[Paleopsych] Bitsakis: Space and Time: The Ongoing Quest

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Space and Time: The Ongoing Quest
Eftichios Bitsakis1,2
1Department of Philosophy, University of Ioannina. 2Department of
Physics, University of Athens. Received October 27, 2004
Foundations of Physics 35(1) (2005.1): 57-83

In this paper, I try to refute the Kantian a priorism. At the same time,
I try to explain the existence of an a priori concerning space and time
on the basis of contemporary neuro-physiology. This a priori is the
opposite of the a-historical a priori of Kant. Concerning space and
time, I argue that relativity concords with the philosophical thesis
that space and time are forms of existence of matter. On the basis of
this ontological principle, I support that by accepting the existence of
local absolute systems of reference, it is possible to explain some
paradoxes of special relativity and at the same time to refute the
relativism related to the theory of Einstein.

KEY WORDS: a priori; a posteriori; determinism; ether; innate ideas;
local absolute systems of reference; space; time.

The debate about space, time and matter, as old as philosophy, took a
new impetus with the creation of Newtonian physics; a second, with the
development of relativity, microphysics and modern cosmology.

The question of the nature of space and time, of the existence of the
void, of the in.nity or not of the Universe, has been-as is well
known-the object of vivid debates between Greek philosophers. For
atomists, the space is void; it is the in.nite scene of the movements of
the atoms, of the creation and the destruction of the worlds. The
Universe was also considered in.nite in the cosmologies of Anaximander,
Anaximenes and Democritus. For Aristotle, on the contrary, the void is
impossible, and the Universe is .nite with the Earth in its center.
Ptolemy, after Aristotle, came forth to elaborate a
geometric-mathematical model of a geocentric Universe, capable of giving
correct predictions, that is to say, "s..e.. ta fa.. o´µe.a". This model
has been imposed as the only true during the Middle Ages. With
Descartes, Galileo, Newton and Laplace, the questions of the space, the
time and the Universe, became one of the central problems of the
emerging science.

The main answers given today to the problem of space and time are: 1.
The realist, according to which space and time are forms of existence of
matter. 2. The positivist: space and time are concepts convenient for
the description of phenomena. For Poincar´e, to take a notorious case,
"the characteristic property of space, that of having three dimensions,
is a property of our distribution board, a property residing, so to
speak, in the human intelligence. The destruction of some of these
connections, that is to say, of these associations of ideas, would be
suf.cient to give us a different distribution board, and that might be
enough to endow space with a fourth dimension".(1) Similarly for E.
Borel, "it is convenient to use intervals, just as it is convenient to
assume that the earth is rotating and the sun is standing still (to a
.rst approximation). Moreover we must not forget that for Poincar´e
convenience is identical to scienti.c truth".(2) Hume, Mach, Poincar´e,
Wittgenstein, the multiform schools of classical and modern empiricism,
deprived the concepts of space and time of their ontic counterpart. 3.
Kant, on the contrary, was, from a certain point of view, a realist. He
accepted the existence of the things in themselves, independent of the
subject. For him, however, space and time are not forms of matter. They
are the a priori forms of intuition.

I will not try to refute the conception of positivism.(3) The case of
Kant is more delicate and intriguing. In fact Kant continues to pose
problems to contemporary epistemology. So I will try to present his
conceptions and to confront them with the ideas of Einstein. I will also
try to outline a conception which goes beyond the Kantian a priori and
at the same time beyond empiricism.

For realism (and materialism) the realist Einstein is right. Not Kant.
However, the problem is not so simple, and contemporary physics and
cosmology provided the debate with new materials and new arguments.

But before passing to Kant, we must make a brief exposition of the
conception of Newton.

1. NEWTON: THE ABSOLUTE SPACE AND TIME

Newton also was a realist. The Universe for him is an objective reality,
independent of the knowing subject. The same holds for space and time.
Matter, on the other hand, is constituted from corpuscles, moving in
space, the in.nite scene of phenomena. Forces, propagated with in.nite
velocity are the cause of phenomena (causality) and the same causes
provoke the same effects (determinism). Consequently, the foundations of
the Newtonian physics were realism, determinism and non-locality.

However, for Newton space is independent of matter: it is a form
independent of its content. Space, therefore, is de.ned independently of
the existence of matter as an absolute existence. Let us recall his
de.nition: "Absolute space, in its own, without relation to anything
external, remains always similar and immovable. Relative space, is some
movable dimension or measure of the absolute space; which our senses
determine by its position to bodies; and which is commonly taken for
immovable space".(4) The same holds for time: "Absolute time, and
mathematical time, of itself, and from its own nature, .ows equably,
without relation to anything external and by another name is called
duration".(5) Absolute motion, consequently, "is the translation of a
body from one absolute place to another, and relative motion, the
translation from one relative place to another".(6) Newton was one of
the great proponents of the mechanistic point of view.

Now arises the question: Is it possible to .nd a system of reference
immobile in absolute space, in order to verify the laws of mechanics? In
fact, according to the principle of relativity, the laws of physics are
the same for all inertial systems, that is to say, for systems in
uniform relative movement. However, do we know a system in absolute
rest, in order to de.ne the class of the privileged inertial systems
related to the absolute Euclidean-Newtonian space? Instead of absolute
places and motions- writes Newton-we use relative ones. However "it is
possible, that in the remote regions of the .xed stars, of perhaps
beyond them there may be some body absolutely at rest; but since it is
impossible to know, from the position of bodies to one another in our
regions, whether any of them do keep the same position to that remote
body, it follows that absolute rest cannot be determined from the
positions of bodies in our region".(7) It follows that since it is
impossible to .nd a body at rest in absolute space, it is also
impossible to ascertain the existence of the class of privileged
inertial systems. Consequently, we simply accept their existence.

The question of the existence of an absolute system of reference has
been examined-as well known-from another point of view, with the
formulation of the laws of electromagnetism. According to the
mechanistic interpretation of these laws, a medium is necessary for the
transmission of the electromagnetic waves. This medium, the ether, has
been identi.ed with absolute space; consequently, with the absolute
system of reference. The con.rmation of the absolute motion through the
ocean of the ether would be a con.rmation of the existence of the
absolute space, of the absolute motion, and of the existence of
privileged inertial systems. It is common knowledge that all experiments
aiming to prove absolute motion through the ether gave negative answer.

However, it is evident that ether was super.uous for the Newtonian,
corpuscular conception of light. In fact, according to Newton: "And for
rejecting such a Medium, we have the Authority of those the oldest and
most celebrated Philosophers of Greece and Phoenicia, who made a Vacuum
and Atoms and the Gravity of Atoms, the .rst Principles of their
Philosophy".(8) The Newtonian particles are moving through the vacuum
and they are attracted by massive bodies when passing in their vicinity.
This conjecture of Newton is an anticipation of one of the predictions
of general relativity, deduced from different ontological postulates.

The Newtonian universe is mechanistic: "All bodies", writes Newton,
"seem to be composed of hard particles and the impenetrability of matter
is a universal principle". The Galilean-Newtonian particle has no other
attribute than inertia. However "vis inertia is a passive Principle by
which Bodies persist in their Motion or Rest". Forces provoke motion.
Consequently, some active principles ought to be the causes of movement.
Concerning the nature of gravity, Newton was content to say: "hypotheses
non .ngo". Concerning material particles: "These particles have not only
Vis-Inertia, accompanied with such passive laws of Motion as naturally
result from that Force, but also that they are moved by certain active
principles, such as Gravity, and that which causes the fermentation and
the Cohesion of Bodies. And these active principles are not occult
qualities. They are manifest qualities; their causes only are occult".
Newton tried to overcome the rigid mechanical character of his model,
and to consider motion as an internal attribute of matter.(9) But it was
too early.

