The traditional conception of cause and effect is one which modern
science shows to be fundamentally erroneous, and requiring to be
replaced by a quite different notion, that of LAWS OF CHANGE. In the
traditional conception, a particular event A caused a particular event
B, and by this it was implied that, given any event B, some earlier
event A could be discovered which had a relation to it, such that--
(1) Whenever A occurred, it was followed by B;
(2) In this sequence, there was something "necessary," not a mere de
facto occurrence of A first and then B.
The second point is illustrated by the old discussion as to whether
it can be said that day causes night, on the ground that day is always
followed by night. The orthodox answer was that day could not be called
the cause of night, because it would not be followed by night if the
earth's rotation were to cease, or rather to grow so slow that one
complete rotation would take a year. A cause, it was held, must be such
that under no conceivable circumstances could it fail to be followed by
its effect.
As a matter of fact, such sequences as were sought by believers in the
traditional form of causation have not so far been found in nature.
Everything in nature is apparently in a state of continuous change,* so
that what we call one "event" turns out to be really a process. If this
event is to cause another event, the two will have to be contiguous in
time; for if there is any interval between them, something may happen
during that interval to prevent the expected effect. Cause and effect,
therefore, will have to be temporally contiguous processes. It is
difficult to believe, at any rate where physical laws are concerned,
that the earlier part of the process which is the cause can make any
difference to the effect, so long as the later part of the process which
is the cause remains unchanged. Suppose, for example, that a man dies
of arsenic poisoning, we say that his taking arsenic was the cause
of death. But clearly the process by which he acquired the arsenic
is irrelevant: everything that happened before he swallowed it may be
ignored, since it cannot alter the effect except in so far as it alters
his condition at the moment of taking the dose. But we may go further:
swallowing arsenic is not really the proximate cause of death, since a
man might be shot through the head immediately after taking the dose,
and then it would not be of arsenic that he would die. The arsenic
produces certain physiological changes, which take a finite time before
they end in death. The earlier parts of these changes can be ruled out
in the same way as we can rule out the process by which the arsenic was
acquired. Proceeding in this way, we can shorten the process which we
are calling the cause more and more. Similarly we shall have to shorten
the effect. It may happen that immediately after the man's death his
body is blown to pieces by a bomb. We cannot say what will happen after
the man's death, through merely knowing that he has died as the result
of arsenic poisoning. Thus, if we are to take the cause as one event and
the effect as another, both must be shortened indefinitely. The result
is that we merely have, as the embodiment of our causal law, a certain
direction of change at each moment. Hence we are brought to differential
equations as embodying causal laws. A physical law does not say "A will
be followed by B," but tells us what acceleration a particle will have
under given circumstances, i.e. it tells us how the particle's motion is
changing at each moment, not where the particle will be at some future
moment.
* The theory of quanta suggests that the continuity is only
apparent. If so, we shall be able theoretically to reach
events which are not processes. But in what is directly
observable there is still apparent continuity, which
justifies the above remarks for the prevent.
Laws embodied in differential equations may possibly be exact,
but cannot be known to be so. All that we can know empirically is
approximate and liable to exceptions; the exact laws that are assumed in
physics are known to be somewhere near the truth, but are not known to
be true just as they stand. The laws that we actually know empirically
have the form of the traditional causal laws, except that they are not
to be regarded as universal or necessary. "Taking arsenic is followed by
death" is a good empirical generalization; it may have exceptions, but
they will be rare. As against the professedly exact laws of physics,
such empirical generalizations have the advantage that they deal with
observable phenomena. We cannot observe infinitesimals, whether in time
or space; we do not even know whether time and space are infinitely
divisible. Therefore rough empirical generalizations have a definite
place in science, in spite of not being exact of universal. They are the
data for more exact laws, and the grounds for believing that they are
USUALLY true are stronger than the grounds for believing that the more
exact laws are ALWAYS true.
Science starts, therefore, from generalizations of the form, "A is
usually followed by B." This is the nearest approach that can be made
to a causal law of the traditional sort. It may happen in any particular
instance that A is ALWAYS followed by B, but we cannot know this, since
we cannot foresee all the perfectly possible circumstances that might
make the sequence fail, or know that none of them will actually occur.
If, however, we know of a very large number of cases in which A is
followed by B, and few or none in which the sequence fails, we shall in
PRACTICE be justified in saying "A causes B," provided we do not attach
to the notion of cause any of the metaphysical superstitions that have
gathered about the word.
