The Analysis of Matter

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 describe as the perception of a motion. We are aware of perceiving a process: if I move my hand from left to right, the impression is different from what it is if I move my hand from right to left, and it is obvious to everyone that the difference is in the "sense" of the motion. We can, in fact, distinguish earlier and later parts of the motion, so that the motion does not appear to be without structure. But the parts of it seem to be other motions, which, presumably, must each have its own structure. This leads to the notion of infinite divisibility, not based upon a definable structure of indivisibles, but upon a process in which the parts are always composed of parts similar in structure to themselves, and simple parts are nowhere attainable. The paradoxes of motion, the antinomies, Bergson's objection to analysis, and the philosophers' insistence that the Cantorian continuum does not resolve their difficulties, are all derived from this one puzzle, that a motion seems to consist of motions—or, as Kant says, that a space consists of spaces. It is important to clear up this problem of the analysis of the percept of motion, since it applies to all perception of change, and has been thought to constitute a difficulty in the attempt to harmonize psychology and physics. To begin with, continuity in the percept is no evidence of continuity in the physical process; it is easy to produce a staccato process which causes a continuous (or apparently continuous) percept—e.g. in the cinema. Next, it is noteworthy that, if a staccato physical process is gradually accelerated, the percept will retain its staccato character longer if we are wide awake and have acute senses than if we are sleepy or have feeble senses. Everybody knows the experience of being awakened from a doze by a striking clock: at first, the noise of the strike seems[Pg 280] continuous. It is therefore a tenable hypothesis, if desirable on other grounds, to maintain that all physical processes are staccato, and continuity in percepts is merely a case of vagueness, in the sense of a many-one relation between stimulus and percept. I am not asserting such a view; I am only saying that it fits in with what we know of the relation between stimulus and percept in the case of swift processes. A fortiori, the mathematical continuum, if it existed in the stimulus process, would produce the percepts we call continuous. There is therefore nothing in our perception of process to make us feel that the mathematical analysis of continuity must be inadequate to physics, nor yet to show that a quantized time and space could not produce the sort of percepts which we call "seeing a motion." All physical possibilities are left open, so far as the immediate character of the percept is concerned. The argument advanced by those who lay stress upon the perceived character of perceptual continuity is, however, not as to the nature of the physical stimulus, but as to the nature of the percept. The continuity of the percept, they maintain, is quite obviously not that of the mathematical continuing nor yet the deceptive appearance of continuity which would exist if the percept were a rapid staccato process. In saying this, they seem to me to go beyond what the evidence warrants. Consider a case which is analogous in some respects, but not in others—namely, the case of slightly different shades of colour. Suppose we have a series of colours, A, , , , ... such that each is sensibly indistinguishable from its neighbour, but not from the rest. That is to say, we can see no difference between and or between and , but we can see a difference between and . We are then compelled to infer a difference between and and between and , although we cannot perceive any difference. There is no theoretical difficulty in such an inference, for, although