No More Learning

For this purpose, we may, at least to begin with, confine ourselves
within a single biography. If we can always say when two "sensibilia"
in a given biography are appearances of one thing, then, since we have
seen how to connect "sensibilia" in different biographies as
appearances of the same momentary state of a thing, we shall have all
that is necessary for the complete construction of the history of a
thing.

It is to be observed, to begin with, that the identity of a thing for
common sense is not always correlated with the identity of matter for
physics. A human body is one persisting thing for common sense, but
for physics its matter is constantly changing. We may say, broadly,
that the common-sense conception is based upon continuity in
appearances at the ordinary distances of sense-data, while the
physical conception is based upon the continuity of appearances at
very small distances from the thing. It is probable that the
common-sense conception is not capable of complete precision. Let us
therefore concentrate our attention upon the conception of the
persistence of matter in physics.

The first characteristic of two appearances of the same piece of
matter at different times is _continuity_. The two appearances must be
connected by a series of intermediaries, which, if time and space form
compact series, must themselves form a compact series. The colour of
the leaves is different in autumn from what it is in summer; but we
believe that the change occurs gradually, and that, if the colours are
different at two given times, there are intermediate times at which
the colours are intermediate between those at the given times.

But there are two considerations that are important as regards
continuity.

First, it is largely hypothetical. We do not observe any one thing
continuously, and it is merely a hypothesis to assume that, while we
are not observing it, it passes through conditions intermediate
between those in which it is perceived. During uninterrupted
observation, it is true, continuity is nearly verified; but even here,
when motions are very rapid, as in the case of explosions, the
continuity is not actually capable of direct verification. Thus we can
only say that the sense-data are found to _permit_ a hypothetical
complement of "sensibilia" such as will preserve continuity, and that
therefore there _may_ be such a complement. Since, however, we have
already made such use of hypothetical "sensibilia," we will let this
point pass, and admit such "sensibilia" as are required to preserve
continuity.

Secondly, continuity is not a sufficient criterion of material
identity. It is true that in many cases, such as rocks, mountains,
tables, chairs, etc. , where the appearances change slowly, continuity
is sufficient, but in other cases, such as the parts of an
approximately homogeneous fluid, it fails us utterly. We can travel by
sensibly continuous gradations from any one drop of the sea at any one
time to any other drop at any other time. We infer the motions of
sea-water from the effects of the current, but they cannot be inferred
from direct sensible observation together with the assumption of
continuity.

The characteristic required in addition to continuity is conformity
with the laws of dynamics. Starting from what common sense regards as
persistent things, and making only such modifications as from time to
time seem reasonable, we arrive at assemblages of "sensibilia" which
are found to obey certain simple laws, namely those of dynamics. By
regarding "sensibilia" at different times as belonging to the same
piece of matter, we are able to define _motion_, which presupposes the
assumption or construction of something persisting throughout the
time of the motion. The motions which are regarded as occurring,
during a period in which all the "sensibilia" and the times of their
appearance are given, will be different according to the manner in
which we combine "sensibilia" at different times as belonging to the
same piece of matter. Thus even when the whole history of the world is
given in every particular, the question what motions take place is
still to a certain extent arbitrary even after the assumption of
continuity. Experience shows that it is possible to determine motions
in such a way as to satisfy the laws of dynamics, and that this
determination, roughly and on the whole, is fairly in agreement with
the common-sense opinions about persistent things. This determination,
therefore, is adopted, and leads to a criterion by which we can
determine, sometimes practically, sometimes only theoretically,
whether two appearances at different times are to be regarded as
belonging to the same piece of matter. The persistence of all matter
throughout all time can, I imagine, be secured by definition.

