[1] "The Grammar of Science," 2d Ed., London, 1900, pp. 60-63.



CHAPTER IV

SENSATIONS AND "THINGS"

15. SENSE AND IMAGINATION.—Every one distinguishes between things perceived and things only imagined. With open eyes I see the desk before me; with eyes closed, I can imagine it. I lay my hand on it and feel it; I can, without laying my hand on it, imagine that I feel it. I raise my eyes, and see the pictures on the wall opposite me; I can sit here and call before my mind the image of the door by which the house is entered.

What is the difference between sense and imagination? It must be a difference of which we are all somehow conscious, for we unhesitatingly distinguish between the things we perceive and the things we merely imagine.

It is well to remember at the outset that the two classes of experiences are not wholly different. The blue color that I imagine seems blue. It does not lose this quality because it is only imaginary. The horse that I imagine seems to have four legs, like a horse perceived. As I call it before my mind, it seems as large as the real horse. Neither the color, nor the size, nor the distribution of parts, nor any other attribute of the sort appears to be different in the imaginary object from what it is in the object as given in sensation.

The two experiences are, nevertheless, not the same; and every one knows that they are not the same. One difference that roughly marks out the two classes of experiences from one another is that, as a rule, our sense-experiences are more vivid than are the images that exist in the imagination.

I say, as a rule, for we cannot always remark this difference. Sensations may be very clear and unmistakable, but they may also be very faint and indefinite. When a man lays his hand firmly on my shoulder, I may be in little doubt whether I feel a sensation or do not; but when he touches my back very lightly, I may easily be in doubt, and may ask myself in perplexity whether I have really been touched or whether I have merely imagined it. As a vessel recedes and becomes a mere speck upon the horizon, I may well wonder, before I feel sure that it is really quite out of sight, whether I still see the dim little point, or whether I merely imagine that I see it.

On the other hand, things merely imagined may sometimes be very vivid and insistent. To some persons, what exists in the imagination is dim and indefinite in the extreme. Others imagine things vividly, and can describe what is present only to the imagination almost as though it were something seen. Finally, we know that an image may become so vivid and insistent as to be mistaken for an external thing. That is to say, there are such things as hallucinations.

The criterion of vividness will not, therefore, always serve to distinguish between what is given in the sense and what is only imagined. And, indeed, it becomes evident, upon reflection, that we do not actually make it our ultimate test. We may be quite willing to admit that faint sensations may come to be confused with what is imagined, with "ideas," but we always regard such a confusion as somebody's error. We are not ready to admit that things perceived faintly are things imagined, or that vivid "ideas" are things perceived by sense.

Let us come back to the illustrations with which we started. How do I know that I perceive the desk before me; and how do I know that, sitting here, I imagine, and do not see, the front door of the house?

My criterion is this: when I have the experience I call "seeing my desk," the bit of experience which presents itself as my desk is in a certain setting. That is to say, the desk seen must be in a certain relation to my body, and this body, as I know it, also consists of experiences. Thus, if I am to know that I see the desk, I must realize that my eyes are open, that the object is in front of me and not behind me, etc.

The desk as seen varies with the relation to the body in certain ways that we regard as natural and explicable. When I am near it, the visual experience is not just what it is when I recede from it. But how can I know that I am near the desk or far from it? What do these expressions mean? Their full meaning will become clearer in the next chapter, but here I may say that nearness and remoteness must be measured for me in experiences of some sort, or I would never know anything as near to or far from my body.

Thus, all our sensory experiences are experiences that fall into a certain system or order. It is a system which we all recognize implicitly, for we all reject as merely imaginary those experiences which lack this setting. If my eyes are shut—I am speaking now of the eyes as experienced, as felt or perceived, as given in sensation—I never say; "I see my desk," no matter how vivid the image of the object. Those who believe in "second sight" sometimes talk of seeing things not in this setting, but the very name they give to the supposed experience indicates that there is something abnormal about it. No one thinks it remarkable that I see the desk before which I perceive myself to be sitting with open eyes. Every one would think it strange if I could see and describe the table in the next room, now shut away from me. When a man thinks he hears his name pronounced, and, turning his head, seeks in vain for the speaker, he sets his experience down as a hallucination. He says, I did not really hear that; I merely imagined it.

May one not, with open eyes, have a hallucination of vision, just as one may seem to hear one's name pronounced when no one is by? Certainly. But in each case the experience may be proved to be a hallucination, nevertheless. It may be recognized that the sensory setting is incomplete, though it may not, at first, seem so. Thus the unreal object which seems to be seen may be found to be a thing that cannot be touched. Or, when one has attained to a relatively complete knowledge of the system of experiences recognized as sensory, one may make use of roundabout methods of ascertaining that the experience in question does not really have the right setting. Thus, the ghost which is seen by the terrified peasant at midnight, but which cannot be photographed, we may unhesitatingly set down as something imagined and not really seen.

All our sensations are, therefore, experiences which take their place in a certain setting. This is our ultimate criterion. We need not take the word of the philosopher for it. We need only reflect, and ask ourselves how we know that, in a given case, we are seeing or hearing or touching something, and are not merely imagining it. In every case, we shall find that we come back to the same test. In common life, we apply the test instinctively, and with little realization of what we are doing.

And if we turn to the psychologist, whose business it is to be more exact and scientific, we find that he gives us only a refinement of this same criterion. It is important to him to distinguish between what is given in sensation and what is furnished by memory or imagination, and he tells us that sensation is the result of a message conducted along a sensory nerve to the brain.

