"CAUSE AND EFFECT. (1) Cause and effect ... are correlative terms
denoting any two distinguishable things, phases, or aspects of
reality, which are so related to each other that whenever the
first ceases to exist the second comes into existence
immediately after, and whenever the second comes into existence
the first has ceased to exist immediately before."
Let us consider these three definitions in turn. The first, obviously,
is unintelligible without a definition of "necessary."
Under this
head, Baldwin's _Dictionary_ gives the following:--
"NECESSARY. That is necessary which not only is true, but would
be true under all circumstances. Something more than brute
compulsion is, therefore, involved in the conception; there is
a general law under which the thing takes place."
The notion of cause is so intimately connected with that of necessity
that it will be no digression to linger over the above definition,
with a view to discovering, if possible, _some_ meaning of which it is
capable; for, as it stands, it is very far from having any definite
signification.
The first point to notice is that, if any meaning is to be given to
the phrase "would be true under all circumstances," the subject of it
must be a propositional function, not a proposition.[35]
A
proposition is simply true or false, and that ends the matter: there
can be no question of "circumstances." "Charles I's head was cut off"
is just as true in summer as in winter, on Sundays as on Mondays. Thus
when it is worth saying that something "would be true under all
circumstances," the something in question must be a propositional
function, i.e. an expression containing a variable, and becoming a
proposition when a value is assigned to the variable; the varying
"circumstances" alluded to are then the different values of which the
variable is capable. Thus if "necessary" means "what is true under all
circumstances," then "if _x_ is a man, _x_ is mortal" is necessary,
because it is true for any possible value of _x_. Thus we should be
led to the following definition:--
"NECESSARY is a predicate of a propositional function, meaning
that it is true for all possible values of its argument or
arguments."
Unfortunately, however, the definition in Baldwin's _Dictionary_ says
that what is necessary is not only "true under all circumstances" but
is also "true." Now these two are incompatible. Only propositions can
be "true," and only propositional functions can be "true under all
circumstances." Hence the definition as it stands is nonsense. What is
meant seems to be this: "A proposition is necessary when it is a value
of a propositional function which is true under all circumstances,
i.e. for all values of its argument or arguments." But if we adopt
this definition, the same proposition will be necessary or contingent
according as we choose one or other of its terms as the argument to
our propositional function. For example, "if Socrates is a man,
Socrates is mortal," is necessary if Socrates is chosen as argument,
but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man,
Plato is mortal," will be necessary if either Socrates or _man_ is
chosen as argument, but not if Plato or _mortal_ is chosen. However,
this difficulty can be overcome by specifying the constituent which is
to be regarded as argument, and we thus arrive at the following
definition:
"A proposition is _necessary_ with respect to a given constituent if
it remains true when that constituent is altered in any way compatible
with the proposition remaining significant."
We may now apply this definition to the definition of causality quoted
above. It is obvious that the argument must be the time at which the
earlier event occurs. Thus an instance of causality will be such as:
"If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will
be followed by the event [Math: e_{2}]." This proposition is intended
to be necessary with respect to [Math: t_{1}], i.e. to remain true
however [Math: t_{1}] may be varied. Causality, as a universal law,
will then be the following: "Given any event [Math: t_{1}], there is
an event [Math: e_{2}] such that, whenever [Math: t_{1}]
occurs,
[Math: e_{2}] occurs later." But before this can be considered
precise, we must specify how much later [Math: e_{2}] is to occur.
Thus the principle becomes:--
"Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a
time-interval τ such that, whenever [Math: e_{1}]
occurs, [Math:
e_{2}] follows after an interval τ."
I am not concerned as yet to consider whether this law is true or
false. For the present, I am merely concerned to discover what the law
of causality is supposed to be. I pass, therefore, to the other
definitions quoted above.
The second definition need not detain us long, for two reasons. First,
because it is psychological: not the "thought or perception" of a
process, but the process itself, must be what concerns us in
considering causality. Secondly, because it is circular: in speaking
of a process as "taking place in consequence of" another process, it
introduces the very notion of cause which was to be defined.