These intuitions coexist with the metaphysical-theological foundations
of the Newtonian universe: Matter is composed of particles, but matter,
is not causa sui. Particles were created by God, space is an objective
reality, and at the same time, "Sensorium Dei". Absolute time in its
turn, and forces propagated with in.nite velocity, correspond to the
omnipresence of God. The atoms of Democretian cosmology were uncreated
and eternal. The particles (atoms) of Newton were created by "God
himself in the .rst creation".(10)

The worldview of the Newtonian physics entails a radical reductionism.
The explanation of motion is problematic. Composite bodies, on the other
hand, are considered as the sum of their constituents. The existence of
the new is inconceivable in the frame of the Newtonian universe and the
reductionism was the logical outcome of the principles of Mechanics. The
linearity of its laws was another presupposition of the mechanistic
reductionism.

Laplace was the most illustrious representative of this radical
reductionism: "Nous devons envisager l'´esent de l'univers comme l'effet

etat pr`de son etat ant´´erieur et comme la cause de celui qui va
suivre. Une intelligence qui, pour un instant donn´e, conna^itrait
toutes les forces dont la ee et la situation respective des ^nature est
anim´etres qui la composent; ´ees a l'analyse, si d'ailleurs elle etait
assez vaste pour soumettre ces donn´`embrasserait dans la m^eme formule
les mouvements des plus grands corps de l'univers et ceux du plus l´eger
atome; rien ne serait incertain pour elle e seraient pr´`et l'avenir
comme le pass´esents a ses yeux".(11) Or, how the Demon of Laplace would
be able to .nd an Archimedean point, in order to grasp the Universe as a
whole? The existence of an absolute system of reference
and-consequently-of the absolute space has never been con.rmed.

On the other hand, Descartes (1596-1650) contemporary of Galileo
(1564-1641) has formulated an interesting conception for the relations
between space, time and matter. Descartes was also a realist. For him
also God had created matter and gave it the necessary quantity of
motion. But for Descartes, contrary to Democritus and to Newton, it is
impossible to conceive corporeal substance without its extension. More
than that: it is not gravity, neither duration, nor color that
constitute the nature of the body, but son extension. Descartes
identi.ed matter with space and, consequently, rejected the existence of
the void.(12) From a certain point of view, Descartes joints the
Aristotelian tradition and foreshadowed certain ideas of Einstein and
the .eld conception of matter. (This conception speci.es the unity of
space and matter, not their identity, as professed Ren´e Descartes).

The Newtonian conception of space and time has been accepted at that
time, because it was conform to intuition and also, with the Christian
conception of the Universe and, above all, because it constituted a
presupposition for the formulation of the prerelativistic physics.
However, this conception has been challenged by a philosopher, Immanuel
Kant (1724-1804), long before the formulation of the laws of
electromagnetism by James Clerk Maxwell (1831-1879).

2. SPACE AND TIME: THE A PRIORI FORMS OF INTUITION

Kant was not only a great philosopher. He was also a man of science. The
.rst to elaborate in modern times a dynamic model of the Universe.(13)
It was natural that Kant has been in.uenced by Newtonian physics and the
mechanistic conceptions of Newton (1643-1727). In particular, it was
natural that he would consider the only available at that time Euclidean
geometry as the only possible one. However, the objective of the
philosopher Kant was the refutation of classical metaphysics.
Consequently, although he accepted as valid the Euclidean geometry and,
tacitly, the mechanistic-Newtonian worldview, Kant deprived space and
time of their status of objectivity.

Kant also was a realist. For him also, knowledge begins with experience.
>From this fact, however, does not follow that all arises out of
experience. Beyond the sphere of experience, Kant accepted the existence
of a "transcendental or supersensible sphere", where experience affords
neither instruction nor guidance. In this sphere lies the investigation
of Reason. Knowledge for Kant is the knowledge of phenomena. Not of the
things in themselves.

Our knowledge relates to objects. However, it relates to them by means
of intuitions. The undetermined object of the empirical intuition is
called by Kant, phenomenon. "That which in the phenomenon corresponds to
the sensation, I term it matter". That, which entails that the content
of the phenomenon can be arranged under certain relations, is called by
Kant, form . The form must be ready a priori for them in mind.
Consequently, form can be regarded separately from sensation: we .nd in
the mind the a priori forms of intuition. Correspondingly, a pure
representation contains nothing belonging to sensation. The pure forms
of intuition, are space and time.

Space, Kant maintains, is a pure, a priori form of intuition. It
contains principles of the relations of objects prior to experience.
Consequently, space is not a form which belongs to a property of things.
It is not a conception derived from outward experiences. It is a
necessary, a priori representation, which serves for the foundation of
all external intuitions. Space, consequently, does not represent any
property of objects as things in themselves. It contains all which can
appear to us externally, but not all things, considered as things in
themselves. Thus, properties belonging to objects as things in
themselves never can be presented to us through the medium of senses.

Correspondingly, time is not an empirical conception. It is given a
priori and constitutes the universal condition of phenomena. Different
times are parts of one and the same time. This form of inward intuition
can be represented before the objects and, consequently, a priori. Time
is the subjective condition of our intuition. All phenomena are in time.
However, independently of the mind, time is nothing.

Space and time do not belong to the things. They are the a priori forms
of sensory perception, in the sense that every phenomenon is posited in
space and time. This is a fact. But this fact raises two questions:
(1) Space and time are forms of matter? The response of Kant is clear
and negative. Spatial and temporal relations are laid by the reasoning
subject in sensory perception. They do not exist in the object. (2) Why
we see, etc., in a three-dimensional space? Kant has not posed this
question. Finally, accepting that space and time are the a priori forms
of intuition entails that the only possible geometry is the Euclidean.
This a-historical conception has been refuted-as we shall see-by modern
science.

Space and time have a certain absolute character for Kant. This fact
recalls the absolute space and time of the Newtonian Physics. However,
as we have noted, space and time for Newton are objective "realities".
The .rst is "Sensorium Dei". The second corresponds to the omnipresence
of the Creator. For Kant, on the contrary, they are "simply" the a
priori forms of intuition.

Space and time are, according to Kant, two sources of knowledge, from
which various a priori synthetic propositions can be drawn. It follows
that "geometry is a science which determines the properties of space
synthetically and yet, a priori". Our representation of space, Kant
maintains, must be an intuition, not a mere conception; an intuition
found in the mind a priori. It is a pure, non-empirical intuition.
Geometrical principles are always apodictic, that is, united with the
consciousness of their necessity, as: "Space has only three dimensions".
Propositions of this kind cannot be empirical judgments, or conclusions
from them.

Yet, the existence of a priori knowledge is not self-evident. Thus, Kant
puts the question: "How can an external intuition anterior to objects
themselves, and in which our conception of objects can be determined a
priori, exist in human mind?" His answer is as follows: "Obviously not
otherwise than in so far as, it has its seat in the subject only, as the
formal capacity of the subjects being affected by objects, and thereby
of obtaining immediate representation, that is, intuition: Consequently,
as the form of the external sense in general". Evidently, this is not an
answer.