Here we see emphasized the relation to the body which has been mentioned above. If we ask the psychologist how he knows that the body he is talking about is a real body, and not merely an imagined one, he has to fall back upon the test which is common to us all. A real hand is one which we see with the eyes open, and which we touch with the other hand. If our experiences of our own body had not the setting which marks all sensory experiences, we could never say: I perceive that my body is near the desk. When we call our body real, as contrasted with things imaginary, we recognize that this group of experiences belongs to the class described; it is given in sensation, and is not merely thought of.

It will be observed that, in distinguishing between sensations and things imaginary, we never go beyond the circle of our experiences. We do not reach out to a something beyond or behind experiences, and say: When such a reality is present, we may affirm that we have a sensation, and when it is not, we may call the experience imaginary. If there were such a reality as this, it would do us little good, for since it is not supposed to be perceived directly, we should have to depend upon the sensations to prove the presence of the reality, and could not turn to the reality and ask it whether we were or were not experiencing a sensation. The distinction between sensations and what is imaginary is an observed distinction. It can be proved that some experiences are sensory and that some are not. This means that, in drawing the distinction, we remain within the circle of our experiences.

There has been much unnecessary mystification touching this supposed reality behind experiences. In the next chapter we shall see in what senses the word "reality" may properly be used, and in what sense it may not. There is a danger in using it loosely and vaguely.

16. MAY WE CALL "THINGS" GROUPS OF SENSATIONS?—Now, the external world seems to the plain man to be directly given in his sense experiences. He is willing to admit that the table in the next room, of which he is merely thinking, is known at one remove, so to speak. But this desk here before him: is it not known directly? Not the mental image, the mere representative, but the desk itself, a something that is physical and not mental?

And the psychologist, whatever his theory of the relation between the mind and the world, seems to support him, at least, in so far as to maintain that in sensation the external world is known as directly as it is possible for the external world to be known, and that one can get no more of it than is presented in sensation. If a sense is lacking, an aspect of the world as given is also lacking; if a sense is defective, as in the color-blind, the defect is reflected in the world upon which one gazes.

Such considerations, especially when taken together with what has been said at the close of the last section about the futility of looking for a reality behind our sensations, may easily suggest rather a startling possibility. May it not be, if we really are shut up to the circle of our experiences, that the physical things, which we have been accustomed to look upon as non-mental, are nothing more than complexes of sensations? Granted that there seems to be presented in our experience a material world as well as a mind, may it not be that this material world is a mental thing of a certain kind—a mental thing contrasted with other mental things, such as imaginary things?

This question has always been answered in the affirmative by the idealists, who claim that all existence must be regarded as psychical existence. Their doctrine we shall consider later (sections 49 and 53). It will be noticed that we seem to be back again with Professor Pearson in the last chapter.

To this question I make the following answer: In the first place, I remark that even the plain man distinguishes somehow between his sensations and external things. He thinks that he has reason to believe that things do not cease to exist when he no longer has sensations. Moreover, he believes that things do not always appear to his senses as they really are. If we tell him that his sensations are the things, it shocks his common sense. He answers: Do you mean to tell me that complexes of sensation can be on a shelf or in a drawer? can be cut with a knife or broken with the hands? He feels that there must be some real distinction between sensations and the things without him.

Now, the notions of the plain man on such matters as these are not very clear, and what he says about sensations and things is not always edifying. But it is clear that he feels strongly that the man who would identify them is obliterating a distinction to which his experience testifies unequivocally. We must not hastily disregard his protest. He is sometimes right in his feeling that things are not identical, even when he cannot prove it.

In the second place, I remark that, in this instance, the plain man is in the right, and can be shown to be in the right. "Things" are not groups of sensations. The distinction between them will be explained in the next section.

17. THE DISTINCTION BETWEEN SENSATIONS AND "THINGS"—Suppose that I stand in my study and look at the fire in the grate. I am experiencing sensations, and am not busied merely with an imaginary fire. But may my whole experience of the fire be summed up as an experience of sensations and their changes? Let us see.

If I shut my eyes, the fire disappears. Does any one suppose that the fire has been annihilated? No. We say, I no longer see it, but nothing has happened to the fire.

Again, I may keep my eyes open, and simply turn my head. The fire disappears once more. Does any one suppose that my turning my head has done anything to the fire? We say unhesitatingly, my sensations have changed, but the fire has remained as it was.

Still, again, I may withdraw from the fire. Its heat seems to be diminished. Has the fire really grown less hot? And if I could withdraw to a sufficient distance, I know that the fire would appear to me smaller and less bright. Could I get far enough away to make it seem the faintest speck in the field of vision, would I be tempted to claim that the fire shrunk and grew faint merely because I walked away from it? Surely not.

Now, suppose that I stand on the same spot and look at the fire without turning my head. The stick at which I am gazing catches the flame, blazes up, turns red, and finally falls together, a little mass of gray ashes. Shall I describe this by saying that my sensations have changed, or may I say that the fire itself has changed? The plain man and the philosopher alike use the latter expression in such a case as this.

Let us take another illustration. I walk towards the distant house on the plain before me. What I see as my goal seems to grow larger and brighter. It does not occur to me to maintain that the house changes as I advance. But, at a given instant, changes of a different sort make their appearance. Smoke arises, and flames burst from the roof. Now I have no hesitation in saying that changes are taking place in the house. It would seem foolish to describe the occurrence as a mere change in my sensations. Before it was my sensations that changed; now it is the house itself.

