Although we cannot rest content with the above theory, in the terms in which it is stated, we must nevertheless treat it with a certain respect, for it is in outline the theory upon which physical science and physiology are built, and it must, therefore, be susceptible of a true interpretation. Let us see how this is to be done.
The first thing to realise is that there are no such things as “illusions of sense.” Objects of sense, even when they occur in dreams, are the most indubitably real objects known to us. What, then, makes us call them unreal in dreams? Merely the unusual nature of their connection with other objects of sense. I dream that I am in America, but I wake up and find myself in England without those intervening days on the Atlantic which, alas! are inseparably connected with a “real” visit to America. Objects of sense are called “real” when they have the kind of connection with other objects of sense which experience has led us to regard as normal; when they fail in this, they are called “illusions.” But what is illusory is only the inferences to which they give rise; in themselves, they are every bit as real as the objects of waking life. And conversely, the sensible objects of waking life must not be expected to have any more intrinsic reality than those of dreams. Dreams and waking life, in our first efforts at construction, must be treated with equal respect; it is only by some reality not merely sensible that dreams can be condemned.
Accepting the indubitable momentary reality of objects of sense, the next thing to notice is the confusion underlying objections derived from their changeableness. As we walk round the table, its aspect changes; but it is thought impossible to maintain either that the table changes, or that its various aspects can all “really” exist in the same place. If we press one eyeball, we shall see two tables; but it is thought preposterous to maintain that there are “really” two tables. Such arguments, however, seem to involve the assumption that there can be something more real than objects of sense. If we see two tables, then there are two visual tables. It is perfectly true that, at the same moment, we may discover by touch that there is only one tactile table. This makes us declare the two visual tables an illusion, because usually one visual object corresponds to one tactile object. But all that we are warranted in saying is that, in this case, the manner of correlation of touch and sight is unusual. Again, when the aspect of the table changes as we walk round it, and we are told there cannot be so many different aspects in the same place, the answer is simple: what does the critic of the table mean by “the same place”? The use of such a phrase presupposes that all our difficulties have been solved; as yet, we have no right to speak of a “place” except with reference to one given set of momentary sense-data. When all are changed by a bodily movement, no place remains the same as it was. Thus the difficulty, if it exists, has at least not been rightly stated.
We will now make a new start, adopting a different method. Instead of inquiring what is the minimum of assumption by which we can explain the world of sense, we will, in order to have a model hypothesis as a help for the imagination, construct one possible (not necessary) explanation of the facts. It may perhaps then be possible to pare away what is superfluous in our hypothesis, leaving a residue which may be regarded as the abstract answer to our problem.
Let us imagine that each mind looks out upon the world, as in Leibniz's monadology, from a point of view peculiar to itself; and for the sake of simplicity let us confine ourselves to the sense of sight, ignoring minds which are devoid of this sense. Each mind sees at each moment an immensely complex three-dimensional world; but there is absolutely nothing which is seen by two minds simultaneously. When we say that two people see the same thing, we always find that, owing to difference of point of view, there are differences, however slight, between their immediate sensible objects. (I am here assuming the validity of testimony, but as we are only constructing a possible theory, that is a legitimate assumption.) The three-dimensional world seen by one mind therefore contains no place in common with that seen by another, for places can only be constituted by the things in or around them. Hence we may suppose, in spite of the differences between the different worlds, that each exists entire exactly as it is perceived, and might be exactly as it is even if it were not perceived. We may further suppose that there are an infinite number of such worlds which are in fact unperceived. If two men are sitting in a room, two somewhat similar worlds are perceived by them; if a third man enters and sits between them, a third world, intermediate between the two previous worlds, begins to be perceived. It is true that we cannot reasonably suppose just this world to have existed before, because it is conditioned by the sense-organs, nerves, and brain of the newly arrived man; but we can reasonably suppose that some aspect of the universe existed from that point of view, though no one was perceiving it. The system consisting of all views of the universe perceived and unperceived, I shall call the system of “perspectives”; I shall confine the expression “private worlds” to such views of the universe as are actually perceived. Thus a “private world” is a perceived “perspective”; but there may be any number of unperceived perspectives.
Two men are sometimes found to perceive very similar perspectives, so similar that they can use the same words to describe them. They say they see the same table, because the differences between the two tables they see are slight and not practically important. Thus it is possible, sometimes, to establish a correlation by similarity between a great many of the things of one perspective, and a great many of the things of another. In case the similarity is very great, we say the points of view of the two perspectives are near together in space; but this space in which they are near together is totally different from the spaces inside the two perspectives. It is a relation between the perspectives, and is not in either of them; no one can perceive it, and if it is to be known it can be only by inference. Between two perceived perspectives which are similar, we can imagine a whole series of other perspectives, some at least unperceived, and such that between any two, however similar, there are others still more similar. In this way the space which consists of relations between perspectives can be rendered continuous, and (if we choose) three-dimensional.