To recommend this conclusion, we must consider what it is that is
proved by the empirical success of physics. What is proved is that its
hypotheses, though unverifiable where they go beyond sense-data, are
at no point in contradiction with sense-data, but, on the contrary,
are ideally such as to render all sense-data calculable when a
sufficient collection of "sensibilia" is given. Now physics has found
it empirically possible to collect sense-data into series, each series
being regarded as belonging to one "thing," and behaving, with regard
to the laws of physics, in a way in which series not belonging to one
thing would in general not behave. If it is to be unambiguous whether
two appearances belong to the same thing or not, there must be only
one way of grouping appearances so that the resulting things obey the
laws of physics. It would be very difficult to prove that this is the
case, but for our present purposes we may let this point pass, and
assume that there is only one way. Thus we may lay down the following
definition: _Physical things are those series of appearances whose
matter obeys the laws of physics_. That such series exist is an
empirical fact, which constitutes the verifiability of physics.


XII. ILLUSIONS, HALLUCINATIONS, AND DREAMS

It remains to ask how, in our system, we are to find a place for
sense-data which apparently fail to have the usual connection with the
world of physics. Such sense-data are of various kinds, requiring
somewhat different treatment. But all are of the sort that would be
called "unreal," and therefore, before embarking upon the discussion,
certain logical remarks must be made upon the conceptions of reality
and unreality.

Mr. A. Wolf[31] says:

"The conception of mind as a system of transparent activities is,
I think, also untenable because of its failure to account for the
very possibility of dreams and hallucinations. It seems impossible
to realise how a bare, transparent activity can be directed to
what is not there, to apprehend what is not given. "

This statement is one which, probably, most people would endorse. But
it is open to two objections. First it is difficult to see how an
activity, however un-"transparent," can be directed towards a nothing:
a term of a relation cannot be a mere nonentity. Secondly, no reason
is given, and I am convinced that none can be given, for the assertion
that dream-objects are not "there" and not "given. " Let us take the
second point first.

(1) The belief that dream-objects are not given comes, I think, from
failure to distinguish, as regards waking life, between the
sense-datum and the corresponding "thing. " In dreams, there is no such
corresponding "thing" as the dreamer supposes; if, therefore, the
"thing" were given in waking life, as e. g. Meinong maintains,[32] then
there would be a difference in respect of givenness between dreams and
waking life. But if, as we have maintained, what is given is never the
thing, but merely one of the "sensibilia" which compose the thing,
then what we apprehend in a dream is just as much given as what we
apprehend in waking life.

Exactly the same argument applies as to the dream-objects being
"there. " They have their position in the private space of the
perspective of the dreamer; where they fail is in their correlation
with other private spaces and therefore with perspective space. But in
the only sense in which "there" can be a datum, they are "there" just
as truly as any of the sense-data of waking life.

(2) The conception of "illusion" or "unreality," and the correlative
conception of "reality," are generally used in a way which embodies
profound logical confusions. Words that go in pairs, such as "real"
and "unreal," "existent" and "non-existent," "valid" and "invalid,"
etc. , are all derived from the one fundamental pair, "true" and
"false. " Now "true" and "false" are applicable only--except in
derivative significations--to _propositions_. Thus wherever the above
pairs can be significantly applied, we must be dealing either with
propositions or with such incomplete phrases as only acquire meaning
when put into a context which, with them, forms a proposition. Thus
such pairs of words can be applied to _descriptions_,[33] but not to
proper names: in other words, they have no application whatever to
data, but only to entities or non-entities described in terms of data.

Let us illustrate by the terms "existence" and "non-existence. " Given
any datum _x_, it is meaningless either to assert or to deny that _x_
"exists. " We might be tempted to say: "Of course _x_ exists, for
otherwise it could not be a datum. " But such a statement is really
meaningless, although it is significant and true to say "My present
sense-datum exists," and it may also be true that "_x_ is my present
sense-datum. " The inference from these two propositions to "_x_
exists" is one which seems irresistible to people unaccustomed to
logic; yet the apparent proposition inferred is not merely false, but
strictly meaningless. To say "My present sense-datum exists" is to say
(roughly): "There is an object of which 'my present sense-datum' is a
description. " But we cannot say: "There is an object of which '_x_' is
a description," because '_x_' is (in the case we are supposing) a
name, not a description. Dr. Whitehead and I have explained this point
fully elsewhere (_loc. cit. _) with the help of symbols, without which
it is hard to understand; I shall not therefore here repeat the
demonstration of the above propositions, but shall proceed with their
application to our present problem.

