The Analysis of Matter

weeks of life) there is a large element of interpretation due to past experience, and this element is subjective when the present situation does not contain the correlations whose past occurrence has caused the interpretation. All these sources of error have to be guarded against if perception is not to mislead us. The ways of guarding against them are those suggested by common sense and perfected by science; they are all such as to substitute laws with few or no exceptions for laws with a comparatively large number of exceptions. It will be seen that very little can be inferred with confidence from a single percept; we need observation from different points of view, and throughout a certain period of time. It is true that we shall usually be right in what we infer from a single percept, but that is because the objects[Pg 226] that surround us mostly belong to familiar kinds—men, horses, motor-cars, etc. But it would not be difficult to construct situations which would deceive at the first glance, especially if we could be suddenly transported into a quite unfamiliar world, like Wells's Martians. Water, for example, would completely puzzle a person who had never seen a liquid, if such a person could exist. In this matter, as elsewhere, we proceed step by step from the easy but precarious inferences of common sense to the difficult but more reliable inferences of science. Where the intervening medium is relevant in inferring other members of a group from a percept, it is obvious that the single percept is theoretically inadequate as a basis for inference, since, by a change in the medium, the same percept might be associated with a different group. In this case, the distorting element in the medium may be directly discovered by other percepts—e.g. glass may be touched—or it may be merely inferred by examining the way in which percepts belonging to one group change from place to place—e.g. refraction in air. When it has been inferred, the inference needs to be tested by examining whether it has further consequences which can be verified. All this is a commonplace. It remains to say something about the inference from percepts to events which no one perceives. It is not its validity that I wish to examine now, but its scope—i.e. how much we can know about unperceived events, assuming the causal theory of perception. It is sometimes urged that an unperceived cause of a perception must be a mere Ding-an-sich or Spencerian Unknowable. This seems to me only very partially true, if we accept the usual canons of scientific inference. We assume that differences in percepts imply differences in stimuli—i.e. if a person hears two sounds at once, or sees two colours at once, two physically different stimuli have reached his ear or his eye. This principle,[Pg 227] together with spatio-temporal continuity, suffices to give a great deal of knowledge as to the structure of stimuli. Their intrinsic characters, it is true, must remain unknown; but we may assume that the stimuli causing us to hear notes of different pitches form a series in respect of some character which corresponds causally with pitch, and we may make similar assumptions in regard to colour or any other character of sensations which is capable of serial arrangement. And we can without difficulty extend geometry to the world outside our perceptions, although the space of that world will only correspond to the space of perception in certain respects, and will be by no means identical with the space of perception. What we assume is, formally, something like this: there is a roughly one-one relation between stimulus and percept—i.e. between the events just outside the sense-organ and the event which we call a perception. This enables us to infer certain mathematical properties of the stimulus when we know the percept, and conversely enables us to infer the percept when we know these mathematical properties of the stimulus Consequently, except when we are studying physiology or psychology, we may suppose that what is happening in a place is what a person would perceive in that place, provided we use, in inference, only those properties of the percept which it shares with the stimulus. E.g. we must not use the blueness of blue, but we may use its difference from red or yellow. We cannot argue that because a picture looks beautiful, therefore there is beauty in the system of stimuli, because beauty may depend upon the actual qualities.[49] But nothing in physical science ever depends upon the actual qualities. Hence for practical purposes in physics the difference between percept and stimulus only compels us to confine ourselves to the structural properties of percepts; so long as we do this,[Pg 228] we need hardly trouble to remember that percept and stimulus are different. In physiology and psychology this does not hold, since we are concerned with the process intervening between stimulus and perception, or with perception itself. Even in physics, it does not hold strictly, because the relation of stimulus and perception is not strictly one-one. It is only approximately so, even when we confine ourselves to stimuli to a given sense of a given person at a given time— e.g. two colours which I perceive side by side. Even here, vagueness comes in, so that slightly different stimuli may give indistinguishable perceptions. This constitutes an essential limitation to our knowledge, enshrined in the notion of "probable error." It can, however, be reduced to a minimum by the usual methods and constitutes, therefore, rather a practical difficulty than a theoretical problem. FOOTNOTES: [49] If we accepted the theory that beauty depends only upon "significant form," we should have to say that a musical score is as beautiful as the music which it represents. [Pg 229] CHAPTER XXII THE BELIEF IN GENERAL LAWS THROUGHOUT out discussion of perception and the