The Analysis of Matter

in virtue of some elaborate argument, whether our percepts are static or rhythmical, nor yet whether their physical stimuli are continuous or discrete. Such knowledge is rendered impossible by the fact that we can only assume semi-similarity, not full similarity, between percept and stimulus. There is therefore no difficulty in the accepted theory that the stimuli to our most important percepts are rapid periodic processes. On the other hand, there is a great advantage in this theory, in that it simplifies the physical world which has to be assumed as the cause of our perceptions. A physical system, conceived merely as a set of material units in space-time, is capable of an indefinite variety of rhythmic movements. Some physical structures are resonant for one period, some for another. Thus our sense-organs can select one sort of movement as the stimulus to which they will respond, and[Pg 270] reject all the rest. In fact, it may be said that the essential characteristic of a sense-organ is sensitiveness to one sort of stimulus, which, in the case of the eye or the ear, must be a periodic movement. In this the sense-organs do not differ from lifeless instruments, such as photographic plates and gramophones. Such instruments have something closely analogous to perception, when we leave out of account the mental consequences which we observe in ourselves as a result of perception. And in a certain extended sense we may say that every body which behaves in a characteristic manner when a certain stimulus is present, and only then, has a "perception" of that stimulus. We can infer the stimulus from the behaviour of such a body just as well as from our own percepts—sometimes better, as in the case of a very sensitive photographic plate. The outcome of the discussion we have been conducting in Part II. has been to justify the ordinary scientific attitude, and to minimize the gulf which seems at first sight to exist between perception and physics. We have seen that the inference from percepts to unperceived physical events, though it cannot be made mathematically cogent, is quite as good as any inductive inference can hope to be. And we have found that there is no ground in philosophy for supposing the physical world to be very different from what physics asserts it to be. But we have found it necessary to emphasize the extremely abstract character of physical knowledge, and the fact that physics leaves open all kinds of possibilities as to the intrinsic character of the world to which its equations apply. There is nothing in physics to prove that the physical world is radically different in character from the mental world. I do not myself believe that the philosophical arguments for the view that all reality must be mental are valid. But I also do not believe that any valid arguments against this view are to be derived from physics. The only legitimate attitude about the physical[Pg 271] world seems to be one of complete agnosticism as regards all but its mathematical properties. However, something can be done in the way of constructing possible physical worlds which fulfil the equations of physics and yet resemble rather more closely the world of perception than does the world ordinarily presented in physics. Such constructions have the merit of making the inference from perception to physics seem more reliable, since they save us from the necessity of assuming anything radically different from what we know. From this point of view, they have a certain interest, and I shall partially develop them, at least as regards space-time, in Part III. But they must not be confounded with scientific knowledge: they are hypotheses which may hereafter prove fruitful, and which have already a certain imaginative value. But they are not to be regarded as necessitated by any recognized principle of scientific inference. [Pg 273] PART III THE STRUCTURE OF THE PHYSICAL WORLD [Pg 275] CHAPTER XXVII PARTICULARS AND EVENTS WE shall be concerned, in what follows, with the construction of a map of the physical world, in part more or less conjectural, but never in contradiction to the physical or epistemological results hitherto considered. We shall seek to construct a metaphysic of matter which shall make the gulf between physics and perception as small, and the inferences involved in the causal theory of perception as little dubious, as possible. We do not want the percept to appear mysteriously at the end of a causal chain composed of events of a totally different nature; if we can construct a theory of the physical world which makes its events continuous with perception, we have improved the metaphysical status of physics, even if we cannot prove more than that our theory is possible. In what follows, some portions will be more conjectural than others, but I shall try to indicate, at each stage, whether I am advancing what I believe to be a well-grounded inference by induction and analogy, or whether I am concerned only with an illustrative hypothesis designed to exhibit the possibilities that are compatible with the abstract scientific knowledge to be derived from physics. We have found, hitherto, that what we know of the physical world falls into two parts: on the one hand, the concrete but disjointed knowledge of percepts; on the other hand, the abstract but systematic knowledge of the physical world as a whole. Certain questions as to structure are answered by physics, while others are left open. The questions which are left open are of a sort of which some must always remain open—namely. Is any further analysis of the terms which are[Pg 276] ultimate for physics possible, and, if so, what means exist of conjecturing its nature? In science, we have evidence of structure down to a certain point, while beyond that point we have no evidence. There can never be evidence that the point we have reached is one beyond which there is no structure—i.e. that we