We can now define the momentary common-sense “thing,” as opposed to its momentary appearances. By the similarity of neighbouring perspectives, many objects in the one can be correlated with objects in the other, namely, with the similar objects. Given an object in one perspective, form the system of all the objects correlated with it in all the perspectives; that system may be identified with the momentary common-sense “thing.” Thus an aspect of a “thing” is a member of the system of aspects which is the “thing” at that moment. (The correlation of the times of different perspectives raises certain complications, of the kind considered in the theory of relativity; but we may ignore these at present.) All the aspects of a thing are real, whereas the thing is a mere logical construction. It has, however, the merit of being neutral as between different points of view, and of being visible to more than one person, in the only sense in which it can ever be visible, namely, in the sense that each sees one of its aspects.
It will be observed that, while each perspective contains its own space, there is only one space in which the perspectives themselves are the elements. There are as many private spaces as there are perspectives; there are therefore at least as many as there are percipients, and there may be any number of others which have a merely material existence and are not seen by anyone. But there is only one perspective-space, whose elements are single perspectives, each with its own private space. We have now to explain how the private space of a single perspective is correlated with part of the one all-embracing perspective space.
Perspective space is the system of “points of view” of private spaces (perspectives), or, since “points of view” have not been defined, we may say it is the system of the private spaces themselves. These private spaces will each count as one point, or at any rate as one element, in perspective space. They are ordered by means of their similarities. Suppose, for example, that we start from one which contains the appearance of a circular disc, such as would be called a penny, and suppose this appearance, in the perspective in question, is circular, not elliptic. We can then form a whole series of perspectives containing a graduated series of circular aspects of varying sizes: for this purpose we only have to move (as we say) towards the penny or away from it. The perspectives in which the penny looks circular will be said to lie on a straight line in perspective space, and their order on this line will be that of the sizes of the circular aspects. Moreover—though this statement must be noticed and subsequently examined—the perspectives in which the penny looks big will be said to be nearer to the penny than those in which it looks small. It is to be remarked also that any other “thing” than our penny might have been chosen to define the relations of our perspectives in perspective space, and that experience shows that the same spatial order of perspectives would have resulted.
In order to explain the correlation of private spaces with perspective space, we have first to explain what is meant by “the place (in perspective space) where a thing is.” For this purpose, let us again consider the penny which appears in many perspectives. We formed a straight line of perspectives in which the penny looked circular, and we agreed that those in which it looked larger were to be considered as nearer to the penny. We can form another straight line of perspectives in which the penny is seen end-on and looks like a straight line of a certain thickness. These two lines will meet in a certain place in perspective space, i.e. in a certain perspective, which may be defined as “the place (in perspective space) where the penny is.” It is true that, in order to prolong our lines until they reach this place, we shall have to make use of other things besides the penny, because, so far as experience goes, the penny ceases to present any appearance after we have come so near to it that it touches the eye. But this raises no real difficulty, because the spatial order of perspectives is found empirically to be independent of the particular “things” chosen for defining the order. We can, for example, remove our penny and prolong each of our two straight lines up to their intersection by placing other pennies further off in such a way that the aspects of the one are circular where those of our original penny were circular, and the aspects of the other are straight where those of our original penny were straight. There will then be just one perspective in which one of the new pennies looks circular and the other straight. This will be, by definition, the place where the original penny was in perspective space.
The above is, of course, only a first rough sketch of the way in which our definition is to be reached. It neglects the size of the penny, and it assumes that we can remove the penny without being disturbed by any simultaneous changes in the positions of other things. But it is plain that such niceties cannot affect the principle, and can only introduce complications in its application.
Having now defined the perspective which is the place where a given thing is, we can understand what is meant by saying that the perspectives in which a thing looks large are nearer to the thing than those in which it looks small: they are, in fact, nearer to the perspective which is the place where the thing is.
We can now also explain the correlation between a private space and parts of perspective space. If there is an aspect of a given thing in a certain private space, then we correlate the place where this aspect is in the private space with the place where the thing is in perspective space.
We may define “here” as the place, in perspective space, which is occupied by our private world. Thus we can now understand what is meant by speaking of a thing as near to or far from “here.” A thing is near to “here” if the place where it is is near to my private world. We can also understand what is meant by saying that our private world is inside our head; for our private world is a place in perspective space, and may be part of the place where our head is.
It will be observed that two places in perspective space are associated with every aspect of a thing: namely, the place where the thing is, and the place which is the perspective of which the aspect in question forms part. Every aspect of a thing is a member of two different classes of aspects, namely: (1) the various aspects of the thing, of which at most one appears in any given perspective; (2) the perspective of which the given aspect is a member, i.e. that in which the thing has the given aspect. The physicist naturally classifies aspects in the first way, the psychologist in the second. The two places associated with a single aspect correspond to the two ways of classifying it. We may distinguish the two places as that at which, and that from which, the aspect appears. The “place at which” is the place of the thing to which the aspect belongs; the “place from which” is the place of the perspective to which the aspect belongs.