Geometry, Kant af.rms, is based on a priori principles. In a similar
way, the science of Natural Philosophy (Physics) contains synthetic
judgments a priori as principles. These propositions are characterized
by universality and necessity. However, the a priori concerns the form.
The content is a posteriori: it is given by experience. Let us take the
case of two concrete propositions. According to Kant, the proposition:
"In all changes of the material world the quantity of matter remains
unchanged", as well as the proposition: "in all communication of motion,
action and reaction must be always equal", are a priori, synthetic
propositions. However, the two above propositions are not a priori
synthetic. They are principles, formulated as the generalization and the
transcendence of the experience. Moreover, their status is not
identical: the .rst one is an ontological principle, while the second is
a law of physics derived from the generalization of the experience.
Consequently, it is a posteriori and not a priori synthetic. Finally,
the status of the above propositions is different, contrary to the
af.rmation of Kant.

But before passing to the criticism of Kant's conception by Einstein, we
must make some preliminary remarks.

All knowledge, Kant accepts, begins with experience. Reason without
experience is void. Yet, at the same time Kant maintains that synthetic
a priori knowledge is possible, that is to say, knowledge independent
and prior to experience. However, in what way we acquire such knowledge?
And how is it possible to justify the assertion that space and time are
a priori pure forms of intuition? Kant considered these assertions as
eternal truths. Yet, as I will try to show, the alleged a priori
knowledge is historically and socially acquired. Its incontestable
verity gives the impression that it is independent of experience and
history. In reality, as knowledge socially and historically acquired and
transmitted, it is prior and independent of the individual experience
and is imposed to individuals as absolute and a-historical truth. Space
and time, in their turn, are forms of intuition genetically-historically
determined. Consequently, it would be in principle possible to explain
our possibility to see, to hear, etc., in a three-dimensional space and
to arrange phenomena in a unique temporal succession. There is a certain
a priori in our intuition. Yet this is "simply" a possibility for a
certain form of representation, not a knowledge. Mathematics, on the
other side, does not represent pure a priori knowledge. Their
propositions are a posteriori, not a priori synthetic. They are acquired
through experience, abstraction, generalization and transcendence of the
experience. The geometrical triangle, for example, has its prototype in
the real and imperfect triangles, not in the ideal triangle of the
platonic world of ideas. The equation: a + b + c = 180 is necessarily
true in the frame of Euclidean geometry. In this sense, it is a priori.
But it is not an a priori synthetic proposition and is falsi.ed by
non-Euclidean geometries. This non-universal proposition was formulated
after a long historical period of practical experience through
generalization and abstraction of the real properties of the real
triangles. In this sense, it is an a posteriori synthetic. The ideal,
mathematical property has its counterpart in the physical reality,
contrary to the Pythagorean, Platonic and Kantian epistemology.

In an analogous way, the laws of theoretical physics are a posteriori;
not a priori synthetic. Necessity and universality are not a suf.cient
reason and proof of an a priori status. The necessity and the
universality of the laws of physics is due to the fact that they are not
formulated by induction, but via a process of abstraction,
generalization and transcendence of their experimental or observational
basis. By this way they express the ideal limit of relations existing in
nature itself, and they acquire thereby their phenomenal independence
from experience. Their alleged absolute and necessary character, on the
other hand, has been proved relative and not necessary by new
observations and the theoretical generalization of the experience (not
to speak of the ideological presuppositions of the "paradigms" of the
theoretical physics). But I will discuss these problems in the last part
of this paper.

One more question: The meaning of the term a priori is not self-evident.
For Kant, a priori means that the truth of a proposition is necessary
and universal. This may appear trivial (Example: 2 + 2 = 4). However,
Kant accepted the existence of knowledge independent of experience.
Knowledge of this kind, he says, is called a priori, contrary to the
empirical, which has its source a posteriori, that is, in experience.

What is the meaning of the expression "knowledge independent of
experience?". This expression recalls the famous problem of innate
ideas. Or, what means innate? A clear response is impossible. Leibniz,
for example, accepted the knowledge of principles independent of
experience. Innate also means the possibility to know a number of ideas
as true. However, it seems that innate for Leibniz means not actual
knowledge, but rather predispositions, inclinations, potentialities.
Similarly, for Descartes, every idea of which we have a clear and
distinct apperception is innate. At the same time Descartes supported
that the child has ideas as potentialities. Finally, the problem of the
existence of innate ideas is not clear and the debate continues even
today without a clear solution.(14)

For Kant, space and time are a priori forms of intuition. However, Kant
was against psychologism and against skepticism. Concerning the category
of causality, that he considers also as a priori, he writes: "The
concept of a cause, which expresses the necessity of an event under a
presupposed condition, would be false if it rested only an arbitrary
necessity, implanted in us, of connecting certain empirical
representations according to the rule of the causal relation. I would
not then be able to say that the affect is connected with the cause in
the object, that is to say, necessarily, but only that I am so
constituted that I cannot think this representation otherwise than as
thus connected. This is exactly what the sceptic most desires".(15) It
seems that Kant strives to attribute an objective to the a priori.
Causality for him is not innate. It is not an arbitrary subjective
necessity inscribed in our intellect. The effect is connected with the
cause, inside the object, that is to say, necessarily. Or this
"objective" relation concerns phenomena. Not things in themselves.

3. RELATIVITY: EINSTEIN AGAINST KANT

We must dispense justice to Kant. In his time only Euclidean geometry
existed. Euclidean space on the other hand, was the indisputable frame
of physics. Newton professed the existence of a space, "absolute in its
nature, without relation to anything external, always similar and
immovable". Kant transformed this objective, three-dimensional space
with its absolute, positive metric, to a subjective a priori pure form
of the intuition. In the same spirit, Newton had admitted the existence
of an absolute mathematical time, which "from its own nature .ows
equably, without relation to anything external". In accord with Newton,
Kant considered the different, local times, as part of one and the same,
universal time. However, and contrary to Newton, he conceived time as a
subjective, a priori form of the inward intuition. Consequently, Kant
transformed the categories of the mechanistic-realist ontology of
Newton, into the incomprehensible a priori forms of the so-called pure
intuition.

It is well known that the conceptual nucleus of classical mechanics is
that of the action-at-a-distance, and that its ontological premises are
expressed by the Galilean group of transformations.(16) Therefore, the
incompatibility of this group with the Maxwellian electromagnetism was
inevitable. Einstein and Minkowski demonstrated that the natural
spatio-temporal frame of electromagnetism was a quadri-dimensional
pseudo-Euclidean space. The Lorentz group ensured the invariance of the
equations of Maxwell in the frame of this spatio-temporal form, which,
contrary to Kant, presupposes the unity of space and time.

The special theory of relativity brought to light the relativity of
space and time. At the same time it revealed their intrinsic unity. The
absolute character of the four-dimensional space-time interval and the
equally absolute character of the new relativistic physical quantities
(velocity, force, acceleration, current, etc.) expressed in a tensorial
form, are incompatible with the formal conception of Kant, as well as
with the modern epistemological relativism and concord with the realist,
causal and local interpretation of relativity. General theory of
relativity in its turn, whose physical content is the theory of
gravitation of Einstein, expresses the law of gravitation in a form
invariant for all systems of references, Galilean or accelerated. This
fact expresses a generalized, stronger objectivity. At the same time
general relativity revealed the intrinsic unity of space, time, matter
and motion, "since the ten functions representing the gravitational
.eld, at the same time de.ne the metrical properties of space".(17)
Special and general relativity are incompatible with the Kantian dogma,
which presupposes the exclusive character of the Euclidean space.

