# An Outline of Philosophy/Chapter 11

In the last chapter we spoke about the substitution of space-time for space and time, and the effect which this has had in substituting strings of events for "things" conceived as substances. In this chapter we will deal with cause and effect as they appear in the light of modern science. It is at least as difficult to purge our imagination of irrelevances in this matter as in regard to substance. The old-fashioned notion of cause appeared in dynamics as "force". We still speak of forces just as we still speak of the sunrise, but we recognise that this is nothing but a convenient way of speaking, in the one case as in the other.
Causation is deeply embedded in language and common sense. We say that people build houses or make roads: to "build" and to "make" are both notions involving causality. We say that a man is "powerful", meaning that his volitions are causes over a wide range. Some examples of causation seem to us quite natural, others less so. It seems natural that our muscles should obey our will, and only reflection makes us perceive the necessity of finding an explanation of this phenomenon. It seems natural that when you hit a billiard-ball with a cue it moves. When we see a horse pulling a cart, or a heavy object being dragged by a rope, we feel as if we understood all about it. It is events of this sort that have given rise to the common-sense belief in causes and forces.
But as a matter of fact the world is incredibly more complicated than it seems to common sense. When we think we ​understand a process—I mean by "we" the non-reflective part in each of us—what really happens is that there is some sequence of events so familiar through past experience that at each stage we expect the next stage. The whole process seems to us peculiarly intelligible when human desires enter in, for example, in watching a game: what the ball does and what the players do seems "natural", and we feel as if we quite understood how the stages succeed each other. We thus arrive at the notion of what is called "necessary" sequence. The text-books say that A is the cause of B if A is "necessarily" followed by B. This notion of "necessity" seems to be purely anthropomorphic, and not based upon anything that is a discoverable feature of the world. Things happen according to certain rules; the rules can be generalised, but in the end remain brute facts. Unless the rules are concealed conventions or definitions, no reason can be given why they should not be completely different.
To say that A is "necessarily" followed by B is thus to say no more than that there is some general rule, exemplified in a very large number of observed instances, and falsified in none, according to which events such as A are followed by events such as B. We must not have any notion of "compulsion", as if the cause forced the effect to happen. A good test for the imagination in this respect is the reversibility of causal laws. We can just as often infer backwards as forwards. When you get a letter, you are justified in inferring that somebody wrote it, but you do not feel that your receiving it compelled the sender to write it. The notion of compulsion is just as little applicable to effects as to causes. To say that causes compel effects is as misleading as to say that effects compel causes. Compulsion is anthropomorphic: a man is compelled to do something when he wishes to do the opposite, but except where human or animal wishes come in the notion of compulsion is inapplicable. Science is concerned merely with what happens, not with what must happen.
When we look for invariable rules of sequence in nature, we find that they are not such as common sense sets up. ​Common sense says: thunder follows lightning, waves at sea follow wind, and so on. Rules of this sort are indispensable in practical life, but in science they are all only approximate. If there is any finite interval of time, however short, between the cause and the effect, something may happen to prevent the effect from occurring. Scientific laws can only be expressed in differential equations. This means that, although you cannot tell what may happen after a finite time, you can say that, if you make the time shorter and shorter, what will happen will be more and more nearly according to such-and-such a rule. To take a very simple case: I am now in this room; you cannot tell where I shall be in another second, because a bomb may explode and blow me sky-high, but if you take any two small fragments of my body which are now very close together, you can be sure that, after some very short finite time, they will still be very close together. If a second is not short enough, you must take a shorter time; you cannot tell in advance how short a time you may have to take, but you may feel fairly certain that there is a short enough time.
The laws of sequence in physics, apart from quantum phenomena, are of two sorts, which appeared in traditional dynamics as laws of velocity and laws of acceleration. In a very short time, the velocity of a body alters very little, and if the time is taken short enough, the change of velocity diminishes without limit. This is what, in the last chapter, we called an "intrinsic" causal law. Then there is the effect of the outer world, as it appeared in traditional dynamics, which is shown in acceleration. The small change which does occur in the velocity in a short time is attributed to surrounding bodies, because it is found to vary as they vary, and to vary according to ascertained laws. Thus we think of surrounding bodies as exerting an influence, which we call "force", though this remains as mysterious as the influence of the stars in astrology.