physical object, we have assumed the validity of general laws. This is always assumed in scientific practice, but the reasons for assuming it are not very dear. Although the subject is not one on which it is easy to say anything definite, yet it seems necessary to examine it. Like other scientific postulates, the belief in general laws is rooted in the properties of nervous tissue—the same properties which make us believe in induction and enable us to learn from experience. This origin, of course, affords no warrant for the truth of the belief, but equally gives no reason against it. Indeed, so far as it goes, it affords a slight presumption in favour of the view that a great many events are in accordance with general laws, since it shows that animals which act in a way which the truth of this belief would render rational can survive. I should not wish, however, to lay stress upon such an argument. When we first begin to think, we find ourselves acting in certain ways which seem to succeed, and we set to work to rationalize our behaviour. The natural way to do this is to say: Things always happen that way. This so often succeeds that we acquire the habit of always supposing that there is some general law according to which any particular event has occurred. This belief has two practical consequences. First, when a set of events are all in accordance with some law, we expect other similar events to be in accordance with it. Secondly, when a set of events appears irregular, we invent hypotheses to regularize it. Both procedures are important. [Pg 230] The first of these procedures is simply induction. As such, it is fundamental, in some form or other, and I propose to say no more about it. The second is more interesting for our purposes. When an induction fails in a surprising way—e.g. when there is an eclipse—there are two things which a primitive man may do. He may regard the failure as a "portent," in no way invalidating the general validity of the induction, but showing that there is something strange, and probably terrifying, in the special circumstances connected with the astonishing event. Or he may look for some general law different from that which has hitherto proved adequate, in the hope that the new law may account for the exceptional occurrence as well. The latter course will seldom be adopted until a high degree of intellectual culture has been attained. If the odd event is on a large scale, it will be considered superstitiously, and if not, it will be simply ignored. Sometimes, however, a general law is found by accident, as a result of the careful records inspired by superstition. This evidently happened with the Egyptian priesthood, who learnt to predict eclipses, and probably only then ceased to regard them with awe. Gradually, the view that there must be some law according to which strange things happened became more widespread. Dr Whitehead, in his Science and the Modern World[50] traces the belief in natural laws to various sources, such as: Fate in Greek tragedy, the supremacy of Roman law, and the rationality of God in mediæval theology. In effect, however, he regards the belief as having only acquired a firm hold of the scientific mind at the renaissance. Everything that he says on this subject is so excellent that it is unnecessary to cover the ground again. Although the belief in the universality of natural law was, at the time of the renaissance, a bold faith going far in advance of the evidence, it has since been so successful that it is now[Pg 231] possible to defend it on inductive grounds. But there is some difficulty in deciding what we are to mean by it. I have dealt with this subject before,[51] and shall now consider it only briefly. The regularities which we first observe, and in which we first believe, are of the simple form: " is always accompanied (or preceded or succeeded) by ." But all such regularities are capable of having exceptions, and science soon seeks laws of a different kind. We arrive in the end (possibly not at the very end) at differential equations. I think that these are of two kinds, those expressing persistence, and those expressing accelerations (in a generalized sense). The former are concealed, more or less, by the assumption of permanent substance; but this is a topic which I shall consider in the next chapter. The latter are the ordinary differential equations of the second order which occur throughout mathematical physics. But in addition to these, in order to produce observed macroscopic results, there must be statistical laws governing quantum changes and radio-active disruptions of atoms. I want to inquire whether we are saying anything significant in assuming that there are laws governing the course of the physical world, or whether any set of percepts must be amenable to law by a sufficiently liberal use of hypothesis. It is by no means clear that the accepted laws of physics make certain imaginable series of percepts impossible; still less that the mere existence of laws would have this effect. Take, e.g. continuity. Changes which appear sudden (e.g. explosions) can be resolved into a number of continuous though rapid changes: per contra, situations in which there appears to be no change (e.g. a steadily glowing gas) are resolved into a number of discontinuous changes. Thus we can neither infer the absence of physical continuity from the absence of[Pg 232] continuity in percepts, nor the presence of physical continuity from the presence of continuity in percepts. Again: if percepts change in unexpected ways, we infer unperceived matter; and by a sufficient amount of unperceived matter almost any series of percepts could be explained. Of course a particular law is strengthened when it enables us to predict percepts, but this belongs to the arguments in favour of such-and-such laws, not to the arguments in favour of laws in general. We can have evidence