Philosophy

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 seem “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 true 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.8 8 These objections are quoted (with kind permission) from a letter written to me by a well-known engineer, Mr. Percy Griffith, who is also a writer on philosophical subjects. “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