We are drawing this distinction between changes in our sensations and changes in things at every hour in the day. I cannot move without making things appear and disappear. If I wag my head, the furniture seems to dance, and I regard it as a mere seeming. I count on the clock's going when I no longer look upon its face. It would be absurd to hold that the distinction is a mere blunder, and has no foundation in our experience. The role it plays is too important for that. If we obliterate it, the real world of material things which seems to be revealed in our experience melts into a chaos of fantastic experiences whose appearances and disappearances seem to be subject to no law.

And it is worthy of remark that it is not merely in common life that the distinction is drawn. Every man of science must give heed to it. The psychologist does, it is true, pay much attention to sensations; but even he distinguishes between the sensations which he is studying and the material things to which he relates them, such as brains and sense-organs. And those who cultivate the physical sciences strive, when they give an account of things and their behavior, to lay before us a history of changes analogous to the burning of the stick and of the house, excluding mere changes in sensations.

There is no physicist or botanist or zooelogist who has not our common experience that things as perceived by us—our experiences of things—appear or disappear or change their character when we open or shut our eyes or move about. But nothing of all this appears in their books. What they are concerned with is things and their changes, and they do not consider such matters as these as falling within their province. If a botanist could not distinguish between the changes which take place in a plant, and the changes which take place in his sensations as he is occupied in studying the plant, but should tell us that the plant grows smaller as one recedes from it, we should set him down as weak-minded.

That the distinction is everywhere drawn, and that we must not obliterate it, is very evident. But we are in the presence of what has seemed to many men a grave difficulty. Are not things presented in our experience only as we have sensations? what is it to perceive a thing? is it not to have sensations? how, then, can we distinguish between sensations and things? We certainly do so all the time, in spite of the protest of the philosopher; but many of us do so with a haunting sense that our behavior can scarcely be justified by the reason.

Our difficulty, however, springs out of an error of our own. Grasping imperfectly the full significance of the word "sensation," we extend its use beyond what is legitimate, and we call by that name experiences which are not sensations at all. Thus the external world comes to seem to us to be not really a something contrasted with the mental, but a part of the mental world. We accord to it the attributes of the latter, and rob it of those distinguishing attributes which belong to it by right. When we have done this, we may feel impelled to say, as did Professor Pearson, that things are not really "outside" of us, as they seem to be, but are merely "projected" outside—thought of as if they were "outside." All this I must explain at length.

Let us come back to the first of the illustrations given above, the case of the fire in my study. As I stand and look at it, what shall I call the red glow which I observe? Shall I call it a quality of a thing, or shall I call it a sensation?

To this I answer: I may call it either the one or the other, according to its setting among other experiences.

We have seen (section 15) that sensations and things merely imaginary are distinguished from one another by their setting. With open eyes we see things; with our eyes closed we can imagine them: we see what is before us; we imagine what lies behind our backs. If we confine our attention to the bit of experience itself, we have no means of determining whether it is sensory or imaginary. Only its setting can decide that point. Here, we have come to another distinction of much the same sort. That red glow, that bit of experience, taken by itself and abstracted from all other experiences, cannot be called either a sensation or the quality of a thing. Only its context can give us the right to call it the one or the other.

This ought to become clear when we reflect upon the illustration of the fire. We have seen that one whole series of changes has been unhesitatingly described as a series of changes in my sensations. Why was this? Because it was observed to depend upon changes in the relations of my body, my senses (a certain group of experiences), to the bit of experience I call the fire. Another series was described as a series of changes in the fire. Why? Because, the relation to my senses remaining unchanged, changes still took place, and had to be accounted for in other ways.

It is a matter of common knowledge that they can be accounted for in other ways. This is not a discovery of the philosopher. He can only invite us to think over the matter and see what the unlearned and the learned are doing at every moment. Sometimes they are noticing that experiences change as they turn their heads or walk toward or away from objects; sometimes they abstract from this, and consider the series of changes that take place independently of this.

That bit of experience, that red glow, is not related only to my body. Such experiences are related also to each other; they stand in a vast independent system of relations, which, as we have seen, the man of science can study without troubling himself to consider sensations at all. This system is the external world—the external world as known or as knowable, the only external world that it means anything for us to talk about. As having its place in this system, a bit of experience is not a sensation, but is a quality or aspect of a thing.

Sensations, then, to be sensations, must be bits of experience considered in their relation to some organ of sense. They should never be confused with qualities of things, which are experiences in a different setting. It is as unpardonable to confound the two as it is to confound sensations with things imaginary.

We may not, therefore, say that "things" are groups of sensations. We may, if we please, describe them as complexes of qualities. And we may not say that the "things" we perceive are really "inside" of us and are merely "projected outside."

What can "inside" and "outside" mean? Only this. We recognize in our experience two distinct orders, the objective order, the system of phenomena which constitutes the material world, and the subjective order, the order of things mental, to which belong sensations and "ideas." That is "outside" which belongs to the objective order. The word has no other meaning when used in this connection. That is "inside" which belongs to the subjective order, and is contrasted with the former.

If we deny that there is an objective order, an external world, and say that everything is "inside," we lose our distinction, and even the word "inside" becomes meaningless. It indicates no contrast. When men fall into the error of talking in this way, what they do is to keep the external world and gain the distinction, and at the same time to deny the existence of the world which has furnished it. In other words, they put the clerk into a telephone exchange, and then tell us that the exchange does not really exist. He is inside—of what? He is inside of nothing. Then, can he really be inside?

We see, thus, that the plain man and the man of science are quite right in accepting the external world. The objective order is known as directly as is the subjective order. Both are orders of experiences; they are open to observation, and we have, in general, little difficulty in distinguishing between them, as the illustrations given above amply prove.

18. THE EXISTENCE OF MATERIAL THINGS.—One difficulty seems to remain and to call for a solution. We all believe that material things exist when we no longer perceive them. We believe that they existed before they came within the field of our observation.

