A minimal event occupies a finite region in space-time. Let us take time alone for purposes of illustration. The event in question may overlap in time with each of two others, although the first of these others wholly precedes the second; for example, you may hear a long note on the violin while you hear two short notes on the piano. (It is not necessary to suppose that these are really minimal events; I merely want to illustrate what is meant.) I assume that every event is contemporaneous with events that are not contemporaneous with each other; this is what is meant by saying that every event lasts for a finite time, as the reader can easily convince himself if he remembers that time is wholly relational. If we look away from the world of physics for a moment, and confine ourselves to the world of one man’s experience, we can easily define an “instant” in his life. It will be a group of events, all belonging to his experience, and having the following two properties: (1) any two of the events overlap; (2) no event outside the group overlaps with every member of the group. By a slightly more complicated but essentially similar method, we can define a point-instant in space-time as a group of events having two properties analogous to those used just now in defining an “instant” in one biography.[13] Thus the “points” (or point-instants) that the mathematician needs are not simple, but are structures composed of events, made up for the convenience of the mathematician. There will be many “points” of which a given minimal event is a member; all these together make up the region of space-time occupied by that event. Space-time order, as well as space-time points, results from the relations between events.
[13] See The Analysis of Matter, by the present author, chap. xxviii.
A piece of matter, like a space-time point, is to be constructed out of events, but the construction is considerably more complicated, and in the end is only an approximation to what the physicist supposes to be really taking place. There are, at the moment, two somewhat different views of matter, one appropriate to the study of atomic structure, the other to the general theory of relativity as affording an explanation of gravitation. The view appropriate to atomic structure has itself two forms, one derived from Heisenberg, the other from De Broglie and Schrödinger. These two forms, it is true, are mathematically equivalent, but in words they are very different. Heisenberg regards a piece of matter as a centre from which radiations travel outward; the radiations are supposed really to occur, but the matter at their centre is reduced to a mere mathematical fiction. The radiations are, for example, such as constitute light; they are all avowedly systems of events, not changes in the conditions or relations of “substances.” In the De Broglie-Schrödinger system, matter consists of wave motions. It is not necessary to the theory to postulate anything about these wave-motions except their mathematical characteristics, but, obviously, since they are to explain matters they cannot serve their purpose if they consist of motions of matter. In this system also, therefore, we are led to construct matter out of systems of events, which just happen, and do not happen “to” matter or “to” anything else.
Gravitation, as explained by the general theory of relativity, is reduced to “crinkles” in space-time. Space-time being, as we have already seen, a system constructed out of events, the “crinkles” in it are also derived from events. There is no reason to suppose that there is a “thing” at the place where the “crinkle” is most crinkly. Thus in this part of physics, also, matter has ceased to be a “thing” and has become merely a mathematical characteristic of the relations between complicated logical structures composed of events.
It was traditionally a property of substance to be permanent, and to a considerable extent matter has retained this property in spite of its loss of substantiality. But its permanence now is only approximate, not absolute. It is thought that an electron and a proton can meet and annihilate each other; in the stars this is supposed to be happening on a large scale.[14] And even while an electron or a proton lasts, it has a different kind of persistence from that formerly attributed to matter. A wave in the sea persists for a longer or shorter time: the waves that I see dashing themselves to pieces on the Cornish coast may have come all the way from Brazil, but that does not mean that a “thing” has travelled across the Atlantic; it means only that a certain process of change has travelled. And just as a wave in the sea comes to grief at last on the rocks, so an electron or a proton may come to grief when it meets some unusual state of affairs.
[14] See The Analysis of Matter, by the present author, chap. xxviii.
Thus “matter” has very definitely come down in the world as a result of recent physics. It used to be the cause of our sensations: Dr. Johnson “disproved” Berkeley’s denial of matter by kicking a stone. If he had known that his foot never touched the stone, and that both were only complicated systems of wave-motions, he might have been less satisfied with his refutation. We cannot say that “matter” is the cause of our sensations. We can say that the events which cause our sensations usually belong to the sort of group that physicists regard as material; but that is a very different thing. Impenetrability used to be a noble property of matter, a kind of Declaration of Independence; now it is a merely tautological result of the way in which matter is defined. The events which are the real stuff of the world are not impenetrable, since they can overlap in space-time. In a word, “matter” has become no more than a convenient shorthand for stating certain causal laws concerning events.
But if matter has fared badly, mind has fared little better. The adjective “mental” is one which is not capable of any exact significance. There is, it is true, an important group of events, namely percepts, all of which may be called “mental”. But it would be arbitrary to say that there are no “mental” events except percepts, and yet it is difficult to find any principle by which we can decide what other events should be included. Perhaps the most essential characteristics of mind are introspection and memory. But memory in some of its forms is, as we have seen, a consequence of the law of conditioned reflexes, which is at least as much physiological as psychological, and characterises living tissue rather than mind. Knowledge, as we have found, is not easy to distinguish from sensitivity, which is a property possessed by scientific instruments. Introspection is a form of knowledge, but turns out, on examination, to be little more than a cautious interpretation of ordinary “knowledge”. Where the philosopher’s child at the Zoo says “There is a hippopotamus over there”, the philosopher should reply: “There is a coloured pattern of a certain shape, which may perhaps be connected with a system of external causes of the sort called a hippopotamus”. (I do not live up to this precept myself.) In saying that there is a coloured pattern, the philosopher is practising introspection in the only sense that I can attach to that term, i.e. his knowledge-reaction is to an event situated in his own brain from the standpoint of physical space, and is consciously avoiding physiological and other inference as far as possible. Events to which a knowledge-reaction of this sort occurs are “mental”; so are, presumably, other events resembling them in certain respects. But I do not see any way of defining this wider group except by saying that mental events are events in a living brain, or, better, in a region combining sensitivity and the law of learned reactions to a marked extent. This definition has at least the merit of showing that mentality is an affair of causal laws, not of the quality of single events, and also that mentality is a matter of degree.
Perhaps it is not unnecessary to repeat, at this point, that events in the brain are not to be regarded as consisting of motions of bits of matter. Matter and motion, as we have seen, are logical constructions using events as their material, and events are therefore something quite different from matter in motion. I take it that, when we have a percept, just what we perceive (if we avoid avoidable sources of error) is an event occupying part of the region which, for physics, is occupied by the brain. In fact, perception gives us the most concrete knowledge we possess as to the stuff of the physical world, but what we perceive is part of the stuff of our brains, not part of the stuff of tables and chairs, sun, moon, and stars. Suppose we are looking at a leaf, and we see a green patch. This patch is not “out there” where the leaf is, but is an event occupying a certain volume in our brains during the time that we see the leaf. Seeing the leaf consists of the existence, in the region occupied by our brain, of a green patch causally connected with the leaf, or rather with a series of events emanating from the place in physical space where physics places the leaf. The percept is one of this series of events, differing from the others in its effects owing to the peculiarities of the region in which it occurs—or perhaps it would be more correct to say that the different effects are the peculiarities of the region.
Thus “mind” and “mental” are merely approximate concepts, giving a convenient shorthand for certain approximate laws. In a completed science, the word “mind” and the word “matter” would both disappear, and would be replaced by causal laws concerning “events”, the only events known to us otherwise than in their mathematical and causal properties being percepts, which are events situated in the same region as a brain and having effects of a peculiar sort called “knowledge-reactions”.