The fact that "existence" is only applicable to descriptions is
concealed by the use of what are grammatically proper names in a way
which really transforms them into descriptions. It is, for example, a
legitimate question whether Homer existed; but here "Homer" means
"the author of the Homeric poems," and is a description. Similarly we
may ask whether God exists; but then "God" means "the Supreme Being"
or "the _ens realissimum_" or whatever other description we may
prefer. If "God" were a proper name, God would have to be a datum; and
then no question could arise as to His existence. The distinction
between existence and other predicates, which Kant obscurely felt, is
brought to light by the theory of descriptions, and is seen to remove
"existence" altogether from the fundamental notions of metaphysics.

What has been said about "existence" applies equally to "reality,"
which may, in fact, be taken as synonymous with "existence. "
Concerning the immediate objects in illusions, hallucinations, and
dreams, it is meaningless to ask whether they "exist" or are "real. "
There they are, and that ends the matter. But we may legitimately
inquire as to the existence or reality of "things" or other
"sensibilia" inferred from such objects. It is the unreality of these
"things" and other "sensibilia," together with a failure to notice
that they are not data, which has led to the view that the objects of
dreams are unreal.

We may now apply these considerations in detail to the stock arguments
against realism, though what is to be said will be mainly a repetition
of what others have said before.

(1) We have first the variety of normal appearances, supposed to be
incompatible. This is the case of the different shapes and colours
which a given thing presents to different spectators. Locke's water
which seems both hot and cold belongs to this class of cases. Our
system of different perspectives fully accounts for these cases, and
shows that they afford no argument against realism.

(2) We have cases where the correlation between different senses is
unusual. The bent stick in water belongs here. People say it looks
bent but is straight: this only means that it is straight to the
touch, though bent to sight. There is no "illusion," but only a false
inference, if we think that the stick would feel bent to the touch.
The stick would look just as bent in a photograph, and, as Mr.
Gladstone used to say, "the photograph cannot lie. "[34] The case of
seeing double also belongs here, though in this case the cause of the
unusual correlation is physiological, and would therefore not operate
in a photograph. It is a mistake to ask whether the "thing" is
duplicated when we see it double. The "thing" is a whole system of
"sensibilia," and it is only those visual "sensibilia" which are data
to the percipient that are duplicated. The phenomenon has a purely
physiological explanation; indeed, in view of our having two eyes, it
is in less need of explanation than the single visual sense-datum
which we normally obtain from the things on which we focus.

(3) We come now to cases like dreams, which may, at the moment of
dreaming, contain nothing to arouse suspicion, but are condemned on the
ground of their supposed incompatibility with earlier and later data. Of
course it often happens that dream-objects fail to behave in the
accustomed manner: heavy objects fly, solid objects melt, babies turn
into pigs or undergo even greater changes. But none of these unusual
occurrences _need_ happen in a dream, and it is not on account of such
occurrences that dream-objects are called "unreal. " It is their lack of
continuity with the dreamer's past and future that makes him, when he
wakes, condemn them; and it is their lack of correlation with other
private worlds that makes others condemn them. Omitting the latter
ground, our reason for condemning them is that the "things" which we
infer from them cannot be combined according to the laws of physics with
the "things" inferred from waking sense-data. This might be used to
condemn the "things" inferred from the data of dreams. Dream-data are no
doubt appearances of "things," but not of such "things" as the dreamer
supposes. I have no wish to combat psychological theories of dreams,
such as those of the psycho-analysts. But there certainly are cases
where (whatever psychological causes may contribute) the presence of
physical causes also is very evident. For instance, a door banging may
produce a dream of a naval engagement, with images of battleships and
sea and smoke. The whole dream will be an appearance of the door
banging, but owing to the peculiar condition of the body (especially the
brain) during sleep, this appearance is not that expected to be produced
by a door banging, and thus the dreamer is led to entertain false
beliefs. But his sense-data are still physical, and are such as a
completed physics would include and calculate.