Let us now endeavour to state the fact that the aspect which a thing presents at a given place is affected by the intervening medium. The aspects of a thing in different perspectives are to be conceived as spreading outwards from the place where the thing is, and undergoing various changes as they get further away from this place. The laws according to which they change cannot be stated if we only take account of the aspects that are near the thing, but require that we should also take account of the things that are at the places from which these aspects appear. This empirical fact can, therefore, be interpreted in terms of our construction.
We have now constructed a largely hypothetical picture of the world, which contains and places the experienced facts, including those derived from testimony. The world we have constructed can, with a certain amount of trouble, be used to interpret the crude facts of sense, the facts of physics, and the facts of physiology. It is therefore a world which may be actual. It fits the facts, and there is no empirical evidence against it; it also is free from logical impossibilities. But have we any good reason to suppose that it is real? This brings us back to our original problem, as to the grounds for believing in the existence of anything outside my private world. What we have derived from our hypothetical construction is that there are no grounds against the truth of this belief, but we have not derived any positive grounds in its favour. We will resume this inquiry by taking up again the question of testimony and the evidence for the existence of other minds.
It must be conceded to begin with that the argument in favour of the existence of other people's minds cannot be conclusive. A phantasm of our dreams will appear to have a mind—a mind to be annoying, as a rule. It will give unexpected answers, refuse to conform to our desires, and show all those other signs of intelligence to which we are accustomed in the acquaintances of our waking hours. And yet, when we are awake, we do not believe that the phantasm was, like the appearances of people in waking life, representative of a private world to which we have no direct access. If we are to believe this of the people we meet when we are awake, it must be on some ground short of demonstration, since it is obviously possible that what we call waking life may be only an unusually persistent and recurrent nightmare. It may be that our imagination brings forth all that other people seem to say to us, all that we read in books, all the daily, weekly, monthly, and quarterly journals that distract our thoughts, all the advertisements of soap and all the speeches of politicians. This may be true, since it cannot be shown to be false, yet no one can really believe it. Is there any logical ground for regarding this possibility as improbable? Or is there nothing beyond habit and prejudice?
The minds of other people are among our data, in the very wide sense in which we used the word at first. That is to say, when we first begin to reflect, we find ourselves already believing in them, not because of any argument, but because the belief is natural to us. It is, however, a psychologically derivative belief, since it results from observation of people's bodies; and along with other such beliefs, it does not belong to the hardest of hard data, but becomes, under the influence of philosophic reflection, just sufficiently questionable to make us desire some argument connecting it with the facts of sense.
The obvious argument is, of course, derived from analogy. Other people's bodies behave as ours do when we have certain thoughts and feelings; hence, by analogy, it is natural to suppose that such behaviour is connected with thoughts and feelings like our own. Someone says, “Look out!” and we find we are on the point of being killed by a motor-car; we therefore attribute the words we heard to the person in question having seen the motor-car first, in which case there are existing things of which we are not directly conscious. But this whole scene, with our inference, may occur in a dream, in which case the inference is generally considered to be mistaken. Is there anything to make the argument from analogy more cogent when we are (as we think) awake?
The analogy in waking life is only to be preferred to that in dreams on the ground of its greater extent and consistency. If a man were to dream every night about a set of people whom he never met by day, who had consistent characters and grew older with the lapse of years, he might, like the man in Calderon's play, find it difficult to decide which was the dream-world and which was the so-called “real” world. It is only the failure of our dreams to form a consistent whole either with each other or with waking life that makes us condemn them. Certain uniformities are observed in waking life, while dreams seem quite erratic. The natural hypothesis would be that demons and the spirits of the dead visit us while we sleep; but the modern mind, as a rule, refuses to entertain this view, though it is hard to see what could be said against it. On the other hand, the mystic, in moments of illumination, seems to awaken from a sleep which has filled all his mundane life: the whole world of sense becomes phantasmal, and he sees, with the clarity and convincingness that belongs to our morning realisation after dreams, a world utterly different from that of our daily cares and troubles. Who shall condemn him? Who shall justify him? Or who shall justify the seeming solidity of the common objects among which we suppose ourselves to live?
The hypothesis that other people have minds must, I think, be allowed to be not susceptible of any very strong support from the analogical argument. At the same time, it is a hypothesis which systematises a vast body of facts and never leads to any consequences which there is reason to think false. There is therefore nothing to be said against its truth, and good reason to use it as a working hypothesis. When once it is admitted, it enables us to extend our knowledge of the sensible world by testimony, and thus leads to the system of private worlds which we assumed in our hypothetical construction. In actual fact, whatever we may try to think as philosophers, we cannot help believing in the minds of other people, so that the question whether our belief is justified has a merely speculative interest. And if it is justified, then there is no further difficulty of principle in that vast extension of our knowledge, beyond our own private data, which we find in science and common sense.
