The Analysis of Matter

In drawing inferences from percepts to their causes, we assume that the stimulus must possess whatever structure is possessed by the percept, though it may also have structural properties not possessed by the percept. The assumption that the structural properties of the percept must exist in the stimulus follows from the maxim "same cause, same effect" in the inverted form "different effects, different causes," from which it follows that if, e.g., we see red and green side by side, there is some difference between the stimulus to the red percept and the stimulus to the green percept. The structural features possessed by the stimulus but not by the percept, when they can be inferred, are inferred by means of general laws—e.g. when two objects look similar to the naked eye but dissimilar under the microscope, we assume that there are differences in the stimuli to the naked-eye percepts which produce either no differences, or no perceptible differences, in the corresponding percepts. These principles enable us to infer a great deal as to the structure of the physical world, but not as to its intrinsic character. They put percepts in their place as occurrences analogous to and connected with other events in the physical world, and they enable us to regard a dictaphone or a photographic plate as having something which, from the standpoint of physics, is not very dissimilar from perception. We no longer have to contend with what used to seem mysterious in the causal theory of perception: a series of light-waves or sound-waves or what not suddenly producing a mental event apparently totally different from themselves in character. As to intrinsic character, we do not know enough about it in the physical world to have a right to say that it is very different from that of percepts; while as to structure we have reason to hold that it is similar in the stimulus and the percept. This has become possible owing to the facts that "matter" can be[Pg 401] regarded as a system of events, not as part of the stuff of the world, and that space-time, as it occurs in physics, has been found to be much more different from perceptual space than was formerly imagined. This brings us to Part III., in which we endeavour to discover a possible structure of the physical world which shall at once justify physics and take account of the connection with perception demanded by the necessity for an empirical basis for physics. Here we are concerned first with the construction of points as systems of events which overlap, or are "co-punctual," in space-time, and then with the purely ordinal properties of space-time. The method employed is very general, and can be adapted to a discrete or to a continuous order; it is proved that , events are sufficient to generate a continuum of points, given certain laws as to the manner of their overlapping. The whole of this theory, however, aims only at constructing such properties of space-time as belong to analysis situs; everything appertaining to intervals and metrics is omitted at this stage, since causal considerations are required for the theory of intervals. The conception of one unit of matter—say one electron—as a "substance," i.e. a single simple entity persisting through time, is not one which we are justified in adopting, since we have no evidence whatever as to whether it is false or true. We define a single material unit as a "causal line," i.e. as a series of events connected with each other by an intrinsic differential causal law which determines first-order changes, leaving second-order changes to be determined by extrinsic causal laws. (In this we are for the moment ignoring quantum phenomena.) If there are light-quanta, these will more or less fulfil this definition of matter, and we shall have returned to a corpuscular theory of light; but this is at present an open question. The whole conception of matter is less fundamental to physics than it used to be, since energy has more and more[Pg 402] taken its place. We find that under terrestrial conditions electrons and protons persist, but there is nothing in theoretical physics to lead us to expect this, and physicists are quite prepared to find that matter can be annihilated. This view is even, put forward to account for the energy of the stars. The question of interval presents great difficulties, when we attempt to construct a picture of the world which shall make its importance seem not surprising. The same may be said of the quantum. I have endeavoured, not, I fear, with much success, to suggest hypotheses which would link these two curious facts into one whole. I suggest that the world consists of steady events accompanied by rhythms, like a long note on the violin while arpeggios are played on the piano, or of rhythms alone. Steady events are of various sorts, and many sorts have their appropriate rhythmic accompaniments. Quantum changes consist of "transactions," i.e. of the substitution, suddenly, of one rhythm for another. When two events have a time-like interval, if space-time is discrete, this interval is the greatest number of transitions on any causal route leading from the one event to the other. The definition of space-like intervals is derived from that of time-like intervals. The whole process of nature may, so far as present evidence goes, be conceived as discontinuous; even the periodic rhythms may consist of a finite number of events per period. The periodic rhythms are required in order to give an account of the uses of the quantum principle. A percept, at any rate when it is visual, will be a steady event, or system of steady events, following upon a transaction. Percepts are the only part of the physical world that we know otherwise than abstractly. As regards the world in general, both physical and mental, everything that we know of its intrinsic character is derived from the mental side, and almost everything that we know of its causal laws is derived from the physical side. But from the standpoint of philosophy the distinction between physical and mental is superficial and unreal.