Historicity of the concepts of space and time? In fact, from the
Euclidean-Newtonian absolute space and time, we passed to the
pseudo-Euclidean space of Minkowski and further to the Riemannian space
of general relativity. However, the historicity of the mathematical
spaces does not constitute an argument in favor of the epistemological
relativism, because their epistemic difference does not exclude their
dialectical compatibility, in opposition to the alleged
incommensurability which is professed by contemporary formalistic
epistemologies. In fact, as is well known, we pass from the space of
Riemann to that of Minkowski, if we consider a space practically void of
matter. And we can dissociate the space of Minkowski into two subspaces,
if we consider very slow velocities. As A. Papapetrou puts is, "the
Minkowski space is the simplest form of a Riemannian space - it is a .at
space".(18) Historicity and commensurability are incompatible with the
gnoseological relativism related to the theory of relativity.

Till now we have to do with mathematical spaces. Consequently, the
historicity of the concepts of space and time concerns the
epistemological aspect of our problem. Yet, what is the ontic status of
space and time? Is there a relation between mathematical spaces and
physical space? Is there a kind of correspondence, of morphism, between
them? And if yes, then how and when mathematics can represent physical
reality? I will try an answer to these questions in the last part of
this paper.

For the moment, let us note the objections of Einstein to the Kantian a
priorism. From a certain point of view Einstein was an empirist. As he
admits in his Autobiographical Notes: "It was Ernst Mach who, in his
Science of Mechanics, shook this dogmatic faith. This book exercised a
profound in.uence upon me in this regard, while I was a student. I see
Mach's greatness in his incorruptible skepticism and independence".
However the philosophy of Mach appeared later to Einstein, "essentially
unten-able".(19) Why? Because Einstein was a realist. Bodily objects for
him are independent of the sense impressions they generate. They have "a
real, objective existence". Subjective time, Einstein writes, leads
through the concept of bodily object and space, to objective time.
"Ahead the notions of objective time there is, however, the concept of
space, and ahead the latter we .nd the concept of bodily objects".(20)

Einstein founded his realist conception of space to the existence of
bodies, independently of being perceived. "In my opinion", he writes,
"the fact that every bodily object situated in any arbitrary manner can
be put into contact with the Bo (body of relation) this fact is the
empirical basis of our conception of space".(21) Space and time have an
empirical basis. And in spite of this, Einstein notes, one may led into
the error of believing that the concepts of space and time are a priori.
"This fatal error arose from the fact that the empirical basis on which
the axiomatic construction of Euclidean geometry rests has fallen into
oblivion".(22)

Einstein insisted on the need that the axiomatic form of the Euclidean
geometry must not conceal its empirical origin. The three dimensions of
space, in particular, and its Euclidean character are, for him, of
empirical origin.(23) In a higher level of abstraction, the general
theory of relativity demonstrated the intrinsic unity of physics and
geometry. As Paul Langevin puts it, "our physics became a geometry of
the universe".(24) And this, because of the fact that the curvature of
space, that is to say, its form, is determined, according to general
relativity, by the potentials of gravitation, that is to say, by the
distribution of the matter in space-time. In an inverse sense, one could
say that our geometry became a branch of Physics.

>From practical experience, to Euclidean absolute space and time. The
laws of electromagnetism postulated the intrinsic unity of space and
time. The relativistic theory of gravitation is formulated in the frame
of a Riemannian geometry, and postulated the intrinsic unity of space,
time, movement and matter. These abstract geometries contradict the
Kantian dogma. At the same time they are not abstract forms. They are
forms corresponding to concrete physical content. Our intellect
transcended the limits of the immediate intuition, and created forms
having no counterpart in our representation. Minkowski and Riemann
demonstrated that Euclidian geometry was not the only possible one.
Relativity postulated the intrinsic unity of form and content. All these
are incompatible with the Kantian "pure forms of the intuition".

Einstein opposed his realist conception to that of Kant. One cannot take
seriously, according to him, the tentative of Kant to deny the
objectivity of space.(25) Einstein maintained that the non-Euclidean
geometries constituted a fatal blow to the conception of Kant. For him
the physical notion of space, as originally used by Physics, is tied to
the existence of rigid bodies. However, as we have noted, according to
Einstein, one may easily led to the error that the notions of space and
time, the origin of which has been forgotten, are necessary and
unalterable accompaniments to our thinking. "This error may constitute a
serious danger for science".(26) Kant, Einstein notes, was misled by the
erroneous opinion- dif.cult to avoid in his time-that Euclidean geometry
is necessary to thinking and offers assured (i.e. not dependent upon
sensory experience) knowledge, concerning the objects of the "external
perception". From this error, Einstein notes, Kant concluded "the
existence of synthetic judgments a priori, which are produced by the
reason alone, and which, consequently, can lay claim to absolute
validity".(27) Finally, Einstein remarked that his attitude is distinct
from that of Kant, by the fact that he does not conceive the categories
"as unalterable (conditioned by the nature of understanding) but as (in
the logical sense) free contentions".(28)

4. EINSTEIN: IN SEARCH OF A REALIST INTERPRETATION

Einstein against Kant. At the same time (but not always) against
conventionalism. Nevertheless, Einstein changed many times his
conceptions about space and ether.

As is well known, Maxwell considered that the electromagnetic waves were
propagated through ether. Lorentz also, in his theory of electron,
accepted the existence of the ether. From another point of view, .nally,
Mach considered as necessary the concept of ether in order to explain
the action-at-a-distance. Einstein, on the contrary, in a letter to
Mileva Maric six years before the formulation of relativity, considered
that it was "impossible to attribute any sense" to the concept of
ether.(29)

Ether has been identi.ed with the absolute frame of reference. But the
experience demonstrated the impossibility to detect the movement of the
earth through this "medium". Einstein rejected this notion, together
with the concept of the absolute, Newtonian space.

In fact, Einstein writes in his paper of 1905: "Maxwell electrodynamics,
when applied to moving bodies leads to asymmetries, which do not appear
to be inherent in the phenomena. The unsuccessful attempts to discover
any motion of the earth relatively to the "light medium" suggest that
the phenomena of electrodynamics as well as of mechanics possess no
properties corresponding to the idea of absolute rest. [ ...].The
introduction of the "luminiferous ether" will prove to be super.uous
inasmuch as the view here to be developed will not require an absolutely
stationary space, provided with special properties".(30)

At this moment, Einstein did not rejected the existence of space,
although his relative character has been a consequence of special
relativity. Three years later (1908), H. Minkowski formulated the
geometric frame of relativity. In his paper Minkowski writes: "The views
of space and time which I wish to lay before you have sprung from the
soil of experimental physics and therein lies their strength. They are
radical. Henceforth space by itself, and time by itself are doomed to
fade into mere shadows, and only a kind of union of the two will
preserve an independent reality".(31)

Space and time intervals are relative. They depend on the velocity of
the system. But this fact does not necessarily imply that space by
itself and time by itself are mere shadows. It is reasonable to af.rm
that space and time are forms of existence of matter, objective forms
determined, as general relativity has shown, by the distribution of the
matter. The objectivity of the space and the time is also ascertained
from the formal point of view. In fact it is possible to dissociate the
space-time into two subspaces: the three-dimensional space and the
unidimensional time. The theory of Einstein demonstrated the relativity
of these notions. At the same time the concept of the absolute
quadri-dimensional space-time interval, is the dialectical unity of
different realities. This unity represents a new absolute, preserving
"an independent reality".

However, some years later, Einstein rejected space and time not only as
a privileged frame of reference but as objective forms of matter: In a
letter to E. Mach (1913) he writes: "For me it is absurd to attribute
physical properties to space". Three years later he maintained that "the
requirement of general covariance, takes away form space and time the
last remnant of physical objectivity." According to L. Kostro, "it can
be proved that in the period from 1913 to 1916, Einstein did not believe
in the existence of physical space endowed with real physical
properties. However, Einstein was not satis.ed with the denial of the
absolute space in special relativity".(32) But the objectivity of space
and time does not necessarily presuppose that they are endowed with
physical properties. As Aristotle af.rmed space is not an object.