This somewhat meagre conclusion must not be regarded as the whole outcome of our long discussion. The problem of the connection of sense with objective reality has commonly been dealt with from a standpoint which did not carry initial doubt so far as we have carried it; most writers, consciously or unconsciously, have assumed that the testimony of others is to be admitted, and therefore (at least by implication) that others have minds. Their difficulties have arisen after this admission, from the differences in the appearance which one physical object presents to two people at the same time, or to one person at two times between which it cannot be supposed to have changed. Such difficulties have made people doubtful how far objective reality could be known by sense at all, and have made them suppose that there were positive arguments against the view that it can be so known. Our hypothetical construction meets these arguments, and shows that the account of the world given by common sense and physical science can be interpreted in a way which is logically unobjectionable, and finds a place for all the data, both hard and soft. It is this hypothetical construction, with its reconciliation of psychology and physics, which is the chief outcome of our discussion. Probably the construction is only in part necessary as an initial assumption, and can be obtained from more slender materials by the logical methods of which we shall have an example in the definitions of points, instants, and particles; but I do not yet know to what lengths this diminution in our initial assumptions can be carried.
LECTURE IV
THE WORLD OF PHYSICS AND
THE WORLD OF SENSE
Among the objections to the reality of objects of sense, there is one which is derived from the apparent difference between matter as it appears in physics and things as they appear in sensation. Men of science, for the most part, are willing to condemn immediate data as “merely subjective,” while yet maintaining the truth of the physics inferred from those data. But such an attitude, though it may be capable of justification, obviously stands in need of it; and the only justification possible must be one which exhibits matter as a logical construction from sense-data—unless, indeed, there were some wholly a priori principle by which unknown entities could be inferred from such as are known. It is therefore necessary to find some way of bridging the gulf between the world of physics and the world of sense, and it is this problem which will occupy us in the present lecture. Physicists appear to be unconscious of the gulf, while psychologists, who are conscious of it, have not the mathematical knowledge required for spanning it. The problem is difficult, and I do not know its solution in detail. All that I can hope to do is to make the problem felt, and to indicate the kind of methods by which a solution is to be sought.
Let us begin by a brief description of the two contrasted worlds. We will take first the world of physics, for, though the other world is given while the physical world is inferred, to us now the world of physics is the more familiar, the world of pure sense having become strange and difficult to rediscover. Physics started from the common-sense belief in fairly permanent and fairly rigid bodies—tables and chairs, stones, mountains, the earth and moon and sun. This common-sense belief, it should be noticed, is a piece of audacious metaphysical theorising; objects are not continually present to sensation, and it may be doubted whether they are there when they are not seen or felt. This problem, which has been acute since the time of Berkeley, is ignored by common sense, and has therefore hitherto been ignored by physicists. We have thus here a first departure from the immediate data of sensation, though it is a departure merely by way of extension, and was probably made by our savage ancestors in some very remote prehistoric epoch.
But tables and chairs, stones and mountains, are not quite permanent or quite rigid. Tables and chairs lose their legs, stones are split by frost, and mountains are cleft by earthquakes and eruptions. Then there are other things, which seem material, and yet present almost no permanence or rigidity. Breath, smoke, clouds, are examples of such things—so, in a lesser degree, are ice and snow; and rivers and seas, though fairly permanent, are not in any degree rigid. Breath, smoke, clouds, and generally things that can be seen but not touched, were thought to be hardly real; to this day the usual mark of a ghost is that it can be seen but not touched. Such objects were peculiar in the fact that they seemed to disappear completely, not merely to be transformed into something else. Ice and snow, when they disappear, are replaced by water; and it required no great theoretical effort to invent the hypothesis that the water was the same thing as the ice and snow, but in a new form. Solid bodies, when they break, break into parts which are practically the same in shape and size as they were before. A stone can be hammered into a powder, but the powder consists of grains which retain the character they had before the pounding. Thus the ideal of absolutely rigid and absolutely permanent bodies, which early physicists pursued throughout the changing appearances, seemed attainable by supposing ordinary bodies to be composed of a vast number of tiny atoms. This billiard-ball view of matter dominated the imagination of physicists until quite modern times, until, in fact, it was replaced by the electromagnetic theory, which in its turn is developing into a new atomism. Apart from the special form of the atomic theory which was invented for the needs of chemistry, some kind of atomism dominated the whole of traditional dynamics, and was implied in every statement of its laws and axioms.