There is another point, besides lack of universality and necessity,
which it is important to realize as regards causes in the above sense,
and that is the lack of uniqueness. It is generally assumed that, given
any event, there is some one phenomenon which is THE cause of the event
in question. This seems to be a mere mistake. Cause, in the only
sense in which it can be practically applied, means "nearly invariable
antecedent." We cannot in practice obtain an antecedent which is QUITE
invariable, for this would require us to take account of the whole
universe, since something not taken account of may prevent the expected
effect. We cannot distinguish, among nearly invariable antecedents, one
as THE cause, and the others as merely its concomitants: the attempt to
do this depends upon a notion of cause which is derived from will, and
will (as we shall see later) is not at all the sort of thing that it is
generally supposed to be, nor is there any reason to think that in the
physical world there is anything even remotely analogous to what will is
supposed to be. If we could find one antecedent, and only one, that was
QUITE invariable, we could call that one THE cause without introducing
any notion derived from mistaken ideas about will. But in fact we cannot
find any antecedent that we know to be quite invariable, and we can find
many that are nearly so. For example, men leave a factory for dinner
when the hooter sounds at twelve o'clock. You may say the hooter is
THE cause of their leaving. But innumerable other hooters in other
factories, which also always sound at twelve o'clock, have just as
good a right to be called the cause. Thus every event has many nearly
invariable antecedents, and therefore many antecedents which may be
called its cause.
The laws of traditional physics, in the form in which they deal with
movements of matter or electricity, have an apparent simplicity which
somewhat conceals the empirical character of what they assert. A piece
of matter, as it is known empirically, is not a single existing thing,
but a system of existing things. When several people simultaneously see
the same table, they all see something different; therefore "the" table,
which they are supposed all to see, must be either a hypothesis or
a construction. "The" table is to be neutral as between different
observers: it does not favour the aspect seen by one man at the expense
of that seen by another. It was natural, though to my mind mistaken, to
regard the "real" table as the common cause of all the appearances which
the table presents (as we say) to different observers. But why should we
suppose that there is some one common cause of all these appearances? As
we have just seen, the notion of "cause" is not so reliable as to allow
us to infer the existence of something that, by its very nature, can
never be observed.
Instead of looking for an impartial source, we can secure neutrality by
the equal representation of all parties. Instead of supposing that there
is some unknown cause, the "real" table, behind the different sensations
of those who are said to be looking at the table, we may take the
whole set of these sensations (together possibly with certain other
particulars) as actually BEING the table. That is to say, the table
which is neutral as between different observers (actual and possible)
is the set of all those particulars which would naturally be called
"aspects" of the table from different points of view. (This is a first
approximation, modified later.)
It may be said: If there is no single existent which is the source of
all these "aspects," how are they collected together? The answer is
simple: Just as they would be if there were such a single existent. The
supposed "real" table underlying its appearances is, in any case, not
itself perceived, but inferred, and the question whether such-and-such
a particular is an "aspect" of this table is only to be settled by
the connection of the particular in question with the one or more
particulars by which the table is defined. That is to say, even if we
assume a "real" table, the particulars which are its aspects have to be
collected together by their relations to each other, not to it, since
it is merely inferred from them. We have only, therefore, to notice how
they are collected together, and we can then keep the collection
without assuming any "real" table as distinct from the collection. When
different people see what they call the same table, they see things
which are not exactly the same, owing to difference of point of view,
but which are sufficiently alike to be described in the same words, so
long as no great accuracy or minuteness is sought. These closely similar
particulars are collected together by their similarity primarily
and, more correctly, by the fact that they are related to each other
approximately according to the laws of perspective and of reflection and
diffraction of light. I suggest, as a first approximation, that these
particulars, together with such correlated others as are unperceived,
jointly ARE the table; and that a similar definition applies to all
physical objects.*
*See "Our Knowledge of the External World" (Allen & Unwin),
chaps. iii and iv.
In order to eliminate the reference to our perceptions, which introduces
an irrelevant psychological suggestion, I will take a different
illustration, namely, stellar photography. A photographic plate exposed
on a clear night reproduces the appearance of the portion of the sky
concerned, with more or fewer stars according to the power of the
telescope that is being used. Each separate star which is photographed
produces its separate effect on the plate, just as it would upon
ourselves if we were looking at the sky. If we assume, as science
normally does, the continuity of physical processes, we are forced
to conclude that, at the place where the plate is, and at all places
between it and a star which it photographs, SOMETHING is happening which
is specially connected with that star. In the days when the aether was
less in doubt, we should have said that what was happening was a certain
kind of transverse vibration in the aether. But it is not necessary
or desirable to be so explicit: all that we need say is that SOMETHING
happens which is specially connected with the star in question. It
must be something specially connected with that star, since that star
produces its own special effect upon the plate. Whatever it is must be
the end of a process which starts from the star and radiates outwards,
partly on general grounds of continuity, partly to account for the fact
that light is transmitted with a certain definite velocity. We thus
arrive at the conclusion that, if a certain star is visible at a certain
place, or could be photographed by a sufficiently sensitive plate at
that place, something is happening there which is specially connected
with that star. Therefore in every place at all times a vast multitude
of things must be happening, namely, at least one for every physical
object which can be seen or photographed from that place. We can
classify such happenings on either of two principles:
(1) We can collect together all the happenings in one place, as is done
by photography so far as light is concerned;
(2) We can collect together all the happenings, in different places,
which are connected in the way that common sense regards as being due to
their emanating from one object.