The third definition is by far the most precise; indeed as regards
clearness it leaves nothing to be desired. But a great difficulty is
caused by the temporal contiguity of cause and effect which the
definition asserts. No two instants are contiguous, since the
time-series is compact; hence either the cause or the effect or both
must, if the definition is correct, endure for a finite time; indeed,
by the wording of the definition it is plain that both are assumed to
endure for a finite time. But then we are faced with a dilemma: if the
cause is a process involving change within itself, we shall require
(if causality is universal) causal relations between its earlier and
later parts; moreover, it would seem that only the later parts can be
relevant to the effect, since the earlier parts are not contiguous to
the effect, and therefore (by the definition) cannot influence the
effect. Thus we shall be led to diminish the duration of the cause
without limit, and however much we may diminish it, there will still
remain an earlier part which might be altered without altering the
effect, so that the true cause, as defined, will not have been
reached, for it will be observed that the definition excludes
plurality of causes. If, on the other hand, the cause is purely
static, involving no change within itself, then, in the first place,
no such cause is to be found in nature, and in the second place, it
seems strange--too strange to be accepted, in spite of bare logical
possibility--that the cause, after existing placidly for some time,
should suddenly explode into the effect, when it might just as well
have done so at any earlier time, or have gone on unchanged without
producing its effect. This dilemma, therefore, is fatal to the view
that cause and effect can be contiguous in time; if there are causes
and effects, they must be separated by a finite time-interval τ, as
was assumed in the above interpretation of the first definition.
What is essentially the same statement of the law of causality as the
one elicited above from the first of Baldwin's definitions is given by
other philosophers. Thus John Stuart Mill says:--
"The Law of Causation, the recognition of which is the main pillar of
inductive science, is but the familiar truth, that invariability of
succession is found by observation to obtain between every fact in
nature and some other fact which has preceded it."[36]
And Bergson, who has rightly perceived that the law as stated by
philosophers is worthless, nevertheless continues to suppose that it
is used in science. Thus he says:--
"Now, it is argued, this law [the law of causality]
means that every
phenomenon is determined by its conditions, or, in other words, that
the same causes produce the same effects."[37]
And again:--
"We perceive physical phenomena, and these phenomena obey laws. This
means: (1) That phenomena _a_, _b_, _c_, _d_, previously perceived,
can occur again in the same shape; (2) that a certain phenomenon P,
which appeared after the conditions _a_, _b_, _c_, _d_, and after
these conditions only, will not fail to recur as soon as the same
conditions are again present."[38]
A great part of Bergson's attack on science rests on the assumption
that it employs this principle. In fact, it employs no such principle,
but philosophers--even Bergson--are too apt to take their views on
science from each other, not from science. As to what the principle
is, there is a fair consensus among philosophers of different schools.
There are, however, a number of difficulties which at once arise. I
omit the question of plurality of causes for the present, since other
graver questions have to be considered. Two of these, which are forced
on our attention by the above statement of the law, are the
following:--
(1) What is meant by an "event"?
(2) How long may the time-interval be between cause and effect?
(1) An "event," in the statement of the law, is obviously intended to
be something that is likely to recur since otherwise the law becomes
trivial. It follows that an "event" is not a particular, but some
universal of which there may be many instances. It follows also that
an "event" must be something short of the whole state of the universe,
since it is highly improbable that this will recur. What is meant by
an "event" is something like striking a match, or dropping a penny
into the slot of an automatic machine. If such an event is to recur,
it must not be defined too narrowly: we must not state with what
degree of force the match is to be struck, nor what is to be the
temperature of the penny. For if such considerations were relevant,
our "event" would occur at most once, and the law would cease to give
information. An "event," then, is a universal defined sufficiently
widely to admit of many particular occurrences in time being instances
of it.
(2) The next question concerns the time-interval.
Philosophers, no
doubt, think of cause and effect as contiguous in time, but this, for
reasons already given, is impossible. Hence, since there are no
infinitesimal time-intervals, there must be some finite lapse of time
τ between cause and effect. This, however, at once raises insuperable
difficulties. However short we make the interval τ, something may
happen during this interval which prevents the expected result. I put
my penny in the slot, but before I can draw out my ticket there is an
earthquake which upsets the machine and my calculations.
In order to
be sure of the expected effect, we must know that there is nothing in
the environment to interfere with it. But this means that the supposed
cause is not, by itself, adequate to insure the effect.
And as soon as
we include the environment, the probability of repetition is
diminished, until at last, when the whole environment is included, the
probability of repetition becomes almost _nil_.
In spite of these difficulties, it must, of course, be admitted that
many fairly dependable regularities of sequence occur in daily life.