have arrived at simple units totally devoid of parts; therefore analysis is essentially incapable of reaching a term known to be final, even if it has in fact reached a final term. I think that, in the case of physics, there is reason to think that its terms are not final, and that it is possible to suggest a further analysis which is at least likely to be true. When we wish to describe a structure, we have to do so by means of terms and relations. It may turn out that the terms themselves have a structure, as, e.g., in arithmetic, when cardinal integers are defined as classes of similar classes. In the technique of mathematical physics, there is a considerable apparatus which belongs to the formal method, and would not be regarded by most physicists as having any physical reality. Such is the manifold of space-time points. Space-time is held to represent a system of physical facts, but its mathematical points are generally conceded to be fictions. Such a state of affairs is unsatisfactory until we can say just what non-fictional assertion is implicit in a true proposition of physics which technically uses "points." I propose to deal with this problem in the next chapter. But what shall we say of electrons? Are they physical realities, or are they mathematical conveniences, like points? Or are they something intermediate between these two extremes? We think of a light-ray as a series of events; is an electron perhaps something similar? But the light-ray also raises problems: it has a certain assigned mathematical structure, but it is difficult to say what we axe to think of the mathematical terms of this structure. Formerly, the conception of a transverse wave in the æther seemed fairly clear:[Pg 277] the æther was composed of particles, each of which could move in the required manner. But nowadays the æther is grown insubstantial and incapable of "motion" in any straightforward sense; certainly few people would venture to regard it as composed of point-particles, like the homogeneous fluid of a hydrodynamical text-book. Thus the light-wave has become a structure in the air, like a genealogical tree whose members are all imaginary. This illustrates a necessity in describing a structure: the terms are as important as the relations, and we cannot rest content with terms which we believe to be fictitious. It is the terms of the physical structure that will concern us in the present chapter. I shall give the name "particulars" to the ultimate terms of the physical structure—ultimate, I mean, in relation to the whole of our present knowledge. A "particular," that is to say, will be something which is concerned in the physical world merely through its qualities or its relations to other things, never through its own structure, if any. The difference between a transverse wave and a longitudinal wave is a difference of structure; therefore neither can be a "particular" in the technical sense in which I mean it. An atom is a structure of electrons and protons; therefore an atom is not a "particular." But when I call something a "particular," I do not mean to assert that it certainly has no structure; I assert only that nothing in the known laws of its behaviour and relations gives us reason to infer a structure. From the standpoint of logic, a particular fulfils the definition of "substance" which we gave in Chapter XXIII. But it fulfils this definition only in the existing state of knowledge; further discoveries may require us to recognize structure within it, and it will then cease to fulfil the definition of substance. This does not falsify former statements as to the structure of the world, in which the particular in question was taken as unanalyzable; it merely adds new propositions, in which it is no[Pg 278] longer so treated. Atoms were formerly particulars; now they have ceased to be so. But that has not falsified the chemical propositions which can be enunciated without taking account of their structure. The word "particular," as above defined, is, therefore, a word relative to our knowledge, not an absolute metaphysical term. Let us begin with a few general considerations as to our knowledge of structure. Part of this knowledge is obtainable by analysis of percepts, part depends upon inferences involving unperceived entities. I shall call a relation "perceived" or "perceptual" if the fact that this relation holds between certain terms can be discovered by mere analysis of percepts. Thus before-and-after is a perceptual relation, when it occurs between terms both of which belong to the specious present. Spatial relations within the visual field are perceptual; so are those between simultaneous tactual sensations in different parts of the body. Tactual sensations in the same part of the body, say a finger-tip, may have perceived relations, if both are within the specious present; these must be important in the recognition of shape by blind people. There are perceived relations between a percept and a recollection, which lead us to refer the latter to the past. There are perceived relations of comparison, which may sometimes be rather complicated—e.g. "The resemblance of blue and green is greater than the resemblance of blue and yellow." (Here the blue and green and yellow are supposed to be particular given patches of colour.) There is also, I should say, a perceived relation of simultaneity. I do not suggest that the above list is complete, but it indicates the kinds of cases in which relations can be perceived. There is a well-advertised type of difficulty in such cases as the analysis of a perceived motion. If I move my hand before my eyes from left to right, and attend to the visual percept, it seems qualitatively different from the successive[Pg 279] perceptions of my hand in a number of different positions. On a watch, we can "see" the motion of the second hand, but not of the minute hand. There is no doubt that there is an occurrence which we naturally