Einstein's theory of gravitation has done away with this conception in so far as gravitational forces are concerned. In this theory, a planet moving round the sun is moving in ​the nearest approach to a straight line that the neighbourhood permits. The neighbourhood is supposed to be non-Euclidean, that is to say, to contain no straight lines such as Euclid imagined. If a body is moving freely, as the planets do, it observes a certain rule. Perhaps the simplest way to state this rule is as follows: Suppose you take any two events which happen on the earth, and you measure the time between them by ideally accurate clocks which move with the earth. Suppose some traveller on a magic carpet had meanwhile cruised about the universe, leaving the earth at the time of the first event and returning at the time of the second. By his clocks the period elapsed will be less than by the terrestial clocks. This is what is meant by saying that the earth moves in a "geodesic", which is the nearest approach to a straight line to be found in the region in which we live. All this is, so to speak, geometrical, and involves no "forces". It is not the sun that makes the earth go round, but the nature of space-time where the earth is.
Even this is not quite correct. Space-time does not make the earth go round the sun; it makes us say the earth goes round the sun. That is to say, it makes this the shortest way of describing what occurs. We could describe it in other language, which would be equally correct, but less convenient.
The abolition of "force" in astronomy is perhaps connected with the fact that astronomy depends only upon the sense of sight. On the earth, we push and pull, we touch things, and we experience muscular strains. This all gives us a notion of "force", but this notion is anthropomorphic. To imagine the laws of motion of heavenly bodies, think of the motions of objects in a mirror; they may move very fast, although in the mirror world there are no forces.
What we really have to substitute for force is laws of correlation. Events can be collected in groups by their correlations. This is all that is true in the old notion of causality. And this is not a "postulate" or "category", but an observed fact—lucky, not necessary.
As we suggested before, it is these correlations of events ​that lead to the definition of permanent "things". There is no essential difference, as regards substantiality, between an electron and a light-ray. Each is really a string of events or of sets of events. In the case of the light-ray, we have no temptation to think otherwise. But in the case of the electron, we think of it as a single persistent entity. There may be such an entity, but we can have no evidence that there is. What we can discover is (a) a group of events spreading outwards from a centre—say, for definiteness, the events constituting a wave of light—and attributed, hypothetically, to a "cause" in that centre; (b) more or less similar groups of events at other times, connected with the first group according to the laws of physics, and therefore attributed to the same hypothetical cause at other times. But all that we ought to assume is series of groups of events, connected by discoverable laws. These series we may define as "matter". Whether there is matter in any other sense, no one can tell.
What is true in the old notion of causality is the fact that events at different times are connected by laws (differential equations). When there is a law connecting an event A with an event B, the two have a definite unambiguous time-order. But if the events are such that a ray of light starting from A would arrive at any body which was present at B after B had occurred, and vice versa, then there is no definite time order, and no possible causal law connecting A and B. A and B must then be regarded as separate facts of geography.
Perhaps the scope and purpose of this and the foregoing chapters may be made clearer by showing their bearing upon certain popular beliefs which may seem self-evident but are really, in my opinion, either false or likely to lead to falsehood. I shall confine myself to objections which have actually been made to me when trying to explain the philosophical outcome of modern physics.
​"We cannot conceive of movement apart from some thing as moving." This is, in a sense, a truism; but in the sense in which it is usually meant, it is a falsehood. We speak of the "movement" of a drama or piece of music, although we do not conceive either as a "thing" which exists complete at every moment of the performance. This is the sort of picture we must have in our minds when we try to conceive the physical world. We must think of a string of events, connected together by certain causal connections, and having enough unity to deserve a single name. We then begin to imagine that the single name denotes a single "thing", and if the events concerned are not all in the same place, we say the "thing" has "moved". But this is only a convenient shorthand. In the cinema, we seem to see a man falling off a skyscraper, catching hold of the telegraph wires, and reaching the ground none the worse. We know that, in fact, there are a number of different photographs, and the appearance of a single "thing" moving is deceptive. In this respect, the real world resembles the cinema.