(4) The last class of illusions are those which cannot be discovered
within one person's experience, except through the discovery of
discrepancies with the experiences of others. Dreams might conceivably
belong to this class, if they were jointed sufficiently neatly into
waking life; but the chief instances are recurrent sensory
hallucinations of the kind that lead to insanity. What makes the
patient, in such cases, become what others call insane is the fact
that, within his own experience, there is nothing to show that the
hallucinatory sense-data do not have the usual kind of connection with
"sensibilia" in other perspectives. Of course he may learn this
through testimony, but he probably finds it simpler to suppose that
the testimony is untrue and that he is being wilfully deceived. There
is, so far as I can see, no theoretical criterion by which the patient
can decide, in such a case, between the two equally satisfactory
hypotheses of his madness and of his friends' mendacity.

From the above instances it would appear that abnormal sense-data, of
the kind which we regard as deceptive, have intrinsically just the
same status as any others, but differ as regards their correlations or
causal connections with other "sensibilia" and with "things. " Since
the usual correlations and connections become part of our unreflective
expectations, and even seem, except to the psychologist, to form part
of our data, it comes to be thought, mistakenly, that in such cases
the data are unreal, whereas they are merely the causes of false
inferences. The fact that correlations and connections of unusual
kinds occur adds to the difficulty of inferring things from sense and
of expressing physics in terms of sense-data. But the unusualness
would seem to be always physically or physiologically explicable, and
therefore raises only a complication, not a philosophical objection.

I conclude, therefore, that no valid objection exists to the view
which regards sense-data as part of the actual substance of the
physical world, and that, on the other hand, this view is the only one
which accounts for the empirical verifiability of physics. In the
present paper, I have given only a rough preliminary sketch. In
particular, the part played by _time_ in the construction of the
physical world is, I think, more fundamental than would appear from
the above account. I should hope that, with further elaboration, the
part played by unperceived "sensibilia" could be indefinitely
diminished, probably by invoking the history of a "thing" to eke out
the inferences derivable from its momentary appearance.

FOOTNOTES:

[29] _Proc. Arist. Soc. _, 1909-1910, pp. 191-218.

[30] On this subject, compare _A Theory of Time and Space_, by Mr.
A. A. Robb (Camb. Univ. Press), which first suggested to me the views
advocated here, though I have, for present purposes, omitted what is
most interesting and novel in his theory. Mr. Robb has given a sketch
of his theory in a pamphlet with the same title (Heffer and Sons,
Cambridge, 1913).

[31] "Natural Realism and Present Tendencies in Philosophy," _Proc.
Arist. Soc. _, 1908-1909, p. 165.

[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.

[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction,
Chap. III. For the definition of _existence_, cf. * 14. 02.

[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a
Realistic World. _ "The New Realism," p. 303, both on this point and as
regards _seeing double_.




IX

ON THE NOTION OF CAUSE


In the following paper I wish, first, to maintain that the word
"cause" is so inextricably bound up with misleading associations as to
make its complete extrusion from the philosophical vocabulary
desirable; secondly, to inquire what principle, if any, is employed in
science in place of the supposed "law of causality" which philosophers
imagine to be employed; thirdly, to exhibit certain confusions,
especially in regard to teleology and determinism, which appear to me
to be connected with erroneous notions as to causality.

All philosophers, of every school, imagine that causation is one of
the fundamental axioms or postulates of science, yet, oddly enough, in
advanced sciences such as gravitational astronomy, the word "cause"
never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_,
makes this a ground of complaint against physics: the business of
those who wish to ascertain the ultimate truth about the world, he
apparently thinks, should be the discovery of causes, yet physics
never even seeks them. To me it seems that philosophy ought not to
assume such legislative functions, and that the reason why physics has
ceased to look for causes is that, in fact, there are no such things.
The law of causality, I believe, like much that passes muster among
philosophers, is a relic of a bygone age, surviving, like the
monarchy, only because it is erroneously supposed to do no harm. In
order to find out what philosophers commonly understand by "cause," I
consulted Baldwin's _Dictionary_, and was rewarded beyond my
expectations, for I found the following three mutually incompatible
definitions:--

"CAUSALITY. (1) The necessary connection of events in the
time-series. . . .

"CAUSE (notion of). Whatever may be included in the thought or
perception of a process as taking place in consequence of
another process. . . .