The pictorial accounts which physicists give of the material world as they conceive it undergo violent changes under the influence of modifications in theory which are much slighter than the layman might suppose from the alterations of the description. Certain features, however, have remained fairly stable. It is always assumed that there is something indestructible which is capable of motion in space; what is indestructible is always very small, but does not always occupy a mere point in space. There is supposed to be one all-embracing space in which the motion takes place, and until lately we might have assumed one all-embracing time also. But the principle of relativity has given prominence to the conception of “local time,” and has somewhat diminished men's confidence in the one even-flowing stream of time. Without dogmatising as to the ultimate outcome of the principle of relativity, however, we may safely say, I think, that it does not destroy the possibility of correlating different local times, and does not therefore have such far-reaching philosophical consequences as is sometimes supposed. In fact, in spite of difficulties as to measurement, the one all-embracing time still, I think, underlies all that physics has to say about motion. We thus have still in physics, as we had in Newton's time, a set of indestructible entities which may be called particles, moving relatively to each other in a single space and a single time.
The world of immediate data is quite different from this. Nothing is permanent; even the things that we think are fairly permanent, such as mountains, only become data when we see them, and are not immediately given as existing at other moments. So far from one all-embracing space being given, there are several spaces for each person, according to the different senses which give relations that may be called spatial. Experience teaches us to obtain one space from these by correlation, and experience, together with instinctive theorising, teaches us to correlate our spaces with those which we believe to exist in the sensible worlds of other people. The construction of a single time offers less difficulty so long as we confine ourselves to one person's private world, but the correlation of one private time with another is a matter of great difficulty. Thus, apart from any of the fluctuating hypotheses of physics, three main problems arise in connecting the world of physics with the world of sense, namely (1) the construction of permanent “things,” (2) the construction of a single space, and (3) the construction of a single time. We will consider these three problems in succession.
(1) The belief in indestructible “things” very early took the form of atomism. The underlying motive in atomism was not, I think, any empirical success in interpreting phenomena, but rather an instinctive belief that beneath all the changes of the sensible world there must be something permanent and unchanging. This belief was, no doubt, fostered and nourished by its practical successes, culminating in the conservation of mass; but it was not produced by these successes. On the contrary, they were produced by it. Philosophical writers on physics sometimes speak as though the conservation of something or other were essential to the possibility of science, but this, I believe, is an entirely erroneous opinion. If the a priori belief in permanence had not existed, the same laws which are now formulated in terms of this belief might just as well have been formulated without it. Why should we suppose that, when ice melts, the water which replaces it is the same thing in a new form? Merely because this supposition enables us to state the phenomena in a way which is consonant with our prejudices. What we really know is that, under certain conditions of temperature, the appearance we call ice is replaced by the appearance we call water. We can give laws according to which the one appearance will be succeeded by the other, but there is no reason except prejudice for regarding both as appearances of the same substance.
One task, if what has just been said is correct, which confronts us in trying to connect the world of sense with the world of physics, is the task of reconstructing the conception of matter without the a priori beliefs which historically gave rise to it. In spite of the revolutionary results of modern physics, the empirical successes of the conception of matter show that there must be some legitimate conception which fulfils roughly the same functions. The time has hardly come when we can state precisely what this legitimate conception is, but we can see in a general way what it must be like. For this purpose, it is only necessary to take our ordinary common-sense statements and reword them without the assumption of permanent substance. We say, for example, that things change gradually—sometimes very quickly, but not without passing through a continuous series of intermediate states. What this means is that, given any sensible appearance, there will usually be, if we watch, a continuous series of appearances connected with the given one, leading on by imperceptible gradations to the new appearances which common-sense regards as those of the same thing. Thus a thing may be defined as a certain series of appearances, connected with each other by continuity and by certain causal laws. In the case of slowly changing things, this is easily seen. Consider, say, a wall-paper which fades in the course of years. It is an effort not to conceive of it as one “thing” whose colour is slightly different at one time from what it is at another. But what do we really know about it? We know that under suitable circumstances—i.e. when we are, as is said, “in the room”—we perceive certain colours in a certain pattern: not always precisely the same colours, but sufficiently similar to feel familiar. If we can state the laws according to which the colour varies, we can state all that is empirically verifiable; the assumption that there is a constant entity, the wall-paper, which “has” these various colours at various times, is a piece of gratuitous metaphysics. We may, if we like, define the wall-paper as the series of its aspects. These are collected together by the same motives which led us to regard the wall-paper as one thing, namely a combination of sensible continuity and causal connection. More generally, a “thing” will be defined as a certain series of aspects, namely those which would commonly be said to be of the thing. To say that a certain aspect is an aspect of a certain thing will merely mean that it is one of those which, taken serially, are the thing. Everything will then proceed as before: whatever was verifiable is unchanged, but our language is so interpreted as to avoid an unnecessary metaphysical assumption of permanence.
The above extrusion of permanent things affords an example of the maxim which inspires all scientific philosophising, namely “Occam's razor”: Entities are not to be multiplied without necessity. In other words, in dealing with any subject-matter, find out what entities are undeniably involved, and state everything in terms of these entities. Very often the resulting statement is more complicated and difficult than one which, like common sense and most philosophy, assumes hypothetical entities whose existence there is no good reason to believe in. We find it easier to imagine a wall-paper with changing colours than to think merely of the series of colours; but it is a mistake to suppose that what is easy and natural in thought is what is most free from unwarrantable assumptions, as the case of “things” very aptly illustrates.