In connection with motion one needs to emphasise the very difficult distinction between experience and prejudice. Experience, roughly, is what you see, and prejudice is what you only think you see. Prejudice tells you that you see the same table on two different occasions; you think that experience tells you this. If it really were experience, you could not be mistaken; yet a similar table may be substituted without altering the experience. If you look at a table on two different occasions, you have very similar sensations, and memory tells you that they are similar; but there is nothing to show that one identical entity causes the two sensations. If the table is in a cinema, you know that there is not such an entity, even though you can watch it changing with apparent continuity. The experience is just like that with a "real" table; so in the case of a "real" table also, there is nothing in the actual experience to show whether there is a persistent entity or not. I say, therefore: I do not know whether there is a persistent entity, but I do know that my experiences can be explained without assuming ​that there is. Therefore it can be no part of legitimate science to assert or deny the persistent entity; if it does either, it goes beyond the warrant of experience.
The following is a verbally cited passage in the letter referred to objecting to what was said above about "force":
"The concept of Force is not of physical but of psychological origin. Rightly or wrongly it arises in the most impersonal contemplation of the Stellar Universe, where we observe an infinite number of spherical bodies revolving on their own axes and gyrating in orbits round each other. Rightly or wrongly, we naturally conceive of these as having been so constituted and so maintained by some Force or Forces."
We do not, in fact, "observe" what it is here said that we observe; all this is inferred. What we observe, in astronomy, is a two-dimensional pattern of points of light, with a few bright surfaces of measurable size when seen through the telescope (the planets), and of course the larger bright surfaces that we call the sun and moon. Most of this pattern (the fixed stars) rotates round the earth once in every twenty-three hours and fifty-six minutes. The sun rotates in varying periods, which average twenty-four hours and never depart very far from the average. The moon and planets have apparent motions which are more irregular. These are the observed facts. There is no logical impossibility about the mediæval doctrine of spheres rotating round the earth, one for each planet and one for the stars. The modern doctrines are simpler, but not one whit more in accordance with observed facts; it is our passion for simple laws that has made us adopt them.
The last sentence of the above quotation raises some further points of interest. "Rightly or wrongly", the writer says, "we naturally conceive of these as having been so constituted and so maintained by some Force or Forces." I do not deny this. It is "natural", and it is "right or wrong"—more specifically, it is wrong. "Force" is part of our love of explanations. Everyone knows about the Hindu who thought that the world does not fall because it ​is supported by an elephant, and the elephant does not fall because it is supported by a tortoise. When his European interlocutor said "But how about the tortoise?" he replied that he was tired of metaphysics and wanted to change the subject. "Force", as an explanation, is no better than the elephant and the tortoise. It is an attempt to get at the "why" of natural processes, not only at the "how". What we observe, to a limited extent, is what happens, and we can arrive at laws according to which observable things happen, but we cannot arrive at a reason for the laws. If we invent a reason, it needs a reason in its turn, and so on. "Force" is a rationalising of natural processes, but a fruitless one since "force" would have to be rationalised also.
When it is said, as it often is, that "force" belongs to the world of experience, we must be careful to understand what can be meant. In the first place, it may be meant that calculations which employ the notion of force work out right in practice. This, broadly speaking, is admitted: no one would suggest that the engineer should alter his methods, or should give up working out stresses and strains. But that does not prove that there are stresses and strains. A medical man works his accounts in guineas, although there are none; he obtains a real payment, though he employs a fictitious coin. Similarly, the engineer is concerned with the question whether his bridge will stand: the fact of experience is that it stands (or does not stand), and the stresses and strains are only a way of explaining what sort of bridge will stand. They are as useful as guineas, but equally imaginary.
But when it is said that force is a fact of experience, there is something quite different that may be meant. It may be meant that we experience force when we experience such things as pressure or muscular exertion. We cannot discuss this contention adequately without going into the relation of physics to psychology, which is a topic we shall consider at length at a later stage. But we may say this much: if you press your finger-tip upon a hard object, you have an experience which you attribute to your finger-tip, ​but there is a long chain of intermediate causes in nerves and brain. If your finger were amputated you could still have the same experience by a suitable operation on the nerves that formerly connected the finger with the brain, so that the force between the finger-tip and the hard object, as a fact of experience, may exist when there is no finger tip. This shows that force, in this sense, cannot be what concerns physics.
As the above example illustrates, we do not, in fact, experience many things that we think we experience. This makes it necessary to ask, without too much assurance, in what sense physics can be based upon experience, and what must be the nature of its entities and its inferences if it is to make good its claim to be empirically grounded. We shall begin this inquiry in the next chapter.