It is these regularities that have suggested the supposed law of
causality; where they are found to fail, it is thought that a better
formulation could have been found which would have never failed. I am
far from denying that there may be such sequences which in fact never
do fail. It may be that there will never be an exception to the rule
that when a stone of more than a certain mass, moving with more than a
certain velocity, comes in contact with a pane of glass of less than
a certain thickness, the glass breaks. I also do not deny that the
observation of such regularities, even when they are not without
exceptions, is useful in the infancy of a science: the observation
that unsupported bodies in air usually fall was a stage on the way to
the law of gravitation. What I deny is that science assumes the
existence of invariable uniformities of sequence of this kind, or that
it aims at discovering them. All such uniformities, as we saw, depend
upon a certain vagueness in the definition of the
"events." That
bodies fall is a vague qualitative statement; science wishes to know
how fast they fall. This depends upon the shape of the bodies and the
density of the air. It is true that there is more nearly uniformity
when they fall in a vacuum; so far as Galileo could observe, the
uniformity is then complete. But later it appeared that even there the
latitude made a difference, and the altitude.
Theoretically, the
position of the sun and moon must make a difference. In short, every
advance in a science takes us farther away from the crude uniformities
which are first observed, into greater differentiation of antecedent
and consequent, and into a continually wider circle of antecedents
recognised as relevant.
The principle "same cause, same effect," which philosophers imagine to
be vital to science, is therefore utterly otiose. As soon as the
antecedents have been given sufficiently fully to enable the
consequent to be calculated with some exactitude, the antecedents have
become so complicated that it is very unlikely they will ever recur.
Hence, if this were the principle involved, science would remain
utterly sterile.
The importance of these considerations lies partly in the fact that
they lead to a more correct account of scientific procedure, partly in
the fact that they remove the analogy with human volition which makes
the conception of cause such a fruitful source of fallacies. The
latter point will become clearer by the help of some illustrations.
For this purpose I shall consider a few maxims which have played a
great part in the history of philosophy.
(1) "Cause and effect must more or less resemble each other." This
principle was prominent in the philosophy of occasionalism, and is
still by no means extinct. It is still often thought, for example,
that mind could not have grown up in a universe which previously
contained nothing mental, and one ground for this belief is that
matter is too dissimilar from mind to have been able to cause it. Or,
more particularly, what are termed the nobler parts of our nature are
supposed to be inexplicable, unless the universe always contained
something at least equally noble which could cause them.
All such
views seem to depend upon assuming some unduly simplified law of
causality; for, in any legitimate sense of "cause" and
"effect,"
science seems to show that they are usually very widely dissimilar,
the "cause" being, in fact, two states of the whole universe, and the
"effect" some particular event.
(2) "Cause is analogous to volition, since there must be an
intelligible _nexus_ between cause and effect." This maxim is, I
think, often unconsciously in the imaginations of philosophers who
would reject it when explicitly stated. It is probably operative in
the view we have just been considering, that mind could not have
resulted from a purely material world. I do not profess to know what
is meant by "intelligible"; it seems to mean "familiar to
imagination." Nothing is less "intelligible," in any other sense, than
the connection between an act of will and its fulfilment. But
obviously the sort of nexus desired between cause and effect is such
as could only hold between the "events" which the supposed law of
causality contemplates; the laws which replace causality in such a
science as physics leave no room for any two events between which a
nexus could be sought.
(3) "The cause _compels_ the effect in some sense in which the effect
does not compel the cause." This belief seems largely operative in the
dislike of determinism; but, as a matter of fact, it is connected with
our second maxim, and falls as soon as that is abandoned. We may
define "compulsion" as follows: "Any set of circumstances is said to
compel A when A desires to do something which the circumstances
prevent, or to abstain from something which the circumstances cause."
This presupposes that some meaning has been found for the word
"cause"--a point to which I shall return later. What I want to make
clear at present is that compulsion is a very complex notion,
involving thwarted desire. So long as a person does what he wishes to
do, there is no compulsion, however much his wishes may be calculable
by the help of earlier events. And where desire does not come in,
there can be no question of compulsion. Hence it is, in general,
misleading to regard the cause as compelling the effect.
A vaguer form of the same maxim substitutes the word
"determine" for
the word "compel"; we are told that the cause _determines_ the effect
in a sense in which the effect does not _determine_ the cause. It is
not quite clear what is meant by "determining"; the only precise
sense, so far as I know, is that of a function or one-many relation.