According to general relativity (1916), space and time constitute a
four-dimensional manifold, whose form is determined by the gravitational
potentials, that is to say, by the distribution of the matter. The
postulated unity of space, time and matter, is a strong argument in
favor of their objective existence. In particular, of the objective
existence of space.

For pre relativistic physics, ether was a medium .lling the Newtonian
space. Relativity contradicts this hypothesis. However, Einstein
considered later that one cannot simply reject ether. He wrote at that
time (1920): "More careful re.ection teaches us that the special theory
of relativity does not compel us to deny ether [ ...].But on the other
hand, there is weighty argument to be adduced in favor of the ether
hypothesis. To deny ether is ultimately to assume that empty space has
no physical qualities whatever. Space is endowed with physical
qualities. Therefore, there exists an ether".(33) According to Einstein
(1919): Once again "empty" space appears endowed with physical
properties, i.e. no longer as physical empty, as seems to be the case
according to special relativity. As L. Kostro notes, in a sense, one can
maintain that the ether is resurrected in the general theory of
relativity though in a more sublimated form.(34)

However, one can object: Why an ether? According to general relativity,
we have to do with material .elds not simply .lling the vacuum, but
intrinsically related to space. More than that. The electromagnetic
waves (or photons) are moving through space as independent realities. In
consequence, they do not need any medium-any king of ether-for their
transmission. From this point of view also, it is more correct to speak
of space endowed with physical properties, than of ether. And instead of
speaking of an ocean of ether, it is more realistic to speak of material
.elds intrinsically related to space. This ocean constitutes a
sub-quantum level from which material particles emerge, passing from
potentiality to actuality. There is today empirical evidence in favor of
this hypothesis.

In a discussion with Lorentz (1916), Einstein identi.ed the
gravitational potential with the ether: "I agree with you that the
general theory of relativity is closer to the ether hypothesis than the
special theory. This new ether hypothesis, however, would not violate
the principle of relativity, because the state of this gµ. = ether,
would not be that of a rigid body in an independent state of motion, but
every state of the motion would be a function of position, determined
through material processes".(35) That which determines the form of the
space-time continuum and the state of motion is matter, in all its
forms: the totality of massif particles, electromagnetic and
gravitational .elds. Consequently: why to use the word ether?

Electromagnetism considered .eld as something .lling the space. In
general relativity, on the contrary, .elds determine the structure of
the space-time manifold and, in consequence, constitute a unity of
differents (of space and matter). However, Einstein identi.ed the ether
with the physical .elds. It is true, as Kostro notes, that he never
considered ether as something in space. He always identi.ed it with
physical space. In this way he wrote to Lorentz (1919) that with the
word ether he meant nothing else than that space has to be viewed as a
carrier of physical properties. In another case (1934) he maintained
that physical space and ether are only different terms of the same
thing. That .elds are physical states of the space. But if .elds are
physical states of the space, then, why an ether? Also four years later,
Einstein supported that we may use the word ether, but only to express
the physical properties of the space. However, the material .elds
determine the physical properties of the space. Consequently, ether
becomes once more super.uous. It is reasonable to af.rm, once more, that
what exists is matter and its forms of existence: space and time.

Yet, Einstein says essentially the same thing, by using always the
concept of ether. As L. Kostro notes, the ether constitutes a material
medium but in another sense. It is material in the sense in which we
attribute materiality to a .eld. Material .elds determine the form of
the space. However, Einstein arrived to af.rm (1930) that space is the
primary and matter the secondary element, opinion which contradicts his,
in general realistic, epis-temology.(36)

5. THE RELATIVE, THE OBJECTIVE AND THE ABSOLUTE: IN SEARCH OF LOCAL
ABSOLUTE SYSTEMS OF REFERENCE

Galilean transformations presuppose and at the same time imply the
absolute character of the Newtonian space and time. Vacuum is an in.nite
"recipient", scene of the existence and the movement of matter. The
quadri dimensional space-time of special relativity is also absolute,
from a certain point of view: his pseudo-Euclidean metric is independent
of matter. The unity of space and time, as is expressed by the
space-time interval, is a unity of different and is absolute. But the
new absolute is intrinsically related with the electromagnetic .eld,
which does not simply .lls the space. Electromagnetic .eld (or photons)
has a real existence, independent of its sources. Consequently, as I
have argued, no "medium" is necessary for its transmission. Yet, some
writers assert the opposite. Harr´e, for example, writes, that "if as
Einstein symmetry argument suggests, there is no ether, then, there is
no material mechanism for the propagation of light".(37) A. Martin and
C. Roy Keys, also support that by eliminating the physical basis for the
transmission of wave phenomena (the ether) special relativity created an
impossible situation: physics needs anew the action-at-a-distance.(38)
However, photons do not need any medium to be transmitted.

The intrinsic unity of space and matter is not evident in the frame of
the special relativity. In general relativity, on the contrary, the form
of the space-time is determined by matter, in all its forms: massive
particles and .elds (electromagnetic and gravitational). This fact
determines the status of objectivity of the theory of general
relativity. According to Vl. Fock, this theory is a chrono-geometrical
theory of gravitation, and at the same time a theory of space and time.
The physical relativity, Fock notes, is not general, and the general
relativity is not physical.(39) Movement, according to general
relativity, is determined by the curvature of the space-time, that is to
say, by the distribution of the matter. Massive particles and .elds
create their own gravitational .elds. Consequently, in general
relativity becomes manifest the unity of differents: of space, time and
matter. The material .elds are transmitted as relatively autonomous
entities through space. Once more ether becomes super.uous. According to
certain authors, on the other hand, the ether is equated with space, a
space which acts as a medium for physical processes.(40) However, one
can maintain that space is not identi.ed neither with ether, nor with
matter. It is their form of existence. Particles of quantum level, as
well as particles emerging from a subquantum level, are moving through
space as relatively autonomous entities.(41)

The general covariance of the laws of physics under the Lorentz
transformations, that is to say, the fact that these laws are
independent of the frame of reference, inertial or not, is an expression
of their objectivity and, in consequence, of the objectivity of the
totality which is the unity of different: of the space, the time and the
matter in all its forms: massive particles plus .elds. In spite of this
"stronger objectivity" relativity and its special version in particular,
nourished a current of gnoseological relativism. To take an example: The
prevailing point of view is that, contrary to the hope of Newton, it is
impossible to distinguish which of two uniformly moving systems is at
rest.

As J. S. Bell notes, since it is experimentally impossible to say which
of two uniformly moving systems is really at rest, Einstein declared
that "the notions "really resting" and "really moving" are
meaningless"(42). Yet, this symmetry, from the kinematic point of view,
excludes the possibility to determine a locally "absolute" frame of
reference, relative to which is moving the particle? Is it impossible to
destroy the relativistic symmetry by taking into consideration the
dynamical aspect of the phenomena?

Let us quote the point of view of Paul Langevin, concerning the
production and the transmission of electromagnetic waves: "Every change
of velocity, every acceleration has an absolute sense. In
electromagnetic theory, in particular, it is a fundamental point that
every change of velocity, every acceleration of an electrical centre, is
accompanied by the emission of a wave which is propagated with the
velocity of light and the existence of this wave has an absolute
sense".(43) The emission of an electromagnetic wave is an objective
phenomenon, due to the fact that the electric charge is accelerated in a
certain region of the space, relatively to a certain system of reference
which is locally absolute. In fact, from the simply kinematical point of
view, we can consider the Earth as immovable, or just the contrary. From
the dynamical point of view, on the contrary, it is evident that the
electric charge is accelerated and that the electromagnetic wave is
moving towards the immobile frame of reference: the Earth. In that case
it is possible to consider the Earth as a locally absolute system of
reference.

