its customary to say that "Field
curves SPACE", which is false, as they are both
"equally ranked" Aspects of a Phenomenon, coexisting
but not causing one another.
Similarly, continuous Field wave and discrete photons
are P-Equivalent Aspects of the Phenomenon "Light".
APPENDIX Newton's and Kant's Paradoxes
Newton's Paradoxes
-First Paradox: Gravity attraction intervenes between such
remote bodies as sun and earth which appears as Action at
Distance violating the basic Mechanistic dogma of "billiard
balls" acting locally on one another.
-Second Paradox: Gravity attraction is determined by space
(distance), but does not affect it in any way, which
violates the Reciprocity Principle (Action / Reaction).
Newton was perfectly aware of the Paradoxes which clearly
called into question the Noumenalistic dogma of absolute
space and its Mechanistic fabric of "billiard balls".
Questioned about them he refused to be dragged into
metaphysical speculations and answered with his famous
"Hypotheses non fingo", implying that Science coordinates
empiric data into consistent, predictable and verifiable
Models, but refrains from explaining them in terms of
Transcendency.
(Closer to us, Dirac repeated it in similar situation with
coarser terms: "Shut up and compute".)
The Paradoxes were solved by Einstein's Relativity replacing
Mechanistic dogma with the Phenomenal concept of Field and
its P-Equivalence with SPACE, both expanding at invariant
speed C as a continuous propagation of Local impulses.
Einstein rated the solution of Newton's Paradoxes as his
topmost achievement, because he admired Newton and considered
him as his Master.
We find it rather diverting that Newton's First Paradox may
be seen in inverted order. His Gravity apparently acting at
distance, in fact anticipated (extended) Locality by the
implication of continuous Field. On the other hand, the
pretended local action of hypothetical "billiard balls"
meant actually Action at Distance, small or rather undefined
distance of "balls" diameter, but distance anyhow.
Kant's Paradoxes
Kant has the historical merit of deriving Ontology of the
First Enlightenment from empirically verifiable Science,
rather than founding it, as it was the habit, in arbitrary,
aprioristic speculations. He derived his system from the
summit of his contemporary Science represented by Newton's
Model with additional postulate of Science being exact,
necessary and universal, thus absolute. Now, Newton's Model,
as all Physics of his time was based upon metaphysical dogma
of absolute time/space affine between time and space (lacking
a common measure) and having the fabric of "billiard balls".
These dogmatic foundations were in contradiction with Model's
physical laws. Facing it, Newton dodged the issue with his
famous "Hypotheses non fingo" implying that he restricted
himself to Physics and dismissed Philosophy.
Kant could of course not follow Newton in dismissing
Philosophy, as it was his essential dedication. Consequently,
and unlike Newton, he did endeavor to "make hypothesis", to
conceive Foundations of Science consistent with Newton's
Model. In doing so he chose the sincere, bona fide attitude
of deriving Ontology from the bedrock premise of empirically
verifiable physical Model. However, no matter how rigorous
the inference, the conclusion is only as good as the
premise: from a paradoxical Model Kant rigorously derived
a paradoxical Ontology.
1.Having rightly banned noumena (Dinge an Sich) from human
cognition, he created a Noumenalistic Ontology based on such
noumena as absolute time and space, and other absolute
categories of "Pure Reason", governing the Transcendency
from the heights of the Olympus of A Priori.
2.His Synthetic (in fact inductive) Propositions A Priori
reposed upon these aprioristic, dogmatic noumena in order
to satisfy the postulate of exact, necessary, absolute
Science.
Now, as Kant was first to admit, scientific induction stems
a posteriori from fuzzy Observations. He attempted
unsuccessfully to replace it with the Synthetic Propositions
A Priori destined but failing to prop up fuzzy Observations
with necessary and absolute categories of "Pure Reason".