In these positions the man of science supports us. The astronomer has no hesitation in saying that the comet, which has sailed away through space, exists, and will return. The geologist describes for us the world as it was in past ages, when no eye was opened upon it.

But has it not been stated above that the material world is an order of experiences? and can there be such a thing as an experience that is not experienced by somebody? In other words, can the world exist, except as it is perceived to exist?

This seeming difficulty has occasioned much trouble to philosophers in the past. Bishop Berkeley (1684-1753) said, "To exist is to be perceived." There are those who agree with him at the present day.

Their difficulty would have disappeared had they examined with sufficient care the meaning of the word "exist." We have no right to pass over the actual uses of such words, and to give them a meaning of our own. If one thing seems as certain as any other, it is that material things exist when we do not perceive them. On what ground may the philosopher combat the universal opinion, the dictum of common sense and of science? When we look into his reasonings, we find that he is influenced by the error discussed at length in the last section—he has confused the phenomena of the two orders of experience.

I have said that, when we concern ourselves with the objective order, we abstract or should abstract, from the relations which things bear to our senses. We account for phenomena by referring to other phenomena which we have reason to accept as their physical conditions or causes. We do not consider that a physical cause is effective only while we perceive it. When we come back to this notion of our perceiving a thing or not perceiving it, we have left the objective order and passed over to the subjective. We have left the consideration of "things" and have turned to sensations.

There is no reason why we should do this. The physical order is an independent order, as we have seen. The man of science, when he is endeavoring to discover whether some thing or quality of a thing really existed at some time in the past, is not in the least concerned to establish the fact that some one saw it. No one ever saw the primitive fire-mist from which, as we are told, the world came into being. But the scientist cares little for that. He is concerned only to prove that the phenomena he is investigating really have a place in the objective order. If he decides that they have, he is satisfied; he has proved something to exist. To belong to the objective order is to exist as a physical thing or quality.

When the plain man and the man of science maintain that a physical thing exists, they use the word in precisely the same sense. The meaning they give to it is the proper meaning of the word. It is justified by immemorial usage, and it marks a real distinction. Shall we allow the philosopher to tell us that we must not use it in this sense, but must say that only sensations and ideas exist? Surely not. This would mean that we permit him to obliterate for us the distinction between the external world and what is mental.

But is it right to use the word "experience" to indicate the phenomena which have a place in the objective order? Can an experience be anything but mental?

There can be no doubt that the suggestions of the word are unfortunate—it has what we may call a subjective flavor. It suggests that, after all, the things we perceive are sensations or percepts, and must, to exist at all, exist in a mind. As we have seen, this is an error, and an error which we all avoid in actual practice. We do not take sensations for things, and we recognize clearly enough that it is one thing for a material object to exist and another for it to be perceived.

Why, then, use the word "experience"? Simply because we have no better word. We must use it, and not be misled by the associations which cling to it. The word has this great advantage: it brings out clearly the fact that all our knowledge of the external world rests ultimately upon those phenomena which, when we consider them in relation to our senses, we recognize as sensations. We cannot start out from mere imaginings to discover what the world was like in the ages past.

It is this truth that is recognized by the plain man, when he maintains that, in the last resort, we can know things only in so far as we see, touch, hear, taste, and smell them; and by the psychologist, when he tells us that, in sensation, the external world is revealed as directly as it is possible that it could be revealed. But it is a travesty on this truth to say that we do not know things, but know only our sensations of sight, touch, taste, hearing, and the like.[1]

[1] See the note on this chapter at the close of the volume.



CHAPTER V

APPEARANCES AND REALITIES

19. THINGS AND THEIR APPEARANCES.—We have seen in the last chapter that there is an external world and that it is given in our experience. There is an objective order, and we are all capable of distinguishing between it and the subjective. He who says that we perceive only sensations and ideas flies in the face of the common experience of mankind.

But we are not yet through with the subject. We all make a distinction between things as they appear and things as they really are.

If we ask the plain man, What is the real external world? the first answer that seems to present itself to his mind is this: Whatever we can see, hear, touch, taste, or smell may be regarded as belonging to the real world. What we merely imagine does not belong to it.

That this answer is not a very satisfactory one occurred to men's minds very early in the history of reflective thought. The ancient skeptic said to himself: The colors of objects vary according to the light, and according to the position and distance of the objects; can we say that any object has a real color of its own? A staff stuck into water looks bent, but feels straight to the touch; why believe the testimony of one sense rather than that of another?

Such questionings led to far-reaching consequences. They resulted in a forlorn distrust of the testimony of the senses, and to a doubt as to our ability to know anything as it really is.

Now, the distinction between appearances and realities exists for us as well as for the ancient skeptic, and without being tempted to make such extravagant statements as that there is no such thing as truth, and that every appearance is as real as any other, we may admit that it is not very easy to see the full significance of the distinction, although we are referring to it constantly.

For example, we look from our window and see, as we say, a tree at a distance. What we are conscious of is a small bluish patch of color. Now, a small bluish patch of color is not, strictly speaking, a tree; but for us it represents the tree. Suppose that we walk toward the tree. Do we continue to see what we saw before? Of course, we say that we continue to see the same tree; but it is plain that what we immediately perceive, what is given in consciousness, does not remain the same as we move. Our blue patch of color grows larger and larger; it ceases to be blue and faint; at the last it has been replaced by an expanse of vivid green, and we see the tree just before us.