Let us take also the case of our planetary system. According to
Reichenbach, e.g., it is a matter of convention to consider the sun
fixed and the earth turning around it, or, to accept the inverse.
However, the center of gravity of our planetary system is the center of
the Sun. From the dynamical point of view, consequently, the cinematic
symmetry is broken: The Sun constitutes a locally absolute system of
reference, for the planets moving around it.

Another interesting case is that of the paradox of the twins (Paul
Langevin). The traveller rests younger than his brother on Earth. This
is an objective phenomenon. However, the paradox arises from the moment
that we accept a symmetry between the two reference systems: the Earth
and the space craft. In that case the brother on Earth will .nd, in his
turn, that he is younger than his brother on the spacecraft. The paradox
disappears from the moment we accept an asymmetry between the two frames
of reference: the space-craft is moving and the earth constitutes a
local absolute system of reference. The kinematic symmetry is broken, in
favor of the real factual asymmetry of the two reference systems.(44) A
different resolution of the paradox is cited by M.A. Tonnelat: the
acceleration of the space-craft at the beginning and the end of the
journey permits the non-reciprocal character of the phenomenon.(45) Yet,
it is possible to realize practically instantaneous accelerations, and
to have a long journey, in order to be possible to apply in good
approximation the laws of special relativity. The above resolution of
the paradox of twins is valid also for the case of clocks.

Finally, let us take now the well known case of muons, which enter in
the atmosphere with a velocity similar to that of light. With a lifetime
of the order of 2.2 × 10-6 s they must make a trajectory of the order of
600 m. However, the observed trajectory is of the order of some
kilometers.(46) It is possible to explain this phenomenon by the fact
that muons are travelling through the space towards the earth, which
constitutes a local absolute frame of reference. The kinematic symmetry
is once more broken. Muons are travelling through the objective space,
in a locally approximately immobile frame of reference, and the increase
of their lifetime is a real, objective phenomenon.(47)

To conclude: We have accepted the violation of the kinematic symmetry of
the special relativity, and the existence of local absolute frames of
reference. The existence of local absolute systems of reference,
contradicts the ontological relativism based on the kinematic symmetry
of the two Galilean systems. At the same time it demonstrates the
objectivity of the related phenomena. Finally, it concords with the
philosophical postulate that space is the form of existence of
matter-form intrinsically related with its content.(48)

6. BEYOND EMPIRICISM AND NAIVE REALISM

Science works with abstractions: From the singular and the speci.c, to
the general and the abstract. With an opposite movement, from the
abstract-general, to the concrete and the speci.c. The special theory of
relativity makes abstraction of the unity of space and matter. The
relativity of the space and time intervals has been sometimes conceived
as the negation of their existence. In this spirit, Einstein in a letter
to M. Schlick (1915) asserted that space and time loose the last remnant
of physical reality. I have noticed that Einstein changed many times his
ideas about space. And it is a curious and interesting fact that the
positivist Schlick helped the realist Einstein to recognize the real
existence of space and time, endowed with physical properties, which are
expressed by the components gµ. of the material tensor g, that is to say
by its material "content", source of gravitational potentials.(49)

In the same period, Paul Langevin emphasized the unity of space and
matter, of physics and geometry: "In the natural geometry of Einstein,
which governs the spatial properties of matter, the laws of the geometry
are dependent of the totality of the matter present in the Universe [ .
. .]. Our physics became a geometry of the universe [ . . .]. What
Riemann had already sensed, it is that one cannot consider geometry as
independent of physics".(50)

The unity of space and matter, and consequently, the objectivity of
space, is today more manifest in the cosmological, as well as in the
microphysical level. Today many phenomena suggest the existence of a
subquantum level, an ocean of unobservable matter. From this ocean are
emerging particles passing from potentiality to actuality. Let us recall
the prediction of the existence of the e+ by Dirac, the phenomenon Lamb-
Retherford, the participation of the vacuum in certain microphysical
phenomena, etc. It seems that the formal antithesis between the void and
plenum, the antithesis between Democritus and Newton from one side, and
Aristotle and Descartes from the other, became today obsolete. The
concept of .eld constitutes the overstepping of the opposition: the
particle is now considered as an excitation or a singularity of the
.eld.(51)

Cosmology, on the other hand, has demonstrated the historical character
of the forms of matter. Cosmogenesis is a process of creation and
destruction of forms. More than that: The steady state universe
presupposes, as is well known, the creation of new matter. The
quasi-stationary model of Burbidge, Narlikar, and Hoyle permits the
creation of matter and the variation of the baryonic number. According
to Arp, also, the more general solutions of the general theory of
relativity permit the creation of matter in every region of the
universe. It seems that the emergence of forms of matter from a deeper
level of existence has already strong theoretical and observational
support. According to Halton Arp: "The creation of matter is no longer
some kind of obscure miracle but we can actually measure the state of
the matter from its radiation properties at various stages of evolution
[···]. The general connection between age and redshift becomes natural
and we can hope to trace the materialization of matter from the quantum
mechanical .eld (or natural vacuum)".(52) The above facts and
conjectures are arguments in favor of the realist epistemology which
postulates the intrinsic unity of space and matter.

7. BEYOND KANTIAN A PRIORISM AND BEYOND EMPIRICISM

Now concerning space and time. Kant makes a clear distinction between a
priori and a posteriori synthetic judgments. From generalization of
experience, he says, there can be derived synthetic judgments a
posteriori. These judgments are neither necessary, nor universal. But
the propositions of theoretical sciences, i.e. mathematics and
theoretical physics, do not stem from experience: they are not a
posteriori synthetic. They are pre-empirical, grounded in the
pre-empirical forms of the intuitions and the pre-empirical categories
of the understanding. The revolutions of physics and the creation of
non-Euclidean geometries are the concrete refutation of the Kantian
dogma. In particular, the existence of a priori synthetic propositions.

Now concerning space and time. Einstein rejected the a priori character
of the space, the time and the categories. Yet, was Kant completely
wrong? And if not, how to explain that our intuition is limited to the
three-dimensional Euclidean space and that we conceive time as
universal?

Empiricism rejects the existence of the a priori synthetic knowledge.
However, the problem is not to reject Kant. It is to go beyond his
philosophy and at the same time beyond empiricism.

Let us recall the question of Kant: "How can an external intuition,
anterior to objects themselves, and in which our capacities of objects
can be determined a priori, exist in human mind? Obviously not otherwise
than in so far as it has its seat in the subject only, as the formal
capacity of the subjects being affected by objects, and thereby of
obtaining immediate representation, that is, intuition".(53) It is
evident that Kant does not give an answer to his question. However, his
question can constitute the starting point for an explanation of the a
priori character on our intuition.

Kant admits "the formal capacity of the subject's being affected by
objects". How this is possible? And why we see objects in a
three-dimen-sional Euclidean space? And this possibility is compatible
with the a-his-torical and incomprehensible a priori of Kant?

