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The
Philosophical Test of the Revelations of Religious Experience (continued)
It was the philosopher
Berkeley who first undertook to refute the theory of matter as the unknown cause
of our sensations.7 In our own times Professor Whitehead - an eminent
mathematician and scientist - has conclusively shown that the traditional theory
of materialism is wholly untenable. It is obvious that, on the theory, colours,
sounds, etc., are subjective states only, and form no part of Nature. What enters
the eye and the ear is not colour or sound, but invisible ether waves and inaudible
air waves. Nature is not what we know her to be; our perceptions are illusions
and cannot be regarded as genuine disclosures of Nature, which, according to
the theory, is bifurcated into mental impressions, on the one hand, and the
unverifiable, imperceptible entities producing these impressions, on the other.
If physics constitutes a really coherent and genuine knowledge of perceptively
known objects, the traditional theory of matter must be rejected for the obvious
reason that it reduces the evidence of our senses, on which alone the physicist,
as observer and experimenter, must rely, to the mere impressions of the observer’s
mind. Between Nature and the observer of Nature, the theory creates a gulf which
he is compelled to bridge over by resorting to the doubtful hypothesis of an
imperceptible something, occupying an absolute space like a thing in a receptacle
and causing our sensation by some kind of impact. In the words of Professor
Whitehead, the theory reduces one-half of Nature to a ‘dream’ and
the other half to a ‘conjecture’.8 Thus physics, finding
it necessary to criticize its own foundations, has eventually found reason to
break its own idol, and the empirical attitude which appeared to necessitate
scientific materialism has finally ended in a revolt against matter. Since objects,
then, are not subjective states caused by something imperceptible called matter,
they are genuine phenomena which constitute the very substance of Nature and
which we know as they are in Nature. But the concept of matter has received
the greatest blow from the hand of Einstein - another eminent physicist, whose
discoveries have laid the foundation of a far-reaching revolution in the entire
domain of human thought. ‘The theory of Relativity by merging time into
spacetime’, says Mr. Russell,
‘has damaged the traditional
notion of substance more than all the arguments of the philosophers. Matter,
for common sense, is something which persists in time and moves in space. But
for modern relativity-physics this view is no longer tenable. A piece of matter
has become not a persistent thing with varying states, but a system of inter-related
events. The old solidity is gone, and with it the characteristics that to the
materialist made matter seem more real than fleeting thoughts.’
According to Professor
Whitehead, therefore, Nature is not a static fact situated in an a-dynamic void,
but a structure of events possessing the character of a continuous creative
flow which thought cuts up into isolated immobilities out of whose mutual relations
arise the concepts of space and time. Thus we see how modern science utters
its agreement with Berkeley’s criticism which it once regarded as an attack
on its very foundation. The scientific view of Nature as pure materiality is
associated with the Newtonian view of space as an absolute void in which things
are situated. This attitude of science has, no doubt, ensured its speedy progress;
but the bifurcation of a total experience into two opposite domains of mind
and matter has today forced it, in view of its own domestic difficulties, to
consider the problems which, in the beginning of its career, it completely ignored.
The criticism of the foundations of the mathematical sciences has fully disclosed
that the hypothesis of a pure materiality, an enduring stuff situated in an
absolute space, is unworkable. Is space an independent void in which things
are situated and which would remain intact if all things were withdrawn? The
ancient Greek philosopher Zeno approached the problem of space through the question
of movement in space. His arguments for the unreality of movement are well known
to the students of philosophy, and ever since his days the problem has persisted
in the history of thought and received the keenest attention from successive
generations of thinkers. Two of these arguments may be noted here.9
Zeno, who took space to be infinitely divisible, argued that movement in space
is impossible. Before the moving body can reach the point of its destination
it must pass through half the space intervening between the point of start and
the point of destination; and before it can pass through that half it must travel
through the half of the half, and so on to infinity. We cannot move from one
point of space to another without passing through an infinite number of points
in the intervening space. But it is impossible to pass through an infinity of
points in a finite time. He further argued that the flying arrow does not move,
because at any time during the course of its flight it is at rest in some point
of space. Thus Zeno held that movement is only a deceptive appearance and that
Reality is one and immutable. The unreality of movement means the unreality
of an independent space. Muslim thinkers of the school of al-Ash‘arādid
not believe in the infinite divisibility of space and time. With them space,
time, and motion are made up of points and instants which cannot be further
subdivided. Thus they proved the possibility of movement on the assumption that
infinitesimals do exist; for if there is a limit to the divisibility of space
and time, movement from one point of space to another point is possible in a
finite time.10 Ibn Ąazm, however, rejected the Ash‘arite notion
of infinitesimals,11 and modern mathematics has confirmed his view.
The Ash‘arite argument, therefore, cannot logically resolve the paradox
of Zeno. Of modern thinkers the French philosopher Bergson and the British mathematician
Bertrand Russell have tried to refute Zeno’s arguments from their respective
standpoints. To Bergson movement, as true change, is the fundamental Reality.
The paradox of Zeno is due to a wrong apprehension of space and time which are
regarded by Bergson only as intellectual views of movement. It is not possible
to develop here the argument of Bergson without a fuller treatment of the metaphysical
concept of life on which the whole argument is based.12 Bertrand
Russell’s argument proceeds on Cantor’s theory of mathematical continuity13
which he looks upon as one of the most important discoveries of modern mathematics.14
Zeno’s argument is obviously based on the assumption that space and time
consist of infinite number of points and instants. On this assumption it is
easy to argue that since between two points the moving body will be out of place,
motion is impossible, for there is no place for it to take place. Cantor’s
discovery shows that space and time are continuous. Between any two points in
space there is an infinite number of points, and in an infinite series no two
points are next to each other. The infinite divisibility of space and time means
the compactness of the points in the series; it does not mean that points are
mutually isolated in the sense of having a gap between one another. Russell’s
answer to Zeno, then, is as follows:
‘Zeno asks how can
you go from one position at one moment to the next position at the next moment
without in the transition being at no position at no moment? The answer is that
there is no next position to any position, no next moment to any moment because
between any two there is always another. If there were infinitesimals movement
would be impossible, but there are none. Zeno therefore is right in saying that
the arrow is at rest at every moment of its flight, wrong in inferring that
therefore it does not move, for there is a one-one correspondence in a movement
between the infinite series of positions and the infinite series of instants.
According to this doctrine, then it is possible to affirm the reality of space,
time, and movement, and yet avoid the paradox in Zeno’s arguments.’15
Thus Bertrand Russell proves
the reality of movement on the basis of Cantor’s theory of continuity.
The reality of movement means the independent reality of space and the objectivity
of Nature. But the identity of continuity and the infinite divisibility of space
is no solution of the difficulty. Assuming that there is a one-one correspondence
between the infinite multiplicity of instants in a finite interval of time and
an infinite multiplicity of points in a finite portion of space, the difficulty
arising from the divisibility remains the same. The mathematical conception
of continuity as infinite series applies not to movement regarded as an act,
but rather to the picture of movement as viewed from the outside. The act of
movement, i.e. movement as lived and not as thought, does not admit of any divisibility.
The flight of the arrow observed as a passage in space is divisible, but its
flight regarded as an act, apart from its realization in space, is one and incapable
of partition into a multiplicity. In partition lies its destruction.
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[See
Notes]
Date/Time Last Modified: 6/18/2002 8:03:04 AM
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