The Analysis of Matter

stimuli can be arranged in an order with respect to corresponding characteristics, but this, by itself, determines only certain logical properties of the stimuli. This applies to all varieties of percepts, and accounts for the fact that our knowledge of physics is mathematical: it is mathematical because no non-mathematical properties of the physical world can be inferred from perception. There is, however, one exception to this limitation, at least apparently. The exception I mean is time. We always assume that the time between percepts is the same as the time in the physical world. I do not know whether this view is correct or not; but I will try to set forth the arguments on either side. In the first place, we must adapt our language to the theory of relativity. I shall assume (what I shall argue in Part III.) that, when we are speaking of physical space, all our percepts are in our head. Consequently psychological time is the same as time measured by our watches, assuming that we carry them on our person. Our head moves along a world-line, and our psychological time-intervals are measured physically by integrating ds along this world-line. Thus there is no difficulty in adapting the statement that psychological and physical time are identical to the requirements of the theory of relativity. In this respect, time differs from space, because physically all our simultaneous percepts are in one place. I think, however, that the time-intervals between percepts are only to be obtained by means of inferences of the same sort as those which lead us to the physical world. Perceived[Pg 254] relations are not between events at different times, but between a percept and a recollection, both of which occur at the same time; or again, where very short times are concerned, between a sensation of maximum vividness and a fading (akoluthic) sensation. Sensations do not decay suddenly, but fade gradually, though very quickly. That is why a quick movement can be apprehended as a whole: the sensations belonging to earlier parts are still present, though less vivid, when the sensations belonging to later parts arise. Thus our knowledge of time seems to be inferred from perceived relations which are not strictly temporal. These relations are, I think, of three sorts. Two sorts have been mentioned: the relation of a vivid to a fading sensation, and the relation of a percept to a recollection. But in addition to these there is an order within recollections: we can recollect a process in the right order. Here, also, however, all that we perceive is in the present, and the time-order of the original events is inferred from relations among the simultaneous events which constitute our present recollection. Thus the conclusion seems to be: Psychological time may be identified with physical time, because neither is a datum, but each is derived from data by inferences of the sort we have found elsewhere, namely, inferences which allow us to know only the logical or mathematical properties of what we infer. Thus it would seem that, wherever we infer from perceptions, it is only structure that we can validly infer; and structure is what can be expressed by mathematical logic, which includes mathematics. Before concluding this discussion, we must consider an extension of the notion of similarity which has considerable importance in relation to the inferences leading to the physical world. In defining similarity, we used a one-one relation . But we may substitute a many-one relation, and still obtain something useful. The importance of this is that, as we have seen, if we take a group of events constituting a physical[Pg 255] object, the relation of the events which are nearer the object to those which are further from it is many-one, not one-one. If we are observing a man half a mile away, his appearance is not changed if he frowns, whereas it is changed for a man observing him from a distance of three feet. Considerable events may happen in the sun without being perceptible to us even with the best telescopes; but near the sun they may have effects which would be important to a percipient situated where these effects occur. It is obvious as a matter of logic that, if our correlating relation is many-one, not one-one, logical inference in the sense in which goes is just as feasible as before, but logical inference in the opposite sense is more difficult. That is why we assume that differing percepts have differing stimuli, but indistinguishable percepts need not have exactly similar stimuli. If we have and , where is many-one, and if and differ, we can infer that and differ; but if and do not differ, we cannot infer that and do not differ. We find often that indistinguishable percepts are followed by different effects—e.g. one glass of water causes typhoid and another does not. In such cases we assume imperceptible differences—which the microscope may render perceptible. But where there is no discoverable difference in the effects, we can still not be sure there is not a difference in the stimuli which may become relevant at some later stage. When the relation is many-one, we shall say that the two systems which it correlates are "semi-similar." This consideration makes all physical inference more or less precarious. We can construct theories which fit the known facts, but we can never be sure that other theories would not fit them equally well. This is an essential limitation on scientific inference, which is generally recognized by men of science: no prudent man of science would maintain that such-and-such a theory is so firmly established that it will never call[Pg 256] for modification. Newtonian gravitation came nearer to this certainty than any other theory has ever done; yet Newtonian gravitation has had to be modified. The fundamental reason for this uncertainty, which remains even when we assume all the canons of scientific inference, is the fact