According to Kant, space and time are pure forms ready a priori in mind.
I will argue that it is possible to reject this unjusti.ed a priori and
at the same time to understand our possibility to see, to hear, etc, in
a three-dimensional Euclidean frame. In fact, Biology and Physics give
us the necessary elements in order to try to give an answer. Let us take
the case of the eye-of-vision. In the inferior animals, the cells
sensible to light were distributed on the surface of the organism. The
photosensibility of these animals was therefore diffused. The .rst
animals having photosensitive cells concentrated in the cephalic
extremity were the worms. With the evolution of the species, these cells
took the form of a plate. This permitted already the orientation of the
animal to the light. In a more developed phase, these plates constituted
an internal photosensitive cavity of spherical form, permitting the
perception of the movement of the objects.(54) More generally, our sense
organs were developed during the long period of phylogenesis, via the
interaction of the organisms with their environment and, in particular,
via the reception of physical signals: light, sons, chemical molecules.
During this period were constituted structures and forms of interaction,
that made possible the perception, the representation and the
orientation of the organism-its survivance. However, why we see and
locate objects in a three-dimensional Euclidean space?

Electromagnetic waves are propagated in space. Then, if we accept the
relativistic conception, according to which out space is locally
Euclidean, then it is in principle possible to understand why we see
objects as existing in a three-dimensional Euclidean space: Kant
postulates the a priori character of space and time. To date it is
possible to explain this fact and at the same time to refuse the Kantian
dogma concerning the uniqueness of the Euclidean space as well as his
thesis that space and time are not forms of existence of matter.

The structure and the function of our sense organs and of our brain were
developed in an a locally Euclidean space in interaction with our
environment. The evolution of our brain was determined later by the
practical relations with nature, the work and the whole of the social
life. From the simple excitation, the stimulus, the sensory-motor
activity and the representation, and by generalization of the empirical
knowledge, we acquired the possibility to use rudimentary symbolic
languages (gestures, cries, etc). Finally, the use of concepts and the
emergence of conceptual thinking. Our scienti.c concepts have an
empirical origin. At the same time they transcend the immediate
intuition.

Consequently there is an a priori concerning our intuition. This a
priori, however, is radically different from the a-historic and
incomprehensible a priori of the Kantian theory of knowledge. This a
priori does not presuppose the existence of knowledge anterior to
experience. It simply means that we have an a priori possibility to see,
to hear, etc, in a three-dimensional space. Consequently, space and time
are not the subjective, a priori forms of intuition. Intuition, on the
contrary, presupposes the existence of space and time. On this
ontological premise it is possible to explain our a priori possibility,
presupposition of the intuition. This conception is incompatible with
the Kantian one and with the conventionalism of Mach, Poincar´e, etc.

Accordingly, Euclidean geometry is not based simply on a priori
principles. It is a science of empirical origin and its axioms are the
outcome of a long process of abstraction and generalization. Euclidean
geometry has its origin in the everyday practice of the farmers and
artisans. The straight line of the Euclidean geometry, for example, is
the ideal limit of the approximately straight lines of the everyday
practice. The same is true for the planes, the cubes or the triangles.
Consequently, the three-dimen-sional Euclidean geometry presupposes an
abstraction from the real physical space, considered as void of matter.
The evident truth of the axioms of the geometry and their universality
and necessity, are not the proof of an abstract a priori. More than
that. These axioms are necessary and universal only in the frame of this
geometry. They are not compatible with other, non-Euclidean geometries.
Finally the distinction between pure geometry and the geometry of
physical space is not absolute. The so called pure geometry is an
abstraction from the real properties of the bodily objects.

We see objects in a three-dimensional space. Let us try now to imagine
the four-dimensional space of Minkowski. This is impossible. Why?
Because intuition cannot go beyond this a priori restriction. From this
point of view, it seems that Kant is right. This conception of the a
priori, however, is radically different from the Kantian one.

Our intuition has this restraint possibility. However, we can think
about things in the absence of things. Our reason is liberated from the
restrictions of the senses, and can create abstract theories having not
a visual counterpart; non-Euclidean geometries in particular.

Let us recall once more the arguments of Kant. The laws of Physics are,
according to the German philosopher, a priori synthetic propositions.
"The Science of Natural Philosophy (Physics)", he writes, "contains in
itself synthetical judgments a priori, as principles. I shall adduce two
propositions. For instance, the proposition: "In all changes of natural
world the quantity of matter remains unchanged" or that "in all
communications of motion, action and reaction must always be equal". In
both of these, not only the necessity, and therefore their origin a
priori is clear, but also that are synthetic propositions(55)".

Three remarks on this subject: 1. The principle of the conservation of
matter is not a law of Physics. It is an ontological postulate. Because
matter is not a concept. It is an ontological category and for that
reason there exists not a measure of matter. Consequently, its alleged
conservation is impossible to be proved or refuted.(56) This, .nally, is
not a synthetic proposition. It is an ontological postulate and its
logical status is to be discussed. 2. The necessary character of a
proposition, as that of the equality of action and reaction, is not a
proof of its a priori synthetic character. This proposition is a
posteriori synthetic, formulated via the generalization of empirical
data. 3. Consequently, Kant confuses an ontological postulate with a law
of physics. 4. More generally, the laws of theoretical physics are not a
priori synthetic propositions. They are theoretical propositions a
posteriori synthetic, generalizing and transcending their empirical
basis and, because of that, formulated axiomatically and not by
induction. The historicity of these laws, on the other hand, is an
argument against the a-historical necessity and universality attributed
to them by Kant.

Space and time are, according to Kant, the a priori forms of intuition.
In an analogous way, the categories (causality, etc) are conditions of
the possibility of experience, and are therefore valid a priori, for all
objects of experience.(57) They are conceptions which prescribe laws a
priori to phenomena, consequently to nature itself as the complex of all
phenomena.

The Kantian conception of causality as an a priori category of reason,
on the other hand, contradicts the agnostic argument of Hume. In fact,
it is impossible to establish the validity of a causal law by induction.
>From this point of view, Hume is right. However, the problem is not a
problem of induction. The validity of a causal law presupposes the
knowledge of the internal and necessary processes determining the
creation of the new. Consequently, the category of causality is a
priori, in the sense that it is a necessary and universal law of nature.
Not an a priori, category of reason. Reason, in that case, formulates a
category, corresponding to physical reality, and the causal laws of
physics, as not a priori synthetic.

Causality etc. are, Kant maintains, the a priori categories of Reason.
However, categories are also historical from the gnoseological point of
view, because they represent the generalization and transcendence of
human experience. The idea of causality, for example, was for the .rst
time formulated in the frame of the animistic conception of nature. It
was embodied later in the religious conception of the world. And after
Galileo and Newton we know at least four forms of causal determination:
the mechanistic, the dynamic, the classical statistical and the
quantum-statis-tical form.(58) This social-politicismic category was
transformed by Kant into an a-historical and unexplained a priori
attribute of Reason.

Finally, concerning space and time. These concepts are also historical.
As Paul Langevin puts it, there is neither space nor time a priori.At
every phase of our theories corresponds a different conception of space
and time. Mechanics implied the ancient conception. Electromagnetism
requires a new one, and nothing permits to maintain that this new
conception will be the .nal one.(59)

The argument of Langevin concerns the concepts of space and time, that
is to say, the gnoseological aspect of the problem. These concepts are
related to different mathematical spaces and their historicity and a
posteriori character is evident. However, Kant is a philosopher and he
speaks about categories. The status of the categories is different from
that of concepts. How then is it possible to pass from the level of
concepts to that of categories? Let us accept that between the concepts
of space and time and the physical space and time there is a certain
correspondence, a certain kind of morphism. The concepts tell us
something about the real properties of space and time. How then is it
possible to pass from the domain of the scienti.c knowledge to the level
of the categories? Scientists use the words of space and time as well
de.ned scienti.c concepts. At the same time they refer to them as the
general frame of their experience and theories. The same words are used
by philosophers, as categories. One could say that in the general case,
space and time are used by scientists as quasi-philo-sophical concepts.
Because of that they assure a kind of junction between the scienti.c and
the ontological level.(60) The historical character of the concepts of
space and time and the deepening of our knowledge concerning these
concepts, determine the historical character of the categories of space
and time from the gnoseological point of view. Matter also has a history
in space and time. In fact, we know today that different forms of matter
correspond to the different phases and regions of the Universe. If,
therefore, we accept a realist epistemology, namely that space and time
are forms of existence of matter, then it would be reasonable to
maintain that space and time are historical categories from the
ontological point of view also, because of the fact that their ontic
counterpart changes, as a consequence of the evolution of the Universe.