During our whole walk we have been seeing the tree. This appears to mean that we have been having a whole series of visual experiences, no two of which were just alike, and each of which was taken as a representative of the tree. Which of these representatives is most like the tree? Is the tree really a faint blue, or is it really a vivid green? Or is it of some intermediate color?

Probably most persons will be inclined to maintain that the tree only seems blue at a distance, but that it really is green, as it appears when one is close to it. In a sense, the statement is just; yet some of those who make it would be puzzled to tell by what right they pick out of the whole series of experiences, each of which represents the tree as seen from some particular position, one individual experience, which they claim not only represents the tree as seen from a given point but also represents it as it is. Does this particular experience bear some peculiar earmark which tells us that it is like the real tree while the others are unlike it?

20. REAL THINGS.—And what is this real tree that we are supposed to see as it is when we are close to it?

About two hundred years ago the philosopher Berkeley pointed out that the distinction commonly made between things as they look, the apparent, and things as they are, the real, is at bottom the distinction between things as presented to the sense of sight and things as presented to the sense of touch. The acute analysis which he made has held its own ever since.

We have seen that, in walking towards the tree, we have a long series of visual experiences, each of which differs more or less from all of the others. Nevertheless, from the beginning of our progress to the end, we say that we are looking at the same tree. The images change color and grow larger. We do not say that the tree changes color and grows larger. Why do we speak as we do? It is because, all along the line, we mean by the real tree, not what is given to the sense of sight, but something for which this stands as a sign. This something must be given in our experience somewhere, we must be able to perceive it under some circumstances or other, or it would never occur to us to recognize the visual experiences as signs, and we should never say that in being conscious of them in succession we are looking at the same tree. They are certainly not the same with each other; how can we know that they all stand for the same thing, unless we have had experience of a connection of the whole series with one thing?

This thing for which so many different visual experiences may serve as signs is the thing revealed in experiences of touch. When we ask: In what direction is the tree? How far away is the tree? How big is the tree? we are always referring to the tree revealed in touch. It is nonsense to say that what we see is far away, if by what we see we mean the visual experience itself. As soon as we move we lose that visual experience and get another, and to recover the one we lost we must go back where we were before. When we say we see a tree at a distance, we must mean, then, that we know from certain visual experiences which we have that by moving a certain distance we will be able to touch a tree. And what does it mean to move a certain distance? In the last analysis it means to us to have a certain quantity of movement sensations.

Thus the real world of things, for which experiences of sight serve as signs, is a world revealed in experiences of touch and movement, and when we speak of real positions, distances, and magnitudes, we are always referring to this world. But this is a world revealed in our experience, and it does not seem a hopeless task to discover what may properly be called real and what should be described as merely apparent, when both the real and the apparent are open to our inspection.

Can we not find in this analysis a satisfactory explanation of the plain man's claim that under certain circumstances he sees the tree as it is and under others he does not? What he is really asserting is that one visual experience gives him better information regarding the real thing, the touch thing, than does another.

But what shall we say of his claim that the tree is really green, and only looks blue under certain circumstances? Is it not just as true that the tree only looks green under certain circumstances? Is color any part of the touch thing? Is it ever more than a sign of the touch thing? How can one color be more real than another?

Now, we may hold to Berkeley's analysis and maintain that, in general, the real world, as contrasted with the apparent, means to us the world that is revealed in experiences of touch and movement; and yet we may admit that the word "real" is sometimes used in rather different senses.

It does not seem absurd for a woman to Say: This piece of silk really is yellow; it only looks white under this light. We all admit that a white house may look pink under the rays of the setting sun, and we never call it a pink house. We have seen that it is not unnatural to say: That tree is really green; it is only its distance that makes it look blue.

When one reflects upon these uses of the word "real," one recognizes the fact that, among all the experiences in which things are revealed to us, certain experiences impress us as being more prominent or important or serviceable than certain others, and they come to be called real. Things are not commonly seen by artificial light; the sun is not always setting; the tree looks green when it is seen most satisfactorily. In each case, the real color of the thing is the color that it has under circumstances that strike us as normal or as important. We cannot say that we always regard as most real that aspect under which we most commonly perceive things, for if a more unusual experience is more serviceable and really gives us more information about the thing, we give the preference to that. Thus we look with the naked eye at a moving speck on the table before us, and we are unable to distinguish its parts. We place a microscope over the speck and perceive an insect with all its members. The second experience is the more unusual one, but would not every one say: Now we perceive the thing as it is?

21. ULTIMATE REAL THINGS.—Let us turn away from the senses of the word "real," which recognize one color or taste or odor as more real than another, and come back to the real world of things presented in sensations of touch. All other classes of sensations may be regarded as related to this as the series of visual experiences above mentioned was related to the one tree which was spoken of as revealed in them all, the touch tree of which they gave information.

Can we say that this world is always to be regarded as reality and never as appearance? We have already seen (section 8) that science does not regard as anything more than appearance the real things which seem to be directly presented in our experience.

This pen that I hold in my hand seems, as I pass my fingers over it, to be continuously extended. It does not appear to present an alternation of filled spaces and empty spaces. I am told that it is composed of molecules in rapid motion and at considerable distances from one another. I am further told that each molecule is composed of atoms, and is, in its turn, not a continuous thing, but, so to speak, a group of little things.

If I accept this doctrine, as it seems I must, am I not forced to conclude that the reality which is given in my experience, the reality with which I have contrasted appearances and to which I have referred them, is, after all, itself only an appearance? The touch things which I have hitherto regarded as the real things that make up the external world, the touch things for which all my visual experiences have served as signs, are, then, not themselves real external things, but only the appearances under which real external things, themselves imperceptible, manifest themselves to me.