The above summary account of the genesis of “things,” though it may be correct in outline, has omitted some serious difficulties which it is necessary briefly to consider. Starting from a world of helter-skelter sense-data, we wish to collect them into series, each of which can be regarded as consisting of the successive appearances of one “thing.” There is, to begin with, some conflict between what common sense regards as one thing, and what physics regards an unchanging collection of particles. To common sense, a human body is one thing, but to science the matter composing it is continually changing. This conflict, however, is not very serious, and may, for our rough preliminary purpose, be largely ignored. The problem is: by what principles shall we select certain data from the chaos, and call them all appearances of the same thing?
A rough and approximate answer to this question is not very difficult. There are certain fairly stable collections of appearances, such as landscapes, the furniture of rooms, the faces of acquaintances. In these cases, we have little hesitation in regarding them on successive occasions as appearances of one thing or collection of things. But, as the Comedy of Errors illustrates, we may be led astray if we judge by mere resemblance. This shows that something more is involved, for two different things may have any degree of likeness up to exact similarity.
Another insufficient criterion of one thing is continuity. As we have already seen, if we watch what we regard as one changing thing, we usually find its changes to be continuous so far as our senses can perceive. We are thus led to assume that, if we see two finitely different appearances at two different times, and if we have reason to regard them as belonging to the same thing, then there was a continuous series of intermediate states of that thing during the time when we were not observing it. And so it comes to be thought that continuity of change is necessary and sufficient to constitute one thing. But in fact it is neither. It is not necessary, because the unobserved states, in the case where our attention has not been concentrated on the thing throughout, are purely hypothetical, and cannot possibly be our ground for supposing the earlier and later appearances to belong to the same thing; on the contrary, it is because we suppose this that we assume intermediate unobserved states. Continuity is also not sufficient, since we can, for example, pass by sensibly continuous gradations from any one drop of the sea to any other drop. The utmost we can say is that discontinuity during uninterrupted observation is as a rule a mark of difference between things, though even this cannot be said in such cases as sudden explosions.
The assumption of continuity is, however, successfully made in physics. This proves something, though not anything of very obvious utility to our present problem: it proves that nothing in the known world is inconsistent with the hypothesis that all changes are really continuous, though from too great rapidity or from our lack of observation they may not always appear continuous. In this hypothetical sense, continuity may be allowed to be a necessary condition if two appearances are to be classed as appearances of the same thing. But it is not a sufficient condition, as appears from the instance of the drops in the sea. Thus something more must be sought before we can give even the roughest definition of a “thing.”
What is wanted further seems to be something in the nature of fulfilment of causal laws. This statement, as it stands, is very vague, but we will endeavour to give it precision. When I speak of “causal laws,” I mean any laws which connect events at different times, or even, as a limiting case, events at the same time provided the connection is not logically demonstrable. In this very general sense, the laws of dynamics are causal laws, and so are the laws correlating the simultaneous appearances of one “thing” to different senses. The question is: How do such laws help in the definition of a “thing”?
To answer this question, we must consider what it is that is proved by the empirical success of physics. What is proved is that its hypotheses, though unverifiable where they go beyond sense-data, are at no point in contradiction with sense-data, but, on the contrary, are ideally such as to render all sense-data calculable from a sufficient collection of data all belonging to a given period of time. Now physics has found it empirically possible to collect sense-data into series, each series being regarded as belonging to one “thing,” and behaving, with regard to the laws of physics, in a way in which series not belonging to one thing would in general not behave. If it is to be unambiguous whether two appearances belong to the same thing or not, there must be only one way of grouping appearances so that the resulting things obey the laws of physics. It would be very difficult to prove that this is the case, but for our present purposes we may let this point pass, and assume that there is only one way. We must include in our definition of a “thing” those of its aspects, if any, which are not observed. Thus we may lay down the following definition: Things are those series of aspects which obey the laws of physics. That such series exist is an empirical fact, which constitutes the verifiability of physics.
It may still be objected that the “matter” of physics is something other than series of sense-data. Sense-data, it may be said, belong to psychology and are, at any rate in some sense, subjective, whereas physics is quite independent of psychological considerations, and does not assume that its matter only exists when it is perceived.
To this objection there are two answers, both of some importance.
(a) We have been considering, in the above account, the question of the verifiability of physics. Now verifiability is by no means the same thing as truth; it is, in fact, something far more subjective and psychological. For a proposition to be verifiable, it is not enough that it should be true, but it must also be such as we can discover to be true. Thus verifiability depends upon our capacity for acquiring knowledge, and not only upon the objective truth. In physics, as ordinarily set forth, there is much that is unverifiable: there are hypotheses as to (α) how things would appear to a spectator in a place where, as it happens, there is no spectator; (β) how things would appear at times when, in fact, they are not appearing to anyone; (γ) things which never appear at all. All these are introduced to simplify the statement of the causal laws, but none of them form an integral part of what is known to be true in physics. This brings us to our second answer.