It is possible to maintain that the Universe is in.nite in space and
time. In.nite, however, is always different and different (Aristotle).
In that case matter and its forms do not correspond to an eternal and
immovable being, but to a changing totality. Any attempt to construct a
metaphysical ontology would be, therefore obsolete.

Final question: How to explain the ef.cacy of natural sciences, if we
can know only phenomena? Not things in themselves? How phenomena are in
a certain correspondence with the inaccessible things in themselves? How
a certain kind of morphism between the laws of nature and nature itself
is possible? The objectivity of the laws of science seems paradoxical in
the light of the Kantian epistemology, because the so-called unity of
consciousness, even if exists, is not able to secure the correspondence
between the laws of science and the real laws of nature. To say that it
is possible for things in themselves to obey laws independent of our
intellect, but that phenomena are mere representations subject to no
other laws than those imposed by our reason, poses a fundamental problem
for the epistemology of Kant.(61)

Kant poses the question in the following term: "Categories are
conceptions which prescribe laws a priori to phenomena, consequently, to
nature as the complex of all phenomena. And now the question arises-in
as much as the categories do not derive from nature and do not regulate
themselves according to her as their model (for in that case they would
be empirical)- how is it conceivable that nature must regulate herself
according to them in other words, how the categories can determine a
priori the synthesis of the manifold of nature and yet not derive their
origin from her". The laws of phenomena, Kant maintains, must harmonize
with the understanding and with its a priori form. However, the laws do
not exist in phenomena any more than the phenomena exist in things in
themselves.(62)

The agnostic position is evident. At the same time Kant tries to
establish a certain correspondence, a certain morphism between phenomena
and their mental association. "The objective ground of all association
of appearances", he writes, "I entitle their af.nity.Itisnowhereto be
found save in the principle of unity of apperception, in respect of all
knowledge which is to belong to me. According to the principle all
appearances, without exception, must so enter in mind or be apprehended,
that then conform to the unity of apperception".(63)

However, it is not the unity of consciousness which determines the unity
of apperception. It is exactly the opposite. The unity of consciousness
has an objective foundation, an objective counterpart, in nature itself.
The unity of nature is expressed in the unity of knowledge. In
particular, these exists a certain morphism between the spatial and
temporal relations established by science, and the objective relation
existing in nature.

Phenomena, Kant maintains, are only representations of things which are
utterly unknown in respect to what they are in themselves. Empiricism
con.nes itself to phenomena that it detaches from their 'fond' and
raises to the status of unique reality. Kant separates phenomena from
things in themselves pronouncing the existence of a certain substratum
of what we call physical reality, to be inaccessible to reason. However,
the history of natural sciences is, from a certain point of view, the
historical movement from phenomena to the knowledge of their internal,
genetic processes, from description to explanation. Science does not
accept the dichotomy between phenomenon and essence. A phenomenon both
brings to light and at the same time conceals deeper structures and
relations, that is to say, it manifest and conceals 'essence'. As
Heraclitus said, "hidden harmony is better than the manifest one" and
Democritus professed that phenomena are the visible of the unknown.

Spatial and temporal relations, Kant maintains, are laid by the
reasoning subject in sensory perception. They do not exist in the
object. This is an agnostic thesis, and constitutes an epistemological
obstacle for science.

The thesis that space and time are forms of existence of matter, on the
contrary, functions as an epistemological catalyst for a more profound
understanding the relations between matter and its spatio-temporal
attributes.

ACKNOWLEDGMENTS

Professor Franco Selleri is not only an eminent physicist. He is, at the
same time, one of the protagonists in the debate concerning the
foundations of Relativity and Quantum Mechanics. My modest contribution
is the expression of great esteem and friendship.
It is also a pleasure to thank Professor C. Antonopoulos for fruitful
discussions and valuable comments on the manuscript.

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5. Newton, Ibid, p. 6.

6. Newton, Ibid, p. 7.

7. Newton, Ibid, p. 68.

8. Newton, Opticks (Dover, New York, 1952), p. 369.

9. Newton, Ibid, pp. 369-401.

10. Newton, Ibid, op. passim.

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15. The	above are r´esum´efromthe Critique of Pure Reason, transl.
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28. A. Einstein, Ibid, p. 674.

29. See, M. Barone, in Open Questions in Relativistic Physics, F.
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30. A. Einstein, in The Principle of Relativity, op. cit. p. 37.

31. H. Minkowski, Ibid. p. 75.

32. L. Kostro,	in Frontiers of Fundamental Physics, M. Barone and F.
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33. L. Kostro, Ibid.

34. Cited by L. Kostro, in Open Questions in Relativistic Physics, op.
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35. Cited by L. Kostro,	Ibid. p. 135. For a general discussion, see: L.
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36. For these problems see also the papers published in	Frontiers of
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43. P. Langevin, La physique depuis vingt ans (Doin, Paris, 1923).

44. For	a similar interpretation, cf, Tr. Morris, in Frontiers of
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47. See also: E. Bitsakis, La Nature dans la Pens´ee Dialectique
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48. For the problem of space-time, synchronization, dilatation,
equivalent versions to special relativity, see, J. Chezniewki, in
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(Plenum, New York, 1994), p. 217; F. Selleri, Ibid, p. 181; H. E.
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F. Selleri, Nuovo Cimento B.; See also: F. Selleri, "Theories,
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49. Cited by L. Kostro, in Open Questions in Relativistic Physics, op.
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50. P. Langevin, La Relativit´e, pp. 14-15 (Hermann, Paris, 1932).

51. See: E. Bitsakis, Physique et Mat´erialisme, op. cit. passim.

52. See: H. Arp, in Frontiers of Fundamental Physics, op. cit.; Id. In
Open Questions in Relativistic Physics, op. cit.; Id., Phys. Essays 8,
350 (1995); H. Bondy, Cosmology (Cambridge University Press, Cambridge,
1960); F. Hoyle, in Science et Vie, 189, 1984.

53. E. Kant, Critique of Pure Reason, op. cit. p. 25.

54. A. Leontiev, Le d´eveloppement du psychisme,p.18(Editions Sociales,
Paris, 1976).

55. E. Kant, Critique of Pure Reason, op. cit., p. 11.

56. E. Bitsakis, Physique et Mat´erialisme, op. cit. chap. 4.

57. E. Kant, Critique of Pure Reason, op. cit., pp. 98-99.

58. E. Bitsakis, Le Nouveau R´ealisme Scienti.que, op. cit.; Id. Sci.
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´
59. P. Langevin, La Pens´ee et l'Action (Editions Sociales, Paris,
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60. E. Bitsakis, La Nature dans la pens´ee dialectique, Introduction,
op. cit.

61. E. Bitsakis, Sci. Soc., 51, 389 (1987).

62. E. Kant, Critique of Pure Reason, op. cit., pp. 99-100.

63. E. Kant, Critique of Pure Reason, (MacMillan, London, 1928), A122.