It seems, then, that I do not directly perceive any real thing, or, at least, anything that can be regarded as more than an appearance. What, then, is the external world? What are things really like? Can we give any true account of them, or are we forced to say with the skeptics that we only know how things seem to us, and must abandon the attempt to tell what they are really like?

Now, before one sets out to answer a question it is well to find out whether it is a sensible question to ask and a sensible question to try to answer. He who asks: Where is the middle of an infinite line? When did all time begin? Where is space as a whole? does not deserve a serious answer to his questions. And it is well to remember that he who asks: What is the external world like? must keep his question a significant one, if he is to retain his right to look for an answer at all. He has manifestly no right to ask us: How does the external world look when no one is looking? How do things feel when no one feels them? How shall I think of things, not as I think of them, but as they are?

If we are to give an account of the external world at all, it must evidently be an account of the external world; i.e. it must be given in terms of our experience of things. The only legitimate problem is to give a true account instead of a false one, to distinguish between what only appears and is not real and what both appears and is real.

Bearing this in mind, let us come back to the plain man's experience of the world. He certainly seems to himself to perceive a real world of things, and he constantly distinguishes, in a way very serviceable to himself, between the merely apparent and the real. There is, of course, a sense in which every experience is real; it is, at least, an experience; but when he contrasts real and apparent he means something more than this. Experiences are not relegated to this class or to that merely at random, but the final decision is the outcome of a long experience of the differences which characterize different individual experiences and is an expression of the relations which are observed to hold between them. Certain experiences are accepted as signs, and certain others come to take the more dignified position of thing signified; the mind rests in them and regards them as the real.

We have seen above that the world of real things in which the plain man finds himself is a world of objects revealed in experiences of touch. When he asks regarding anything: How far away is it? How big is it? In what direction is it? it is always the touch thing that interests him. What is given to the other senses is only a sign of this.

We have also seen (section 8) that the world of atoms and molecules of which the man of science tells us is nothing more than a further development of the world of the plain man. The real things with which science concerns itself are, after all, only minute touch things, conceived just as are the things with which the plain man is familiar. They exist in space and move about in space, as the things about us are perceived to exist in space and move about in space. They have size and position, and are separated by distances. We do not perceive them, it is true; but we conceive them after the analogy of the things that we do perceive, and it is not inconceivable that, if our senses were vastly more acute, we might perceive them directly.

Now, when we conclude that the things directly perceptible to the sense of touch are to be regarded as appearances, as signs of the presence of these minuter things, do we draw such a conclusion arbitrarily? By no means. The distinction between appearance and reality is drawn here just as it is drawn in the world of our common everyday experiences. The great majority of the touch things about us we are not actually touching at any given moment. We only see the things, i.e. we have certain signs of their presence. None the less we believe that the things exist all the time. And in the same way the man of science does not doubt the existence of the real things of which he speaks; he perceives their signs. That certain experiences are to be taken as signs of such realities he has established by innumerable observations and careful deductions from those observations. To see the full force of his reasonings one must read some work setting forth the history of the atomic theory.

If, then, we ask the question: What is the real external world? it is clear that we cannot answer it satisfactorily without taking into consideration the somewhat shifting senses of the word "real." What is the real external world to the plain man? It is the world of touch things, of objects upon which he can lay his hands. What is the real external world to the man of science? It is the world of atoms and molecules, of minuter touch things that he cannot actually touch, but which he conceives as though he could touch them.

It should be observed that the man of science has no right to deny the real world which is revealed in the experience of the plain man. In all his dealings with the things which interest him in common life, he refers to this world just as the plain man does. He sees a tree and walks towards it, and distinguishes between its real and its apparent color, its real and its apparent size. He talks about seeing things as they are, or not seeing things as they are. These distinctions in his experience of things remain even after he has come to believe in atoms and molecules.

Thus, the touch object, the tree as he feels it under his hand, may come to be regarded as the sign of the presence of those entities that science seems, at present, to regard as ultimate. Does this prevent it from being the object which has stood as the interpreter of all those diverse visual sensations that we have called different views of the tree? They are still the appearances, and it, relatively to them, is the reality. Now we find that it, in its turn, can be used as a sign of something else, can be regarded as an appearance of a reality more ultimate. It is clear, then, that the same thing may be regarded both as appearance and as reality—appearance as contrasted with one thing, and reality as contrasted with another.

But suppose one says: I do not want to know what the real external world is to this man or to that man; I want to know what the real external world is. What shall we say to such a demand?

There is a sense in which such a demand is not purely meaningless, though it may not be a very sensible demand to make. We have seen that an increase of knowledge about things compels a man to pass from the real things of common life to the real things of science, and to look upon the former as appearance. Now, a man may arbitrarily decide that he will use the word "reality" to indicate only that which can never in its turn be regarded as appearance, a reality which must remain an ultimate reality; and he may insist upon our telling him about that. How a man not a soothsayer can tell when he has come to ultimate reality, it is not easy to see.

Suppose, however, that we could give any one such information. We should then be telling him about things as they are, it is true, but his knowledge of things would not be different in kind from what it was before. The only difference between such a knowledge of things and a knowledge of things not known to be ultimate would be that, in the former case, it would be recognized that no further extension of knowledge was possible. The distinction between appearance and reality would remain just what it was in the experience of the plain man.

22. THE BUGBEAR OF THE "UNKNOWABLE."—It is very important to recognize that we must not go on talking about appearance and reality, as if our words really meant something, when we have quite turned our backs upon our experience of appearances and the realities which they represent.