(b) If physics is to consist wholly of propositions known to be true, or at least capable of being proved or disproved, the three kinds of hypothetical entities we have just enumerated must all be capable of being exhibited as logical functions of sense-data. In order to show how this might possibly be done, let us recall the hypothetical Leibnizian universe of Lecture III. In that universe, we had a number of perspectives, two of which never had any entity in common, but often contained entities which could be sufficiently correlated to be regarded as belonging to the same thing. We will call one of these an “actual” private world when there is an actual spectator to which it appears, and “ideal” when it is merely constructed on principles of continuity. A physical thing consists, at each instant, of the whole set of its aspects at that instant, in all the different worlds; thus a momentary state of a thing is a whole set of aspects. An “ideal” appearance will be an aspect merely calculated, but not actually perceived by any spectator. An “ideal” state of a thing will be a state at a moment when all its appearances are ideal. An ideal thing will be one whose states at all times are ideal. Ideal appearances, states, and things, since they are calculated, must be functions of actual appearances, states, and things; in fact, ultimately, they must be functions of actual appearances. Thus it is unnecessary, for the enunciation of the laws of physics, to assign any reality to ideal elements: it is enough to accept them as logical constructions, provided we have means of knowing how to determine when they become actual. This, in fact, we have with some degree of approximation; the starry heaven, for instance, becomes actual whenever we choose to look at it. It is open to us to believe that the ideal elements exist, and there can be no reason for disbelieving this; but unless in virtue of some a priori law we cannot know it, for empirical knowledge is confined to what we actually observe.
(2) The three main conceptions of physics are space, time, and matter. Some of the problems raised by the conception of matter have been indicated in the above discussion of “things.” But space and time also raise difficult problems of much the same kind, namely, difficulties in reducing the haphazard untidy world of immediate sensation to the smooth orderly world of geometry and kinematics. Let us begin with the consideration of space.
People who have never read any psychology seldom realise how much mental labour has gone into the construction of the one all-embracing space into which all sensible objects are supposed to fit. Kant, who was unusually ignorant of psychology, described space as “an infinite given whole,” whereas a moment's psychological reflection shows that a space which is infinite is not given, while a space which can be called given is not infinite. What the nature of “given” space really is, is a difficult question, upon which psychologists are by no means agreed. But some general remarks may be made, which will suffice to show the problems, without taking sides on any psychological issue still in debate.
The first thing to notice is that different senses have different spaces. The space of sight is quite different from the space of touch: it is only by experience in infancy that we learn to correlate them. In later life, when we see an object within reach, we know how to touch it, and more or less what it will feel like; if we touch an object with our eyes shut, we know where we should have to look for it, and more or less what it would look like. But this knowledge is derived from early experience of the correlation of certain kinds of touch-sensations with certain kinds of sight-sensations. The one space into which both kinds of sensations fit is an intellectual construction, not a datum. And besides touch and sight, there are other kinds of sensation which give other, though less important spaces: these also have to be fitted into the one space by means of experienced correlations. And as in the case of things, so here: the one all-embracing space, though convenient as a way of speaking, need not be supposed really to exist. All that experience makes certain is the several spaces of the several senses, correlated by empirically discovered laws. The one space may turn out to be valid as a logical construction, compounded of the several spaces, but there is no good reason to assume its independent metaphysical reality.
Another respect in which the spaces of immediate experience differ from the space of geometry and physics is in regard to points. The space of geometry and physics consists of an infinite number of points, but no one has ever seen or touched a point. If there are points in a sensible space, they must be an inference. It is not easy to see any way in which, as independent entities, they could be validly inferred from the data; thus here again, we shall have, if possible, to find some logical construction, some complex assemblage of immediately given objects, which will have the geometrical properties required of points. It is customary to think of points as simple and infinitely small, but geometry in no way demands that we should think of them in this way. All that is necessary for geometry is that they should have mutual relations possessing certain enumerated abstract properties, and it may be that an assemblage of data of sensation will serve this purpose. Exactly how this is to be done, I do not yet know, but it seems fairly certain that it can be done.