"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 ? such that, whenever [Math: e_{1}] occurs, [Math:
e_{2}] follows after an interval ? . "

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 ? , 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
? between cause and effect. This, however, at once raises insuperable
difficulties. However short we make the interval ? , 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 "_duree_": 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:--

"It is necessary to our using the word cause, that we should believe
not only that the antecedent always _has_ been followed by the
consequent, but that as long as the present constitution of things
endures, it always _will_ be so. "[39]

In this sense, we shall have to give up the hope of finding causal
laws such as Mill contemplated; any causal sequence which we have
observed may at any moment be falsified without a falsification of any
laws of the kind that the more advanced sciences aim at establishing.

In the fourth place, such laws of probable sequence, though useful in
daily life and in the infancy of a science, tend to be displaced by
quite different laws as soon as a science is successful. The law of
gravitation will illustrate what occurs in any advanced science. In
the motions of mutually gravitating bodies, there is nothing that can
be called a cause, and nothing that can be called an effect; there is
merely a formula. Certain differential equations can be found, which
hold at every instant for every particle of the system, and which,
given the configuration and velocities at one instant, or the
configurations at two instants, render the configuration at any other
earlier or later instant theoretically calculable. That is to say, the
configuration at any instant is a function of that instant and the
configurations at two given instants. This statement holds throughout
physics, and not only in the special case of gravitation. But there is
nothing that could be properly called "cause" and nothing that could
be properly called "effect" in such a system.

No doubt the reason why the old "law of causality" has so long
continued to pervade the books of philosophers is simply that the idea
of a function is unfamiliar to most of them, and therefore they seek
an unduly simplified statement. There is no question of repetitions of
the "same" cause producing the "same" effect; it is not in any
sameness of causes and effects that the constancy of scientific law
consists, but in sameness of relations. And even "sameness of
relations" is too simple a phrase; "sameness of differential
equations" is the only correct phrase. It is impossible to state this
accurately in non-mathematical language; the nearest approach would be
as follows: "There is a constant relation between the state of the
universe at any instant and the rate of change in the rate at which
any part of the universe is changing at that instant, and this
relation is many-one, i. e. such that the rate of change in the rate of
change is determinate when the state of the universe is given. " If the
"law of causality" is to be something actually discoverable in the
practice of science, the above proposition has a better right to the
name than any "law of causality" to be found in the books of
philosophers.

In regard to the above principle, several observations must be made--

(1) No one can pretend that the above principle is _a priori_ or
self-evident or a "necessity of thought. " Nor is it, in any sense, a
premiss of science: it is an empirical generalisation from a number of
laws which are themselves empirical generalisations.

(2) The law makes no difference between past and future: the future
"determines" the past in exactly the same sense in which the past
"determines" the future. The word "determine," here, has a purely
logical significance: a certain number of variables "determine"
another variable if that other variable is a function of them.

(3) The law will not be empirically verifiable unless the course of
events within some sufficiently small volume will be approximately
the same in any two states of the universe which only differ in regard
to what is at a considerable distance from the small volume in
question. For example, motions of planets in the solar system must be
approximately the same however the fixed stars may be distributed,
provided that all the fixed stars are very much farther from the sun
than the planets are. If gravitation varied directly as the distance,
so that the most remote stars made the most difference to the motions
of the planets, the world might be just as regular and just as much
subject to mathematical laws as it is at present, but we could never
discover the fact.

(4) Although the old "law of causality" is not assumed by science,
something which we may call the "uniformity of nature" is assumed, or
rather is accepted on inductive grounds. The uniformity of nature does
not assert the trivial principle "same cause, same effect," but the
principle of the permanence of laws. That is to say, when a law
exhibiting, e. g. an acceleration as a function of the configuration
has been found to hold throughout the observable past, it is expected
that it will continue to hold in the future, or that, if it does not
itself hold, there is some other law, agreeing with the supposed law
as regards the past, which will hold for the future. The ground of
this principle is simply the inductive ground that it has been found
to be true in very many instances; hence the principle cannot be
considered certain, but only probable to a degree which cannot be
accurately estimated.