That appearances and realities are connected we know very well, for we perceive them to be connected. What we see, we can touch. And we not only know that appearances and realities are connected, but we know with much detail what appearances are to be taken as signs of what realities. The visual experience which I call the house as seen from a distance I never think of taking for a representative of the hat which I hold in my hand. This visual experience I refer to its own appropriate touch thing, and not to another. If what looks like a beefsteak could really be a fork or a mountain or a kitten indifferently,—but I must not even finish the sentence, for the words "look like" and "could really be" lose all significance when we loosen the bond between appearances and the realities to which they are properly referred.

Each appearance, then, must be referred to some particular real thing and not to any other. This is true of the appearances which we recognize as such in common life, and it is equally true of the appearances recognized as such in science. The pen which I feel between my fingers I may regard as appearance and refer to a swarm of moving atoms. But it would be silly for me to refer it to atoms "in general." The reality to which I refer the appearance in question is a particular group of atoms existing at a particular point in space. The chemist never supposes that the atoms within the walls of his test-tube are identical with those in the vial on the shelf. Neither in common life nor in science would the distinction between appearances and real things be of the smallest service were it not possible to distinguish between this appearance and that, and this reality and that, and to refer each appearance to its appropriate reality. Indeed, it is inconceivable that, under such circumstances, the distinction should have been drawn at all.

These points ought to be strongly insisted upon, for we find certain philosophic writers falling constantly into a very curious abuse of the distinction and making much capital of it. It is argued that what we see, what we touch, what we conceive as a result of scientific observation and reflection—all is, in the last analysis, material which is given us in sensation. The various senses furnish us with different classes of sensations; we work these up into certain complexes. But sensations are only the impressions which something outside of us makes upon us. Hence, although we seem to ourselves to know the external world as it is, our knowledge can never extend beyond the impressions made upon us. Thus, we are absolutely shut up to appearances, and can know nothing about the reality to which they must be referred.

Touching this matter Herbert Spencer writes[1] as follows: "When we are taught that a piece of matter, regarded by us as existing externally, cannot be really known, but that we can know only certain impressions produced on us, we are yet, by the relativity of thought, compelled to think of these in relation to a cause—the notion of a real existence which generated these impressions becomes nascent. If it be proved that every notion of a real existence which we can frame is inconsistent with itself,—that matter, however conceived by us, cannot be matter as it actually is,—our conception, though transfigured, is not destroyed: there remains the sense of reality, dissociated as far as possible from those special forms under which it was before represented in thought."

This means, in plain language, that we must regard everything we know and can know as appearance and must refer it to an unknown reality. Sometimes Mr. Spencer calls this reality the Unknowable, sometimes he calls it the Absolute, and sometimes he allows it to pass by a variety of other names, such as Power, Cause, etc. He wishes us to think of it as "lying behind appearances" or as "underlying appearances."

Probably it has already been remarked that this Unknowable has brought us around again to that amusing "telephone exchange" discussed in the third chapter. But if the reader feels within himself the least weakness for the Unknowable, I beg him to consider carefully, before he pins his faith to it, the following:—

(1) If we do perceive external bodies, our own bodies and others, then it is conceivable that we may have evidence from observation to the effect that other bodies affecting our bodies may give rise to sensations. In this case we cannot say that we know nothing but sensations; we know real bodies as well as sensations, and we may refer the sensations to the real bodies.

(2) If we do not perceive that we have bodies, and that our bodies are acted upon by others, we have no evidence that what we call our sensations are due to messages which come from "external things" and are conducted along the nerves. It is then, absurd to talk of such "external things" as though they existed, and to call them the reality to which sensations, as appearances, must be referred,

(3) In other words, if there is perceived to be a telephone exchange with its wires and subscribers, we may refer the messages received to the subscribers, and call this, if we choose, a reference of appearance to reality.

But if there is perceived no telephone exchange, and if it is concluded that any wires or subscribers of which it means anything to speak must be composed of what we have heretofore called "messages," then it is palpably absurd to refer the "messages" as a whole to subscribers not supposed to be composed of "messages"; and it is a blunder to go on calling the things that we know "messages," as though we had evidence that they came from, and must be referred to, something beyond themselves.

We must recognize that, with the general demolition of the exchange, we lose not only known subscribers, but the very notion of a subscriber. It will not do to try to save from this wreck some "unknowable" subscriber, and still pin our faith to him.

(4) We have seen that the relation of appearance to reality is that of certain experiences to certain other experiences. When we take the liberty of calling the Unknowable a reality, we blunder in our use of the word. The Unknowable cannot be an experience either actual, possible, or conceived as possible, and it cannot possibly hold the relation to any of our experiences that a real thing of any kind holds to the appearances that stand as its signs.

(5) Finally, no man has ever made an assumption more perfectly useless and purposeless than the assumption of the Unknowable. We have seen that the distinction between appearance and reality is a serviceable one, and it has been pointed out that it would be of no service whatever if it were not possible to refer particular appearances to their own appropriate realities. The realities to which we actually refer appearances serve to explain them. Thus, when I ask: Why do I perceive that tree now as faint and blue and now as vivid and green? the answer to the question is found in the notion of distance and position in space; it is found, in other words, in a reference to the real world of touch things, for which visual experiences serve as signs. Under certain circumstances, the mountain ought to be robed in its azure hue, and, under certain circumstances, it ought not. The circumstances in each case are open to investigation.

