The Analysis of Matter

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 and and [Pg 281] are percepts, and the difference between and is a percept, there is no reason why the differences between and and between and should be percepts: the relations between percepts are sometimes percepts and sometimes not. Now, instead of different static shades of colour, let us suppose that we are watching a chameleon gradually changing. We may be quite unable to "see" a process of change, and yet able to know that, after a time, a change has taken place. This will occur if, supposing and to be the shades at the beginning and end of a specious present, and are indistinguishable, while A recollected is distinguishable from when occurs. The supposition we have to make about a perceived motion is not quite analogous to this, but has certain points in common with it. Suppose that we are perceiving a motion in a case where we know the physical stimulus to consist of a discrete series, as in the cinema. Let us suppose that of these stimuli can be comprised within one specious present, and that each produces an element in the percept. Then the percept at one instant consists of elements , , ... , which are arranged in an order by the degree of fading. Let us suppose that we cannot distinguish from nor from , but that we can distinguish from . In that case our present percept will be indistinguishable from the percept of a continuous motion. The percept will in fact contain parts that are not processes, but these parts will be imperceptible. The analogy with the case of the colours arises through the existence, in each case, of a series in which differences of neighbouring terms are imperceptible while those of distant terms are perceptible. And it elicits the important principle that a percept may have parts which are not percepts, so that the structure of a percept may be only discoverable by inference. It follows also that we need not assume anything mysterious about the kind of complexity belonging to a percept of motion, but may regard its complexity[Pg 282] as of the same kind as that belonging to the stimulus according to mathematical physics. I wish now to consider the general question: how can we infer structure when it is not perceived? The above discussion of motion involved a particular case of such inference, but now I wish to consider the problem more generally. For reasons analogous to those which arise in analyzing motion, we are led to the view that all our percepts are composed of imperceptible parts. We can, for instance, perceive a heap of fine powder, and remove the whole heap grain by grain, where at each stage there is no perceptible difference. Our original percept may have had perceptible parts, but these were apparently always complex. It is not strictly necessary to suppose the percepts complex; they might form a series of gradually varying quality. But we may say, in a sense, that the difference of and (supposed perceptible) is compounded of the differences between and , and (supposed imperceptible). Thus we arrive at virtually the same result in regard to qualitative differences as we have otherwise in regard to substantial parts. All such arguments rest ultimately upon the logical premiss that exact similarity is transitive, and the empirical premiss that indistinguishability is not transitive. These two together are the source of much of our inference as regards structure. There is, however, another source, derived from causal arguments. Two indistinguishable percepts are found to be followed by different results. Inverting the maxim "same cause, same effect," we argue: "Different effects, different causes." Often the difference in the causes becomes perceptible under the microscope; but we assume it in any case. It is this, more than anything else, that has led to the minuteness of the processes inferred by physics. There are noticeable differences in the effects in cases where we know that the difference in the causes, if any, must be very small; we are[Pg 283] therefore compelled to attribute to the physical world a structure which is very fine-grained relatively to perception. It is necessary to consider the very usual form of analysis into diversity of "substance," because, for reasons already given, we cannot regard this form of analysis as ultimate. Let us take the most elementary of scientific examples: the analysis of water into hydrogen and oxygen. We recognize water by a group of characteristic percepts and processes; by another group we recognize hydrogen, and by yet another oxygen. We find that we can—e.g. by electrolysis—produce hydrogen and oxygen where formerly there was water; we find that the masses of the two bear a fixed proportion to each other, and add up to the mass of the previous water; we find further that, if we let them come together, water reappears, equal in amount to what was lost by electrolysis. Such facts are interpreted in science by means of the postulate that matter is indestructible. If we accept this postulate, the facts prove that water consists of hydrogen and oxygen. Exactly similar arguments lead us on from atoms to electrons and protons, where, for the present, the process of substantial analysis ceases. Without questioning the convenience of substantial analysis, it may be asked whether it is metaphysically