that our relation , which connects the physical object with the percept, is many-one and not one-one. FOOTNOTES: [56] Vol. II., part IV., *150 ff. [Pg 257] CHAPTER XXV PERCEPTION FROM THE STANDPOINT OF PHYSICS HITHERTO we have been taking perception as our starting-point, and considering how physics could be obtained as an inference from perception. In the present chapter, I want to pursue the opposite course, and consider how, assuming physics, percepts can find their place in the physical world. Let us first of all exclude certain problems which are not relevant to this inquiry. A "percept," considered as the epistemological basis of physics, must be a "datum"—it must be something noticed. Obviously, therefore, whatever may be true of percepts in general, those which afford empirical premisses for physics have to be "known." But it is unnecessary for us to define "knowing": for physics, only the percepts are important, and our relation to them may be taken for granted. Similarly we need not consider whether, when we perceive, the occurrence is relational, involving a percept and a percipient, or whether the occurrence of the percept is all that happens at the moment, and its "mental" character is conferred by memory (in its most general sense). Such psychological questions need not concern us. What I wish to discuss is the physical status of percepts, i.e. of patches of colour, noises, smells, hardnesses, etc., as well as perceived spatial relations. And in this discussion I am now assuming ordinary physics, subject to the latitude of interpretation explained in Chapter I. Dr Whitehead's books are a protest against the "bifurcation of nature" which has resulted from the causal theory of perception. With this protest I am in complete agreement. Locke's belief, that the primary qualities belong to the object[Pg 258] and the secondary to the percipient, has been that of science in practice, whatever individual scientific men may have thought in their philosophic moments. The view which I wish to advocate is quite different. I hold that the world is very full of events, that often a group of these events, or some characteristic which the members of the group possess in varying degrees, is such as to suggest arrangement in an order, generally a symmetrical order about a centre—e.g. the percepts of different people when they look at a penny may be ordered by their size and by their shape. The orders derived from different sources are roughly identical: e.g. if we move so as to make the big drum look larger, we also move so as to make it sound louder. In this way we construct a space containing both percipients and physical objects; but percepts have a twofold location in this space, namely that of the percipient and that of the physical object. Keeping one half of this location fixed, we obtain the view of the world from a given place; keeping the other half fixed, we obtain the views of a given physical object from different places. The first of these is a percipient, the second is a physical object. But the first half of this statement is to be taken with a grain of salt. The physical world, I suggest, considered as perceptible, consists of occurrences having this twofold location. For the moment I am concerned to assign the place of perception in such a scheme. Consider a spherical light-wave proceeding from a momentary flash. In vacuo, it advances in accordance with Maxwell's equations, but when it encounters matter it becomes transformed in one way or another according to circumstances. What do I mean by saying that it "encounters matter"? The answer is quite straightforward. Connected with each electron or proton there is a gravitational field and an electromagnetic field; these are displayed by laws modifying the "undisturbed" distribution about other centres of such[Pg 259] things as light-waves. In fact, the fields may be said actually to consist of the formulæ of such modification. Therefore when I say that a light-wave "encounters matter," I mean that it is near the centre of some such systematic modification. The eye is a collection of such centres, and after traversing it the process which was a light-wave obeys a different set of laws. The percept is a term of this process, characterized by the fact that it occurs after traversing a region of a certain sort—to wit, an eye, an optic nerve, and part of a brain. Owing to its causal continuity with other parts of the process, it has, as its twofold location, on the one hand the source of light, on the other hand the brain. If it is said that a percept is "obviously" not in the brain, that is because we are thinking of its location in the physical object, and comparing this with the location of the brain as a physical object. Certain explanations are called for, chiefly in virtue of Dr Broad's criticisms.[57] In the first place, it is suggested that the above theory takes a common-sense view of the percipient's body, and derives from this an undue plausibility for the view which it suggests as to external objects. This is not the case, but in order to dispel the appearance of such an error it is necessary to explain the twofold character of a physical object. On the one hand, it is a group of "appearances"—i.e. of connected events—differing, from next to next, approximately according to the laws of perspective. On the other hand, a physical object has an influence upon the appearances of other objects, especially appearances in its neighbourhood, causing these to depart, in a greater or less degree, from what they would be if they followed the laws of perspective strictly. The sense organs have only this second function to perform in the theory of perception, while the object perceived has the first function. It is this difference of function, in the theory of perception, which makes it seem as if we were treating the[Pg 260] percipient's body more realistically than external objects. But this is