The following illustrative method, simplified so as to be easily manipulated, has been invented by Dr Whitehead for the purpose of showing how points might be manufactured from sense-data. We have first of all to observe that there are no infinitesimal sense-data: any surface we can see, for example, must be of some finite extent. But what at first appears as one undivided whole is often found, under the influence of attention, to split up into parts contained within the whole. Thus one spatial object may be contained within another, and entirely enclosed by the other. This relation of enclosure, by the help of some very natural hypotheses, will enable us to define a “point” as a certain class of spatial objects, namely all those (as it will turn out in the end) which would naturally be said to contain the point. In order to obtain a definition of a “point” in this way, we proceed as follows:
Given any set of volumes or surfaces, they will not in general converge into one point. But if they get smaller and smaller, while of any two of the set there is always one that encloses the other, then we begin to have the kind of conditions which would enable us to treat them as having a point for their limit. The hypotheses required for the relation of enclosure are that (1) it must be transitive; (2) of two different spatial objects, it is impossible for each to enclose the other, but a single spatial object always encloses itself; (3) any set of spatial objects such that there is at least one spatial object enclosed by them all has a lower limit or minimum, i.e. an object enclosed by all of them and enclosing all objects which are enclosed by all of them; (4) to prevent trivial exceptions, we must add that there are to be instances of enclosure, i.e. there are really to be objects of which one encloses the other. When an enclosure-relation has these properties, we will call it a “point-producer.” Given any relation of enclosure, we will call a set of objects an “enclosure-series” if, of any two of them, one is contained in the other. We require a condition which shall secure that an enclosure-series converges to a point, and this is obtained as follows: Let our enclosure-series be such that, given any other enclosure-series of which there are members enclosed in any arbitrarily chosen member of our first series, then there are members of our first series enclosed in any arbitrarily chosen member of our second series. In this case, our first enclosure-series may be called a “punctual enclosure-series.” Then a “point” is all the objects which enclose members of a given punctual enclosure-series. In order to ensure infinite divisibility, we require one further property to be added to those defining point-producers, namely that any object which encloses itself also encloses an object other than itself. The “points” generated by point-producers with this property will be found to be such as geometry requires.
(3) The question of time, so long as we confine ourselves to one private world, is rather less complicated than that of space, and we can see pretty clearly how it might be dealt with by such methods as we have been considering. Events of which we are conscious do not last merely for a mathematical instant, but always for some finite time, however short. Even if there be a physical world such as the mathematical theory of motion supposes, impressions on our sense-organs produce sensations which are not merely and strictly instantaneous, and therefore the objects of sense of which we are immediately conscious are not strictly instantaneous. Instants, therefore, are not among the data of experience, and, if legitimate, must be either inferred or constructed. It is difficult to see how they can be validly inferred; thus we are left with the alternative that they must be constructed. How is this to be done?
Immediate experience provides us with two time-relations among events: they may be simultaneous, or one may be earlier and the other later. These two are both part of the crude data; it is not the case that only the events are given, and their time-order is added by our subjective activity. The time-order, within certain limits, is as much given as the events. In any story of adventure you will find such passages as the following: “With a cynical smile he pointed the revolver at the breast of the dauntless youth. ‘At the word three I shall fire,’ he said. The words one and two had already been spoken with a cool and deliberate distinctness. The word three was forming on his lips. At this moment a blinding flash of lightning rent the air.” Here we have simultaneity—not due, as Kant would have us believe, to the subjective mental apparatus of the dauntless youth, but given as objectively as the revolver and the lightning. And it is equally given in immediate experience that the words one and two come earlier than the flash. These time-relations hold between events which are not strictly instantaneous. Thus one event may begin sooner than another, and therefore be before it, but may continue after the other has begun, and therefore be also simultaneous with it. If it persists after the other is over, it will also be later than the other. Earlier, simultaneous, and later, are not inconsistent with each other when we are concerned with events which last for a finite time, however short; they only become inconsistent when we are dealing with something instantaneous.
It is to be observed that we cannot give what may be called absolute dates, but only dates determined by events. We cannot point to a time itself, but only to some event occurring at that time. There is therefore no reason in experience to suppose that there are times as opposed to events: the events, ordered by the relations of simultaneity and succession, are all that experience provides. Hence, unless we are to introduce superfluous metaphysical entities, we must, in defining what mathematical physics can regard as an instant, proceed by means of some construction which assumes nothing beyond events and their temporal relations.
If we wish to assign a date exactly by means of events, how shall we proceed? If we take any one event, we cannot assign our date exactly, because the event is not instantaneous, that is to say, it may be simultaneous with two events which are not simultaneous with each other. In order to assign a date exactly, we must be able, theoretically, to determine whether any given event is before, at, or after this date, and we must know that any other date is either before or after this date, but not simultaneous with it. Suppose, now, instead of taking one event A, we take two events A and B, and suppose A and B partly overlap, but B ends before A ends. Then an event which is simultaneous with both A and B must exist during the time when A and B overlap; thus we have come rather nearer to a precise date than when we considered A and B alone. Let C be an event which is simultaneous with both A and B, but which ends before either A or B has ended. Then an event which is simultaneous with A and B and C must exist during the time when all three overlap, which is a still shorter time. Proceeding in this way, by taking more and more events, a new event which is dated as simultaneous with all of them becomes gradually more and more accurately dated. This suggests a way by which a completely accurate date can be defined.