If we admit plurality of causes, but not of effects, that is, if we
suppose that, given the cause, the effect must be such and such, but,
given the effect, the cause may have been one of many alternatives,
then we may say that the cause determines the effect, but not the
effect the cause. Plurality of causes, however, results only from
conceiving the effect vaguely and narrowly and the cause precisely and
widely. Many antecedents may "cause" a man's death, because his death
is vague and narrow. But if we adopt the opposite course, taking as
the "cause" the drinking of a dose of arsenic, and as the "effect" the
whole state of the world five minutes later, we shall have plurality
of effects instead of plurality of causes. Thus the supposed lack of
symmetry between "cause" and "effect" is illusory.
(4) "A cause cannot operate when it has ceased to exist, because what
has ceased to exist is nothing." This is a common maxim, and a still
more common unexpressed prejudice. It has, I fancy, a good deal to do
with the attractiveness of Bergson's "_durée_": since the past has
effects now, it must still exist in some sense. The mistake in this
maxim consists in the supposition that causes "operate"
at all. A
volition "operates" when what it wills takes place; but nothing can
operate except a volition. The belief that causes
"operate" results
from assimilating them, consciously or unconsciously, to volitions. We
have already seen that, if there are causes at all, they must be
separated by a finite interval of time from their effects, and thus
cause their effects after they have ceased to exist.
It may be objected to the above definition of a volition
"operating"
that it only operates when it "causes" what it wills, not when it
merely happens to be followed by what it wills. This certainly
represents the usual view of what is meant by a volition
"operating,"
but as it involves the very view of causation which we are engaged in
combating, it is not open to us as a definition. We may say that a
volition "operates" when there is some law in virtue of which a
similar volition in rather similar circumstances will usually be
followed by what it wills. But this is a vague conception, and
introduces ideas which we have not yet considered. What is chiefly
important to notice is that the usual notion of
"operating" is not
open to us if we reject, as I contend that we should, the usual notion
of causation.
(5) "A cause cannot operate except where it is." This maxim is very
widespread; it was urged against Newton, and has remained a source of
prejudice against "action at a distance." In philosophy it has led to
a denial of transient action, and thence to monism or Leibnizian
monadism. Like the analogous maxim concerning temporal contiguity, it
rests upon the assumption that causes "operate," i.e.
that they are in
some obscure way analogous to volitions. And, as in the case of
temporal contiguity, the inferences drawn from this maxim are wholly
groundless.
I return now to the question, What law or laws can be found to take
the place of the supposed law of causality?
First, without passing beyond such uniformities of sequence as are
contemplated by the traditional law, we may admit that, if any such
sequence has been observed in a great many cases, and has never been
found to fail, there is an inductive probability that it will be found
to hold in future cases. If stones have hitherto been found to break
windows, it is probable that they will continue to do so. This, of
course, assumes the inductive principle, of which the truth may
reasonably be questioned; but as this principle is not our present
concern, I shall in this discussion treat it as indubitable. We may
then say, in the case of any such frequently observed sequence, that
the earlier event is the _cause_ and the later event the _effect_.
Several considerations, however, make such special sequences very
different from the traditional relation of cause and effect. In the
first place, the sequence, in any hitherto unobserved instance, is no
more than probable, whereas the relation of cause and effect was
supposed to be necessary. I do not mean by this merely that we are not
sure of having discovered a true case of cause and effect; I mean
that, even when we have a case of cause and effect in our present
sense, all that is meant is that on grounds of observation, it is
probable that when one occurs the other will also occur.
Thus in our
present sense, A may be the cause of B even if there actually are
cases where B does not follow A. Striking a match will be the cause of
its igniting, in spite of the fact that some matches are damp and fail
to ignite.
In the second place, it will not be assumed that _every_
event has
some antecedent which is its cause in this sense; we shall only
believe in causal sequences where we find them, without any
presumption that they always are to be found.
In the third place, _any_ case of sufficiently frequent sequence will
be causal in our present sense; for example, we shall not refuse to
say that night is the cause of day. Our repugnance to saying this
arises from the ease with which we can imagine the sequence to fail,
but owing to the fact that cause and effect must be separated by a
finite interval of time, _any_ such sequence _might_
fail through the
interposition of other circumstances in the interval.
Mill, discussing
this instance of night and day, says:--