The uniformity of nature, in the above sense, although it is assumed
in the practice of science, must not, in its generality, be regarded
as a kind of major premiss, without which all scientific reasoning
would be in error. The assumption that _all_ laws of nature are
permanent has, of course, less probability than the assumption that
this or that particular law is permanent; and the assumption that a
particular law is permanent for all time has less probability than the
assumption that it will be valid up to such and such a date. Science,
in any given case, will assume what the case requires, but no more. In
constructing the _Nautical Almanac_ for 1915 it will assume that the
law of gravitation will remain true up to the end of that year; but it
will make no assumption as to 1916 until it comes to the next volume
of the almanac. This procedure is, of course, dictated by the fact
that the uniformity of nature is not known _a priori_, but is an
empirical generalisation, like "all men are mortal. " In all such
cases, it is better to argue immediately from the given particular
instances to the new instance, than to argue by way of a major
premiss; the conclusion is only probable in either case, but acquires
a higher probability by the former method than by the latter.

In all science we have to distinguish two sorts of laws: first, those
that are empirically verifiable but probably only approximate;
secondly, those that are not verifiable, but may be exact. The law of
gravitation, for example, in its applications to the solar system, is
only empirically verifiable when it is assumed that matter outside the
solar system may be ignored for such purposes; we believe this to be
only approximately true, but we cannot empirically verify the law of
universal gravitation which we believe to be exact. This point is very
important in connection with what we may call "relatively isolated
systems. " These may be defined as follows:--

A system relatively isolated during a given period is one which,
within some assignable margin of error, will behave in the same way
throughout that period, however the rest of the universe may be
constituted.

A system may be called "practically isolated" during a given period
if, although there _might_ be states of the rest of the universe which
would produce more than the assigned margin of error, there is reason
to believe that such states do not in fact occur.

Strictly speaking, we ought to specify the respect in which the system
is relatively isolated. For example, the earth is relatively isolated
as regards falling bodies, but not as regards tides; it is
_practically_ isolated as regards economic phenomena, although, if
Jevons' sunspot theory of commercial crises had been true, it would
not have been even practically isolated in this respect.

It will be observed that we cannot prove in advance that a system is
isolated. This will be inferred from the observed fact that
approximate uniformities can be stated for this system alone. If the
complete laws for the whole universe were known, the isolation of a
system could be deduced from them; assuming, for example, the law of
universal gravitation, the practical isolation of the solar system in
this respect can be deduced by the help of the fact that there is very
little matter in its neighbourhood. But it should be observed that
isolated systems are only important as providing a possibility of
_discovering_ scientific laws; they have no theoretical importance in
the finished structure of a science.

The case where one event A is said to "cause" another event B, which
philosophers take as fundamental, is really only the most simplified
instance of a practically isolated system. It may happen that, as a
result of general scientific laws, whenever A occurs throughout a
certain period, it is followed by B; in that case, A and B form a
system which is practically isolated throughout that period. It is,
however, to be regarded as a piece of good fortune if this occurs; it
will always be due to special circumstances, and would not have been
true if the rest of the universe had been different though subject to
the same laws.

The essential function which causality has been supposed to perform is
the possibility of inferring the future from the past, or, more
generally, events at any time from events at certain assigned times.
Any system in which such inference is possible may be called a
"deterministic" system. We may define a deterministic system as
follows:--

A system is said to be "deterministic" when, given certain data,
[Math: e_{1}, e_{2}, . . . , e_{n}, at times t_{1}, t_{2}, . . . ,
t_{n}] respectively, concerning this system, if [Math: E_{t}] is
the state of the system at any time _t_, there is a functional
relation of the form

[Math: E_{t} = f (e_{1}, t_{1}, e_{2}, t_{2}, . . . , e_{n}, t_{n}, t)]. (A)

The system will be "deterministic throughout a given period" if
_t_, in the above formula, may be any time within that period,
though outside that period the formula may be no longer true. If
the universe, as a whole, is such a system, determinism is true of
the universe; if not, not. A system which is part of a
deterministic system I shall call "determined"; one which is not
part of any such system I shall call "capricious. "

The events [Math: e_{1}, e_{2}, . .