Now, let us substitute for the real world of touch things, which furnishes the explanation of given visual experiences, that philosophic fiction, that pseudo-real nonentity, the Unknowable. Now I perceive a tree as faint and blue, now as bright and green; will a reference to the Unknowable explain why the experiences differed? Was the Unknowable in the one instance farther off in an unknowable space, and in the other nearer? This, even if it means anything, must remain unknowable. And when the chemist puts together a volume of chlorine gas and a volume of hydrogen gas to get two volumes of hydrochloric acid gas, shall we explain the change which has taken place by a reference to the Unknowable, or shall we turn to the doctrine of atoms and their combinations?

The fact is that no man in his senses tries to account for any individual fact by turning for an explanation to the Unknowable. It is a life-preserver by which some set great store, but which no man dreams of using when he really falls into the water.

If, then, we have any reason to believe that there is a real external world at all, we have reason to believe that we know what it is. That some know it imperfectly, that others know it better, and that we may hope that some day it will be known still more perfectly, is surely no good reason for concluding that we do not know it at all.

[1] "First Principles," Part I, Chapter IV, section 26.



CHAPTER VI

OF SPACE

23. WHAT ARE WE SUPPOSED TO KNOW ABOUT IT.—The plain man may admit that he is not ready to hazard a definition of space, but he is certainly not willing to admit that he is wholly ignorant of space and of its attributes. He knows that it is something in which material objects have position and in which they move about; he knows that it has not merely length, like a line, nor length and breadth, like a surface, but has the three dimensions of length, breadth, and depth; he knows that, except in the one circumstance of its position, every part of space is exactly like every other part, and that, although objects may move about in space, it is incredible that the spaces themselves should be shifted about.

Those who are familiar with the literature of the subject know that it has long been customary to make regarding space certain other statements to which the plain man does not usually make serious objection when he is introduced to them. Thus it is said:—

(1) The idea of space is necessary. We can think of objects in space as annihilated, but we cannot conceive space to be annihilated. We can clear space of things, but we cannot clear away space itself, even in thought.

(2) Space must be infinite. We cannot conceive that we should come to the end of space.

(3) Every space, however small, is infinitely divisible. That is to say, even the most minute space must be composed of spaces. We cannot, even theoretically, split a solid into mere surfaces, a surface into mere lines, or a line into mere points.

Against such statements the plain man is not impelled to rise in rebellion, for he can see that there seems to be some ground for making them. He can conceive of any particular material object as annihilated, and of the place which it occupied as standing empty; but he cannot go on and conceive of the annihilation of this bit of empty space. Its annihilation would not leave a gap, for a gap means a bit of empty space; nor could it bring the surrounding spaces into juxtaposition, for one cannot shift spaces, and, in any case, a shifting that is not a shifting through space is an absurdity.

Again, he cannot conceive of any journey that would bring him to the end of space. There is no more reason for stopping at one point than at another; why not go on? What could end space?

As to the infinite divisibility of space, have we not, in addition to the seeming reasonableness of the doctrine, the testimony of all the mathematicians? Does any one of them ever dream of a line so short that it cannot be divided into two shorter lines, or of an angle so small that it cannot be bisected?

24. SPACE AS NECESSARY AND SPACE AS INFINITE.—That these statements about space contain truth one should not be in haste to deny. It seems silly to say that space can be annihilated, or that one can travel "over the mountains of the moon" in the hope of reaching the end of it. And certainly no prudent man wishes to quarrel with that coldly rational creature the mathematician.

But it is well worth while to examine the statements carefully and to see whether there is not some danger that they may be understood in such a way as to lead to error. Let us begin with the doctrine that space is necessary and cannot be "thought away."

As we have seen above, it is manifestly impossible to annihilate in thought a certain portion of space and leave the other portions intact. There are many things in the same case. We cannot annihilate in thought one side of a door and leave the other side; we cannot rob a man of the outside of his hat and leave him the inside. But we can conceive of a whole door as annihilated, and of a man as losing a whole hat. May we or may we not conceive of space as a whole as nonexistent?

I do not say, be it observed, can we conceive of something as attacking and annihilating space? Whatever space may be, we none of us think of it as a something that may be threatened and demolished. I only say, may we not think of a system of things—not a world such as ours, of course, but still a system of things of some sort—in which space relations have no part? May we not conceive such to be possible?

It should be remarked that space relations are by no means the only ones in which we think of things as existing. We attribute to them time relations as well. Now, when we think of occurrences as related to each other in time, we do, in so far as we concentrate our attention upon these relations, turn our attention away from space and contemplate another aspect of the system of things. Space is not such a necessity of thought that we must keep thinking of space when we have turned our attention to something else. And is it, indeed, inconceivable that there should be a system of things (not extended things in space, of course), characterized by time relations and perhaps other relations, but not by space relations?

It goes without saying that we cannot go on thinking of space and at the same time not think of space. Those who keep insisting upon space as a necessity of thought seem to set us such a task as this, and to found their conclusion upon our failure to accomplish it. "We can never represent to ourselves the nonexistence of space," says the German philosopher Kant (1724-1804), "although we can easily conceive that there are no objects in space."

It would, perhaps, be fairer to translate the first half of this sentence as follows: "We can never picture to ourselves the nonexistence of space." Kant says we cannot make of it a Vorstellung, a representation. This we may freely admit, for what does one try to do when one makes the effort to imagine the nonexistence of space? Does not one first clear space of objects, and then try to clear space of space in much the same way? We try to "think space away," i.e. to remove it from the place where it was and yet keep that place.

What does it mean to imagine or represent to oneself the nonexistence of material objects? Is it not to represent to oneself the objects as no longer in space, i.e. to imagine the space as empty, as cleared of the objects? It means something in this case to speak of a Vorstellung, or representation. We can call before our minds the empty space. But if we are to think of space as nonexistent, what shall we call before our minds? Our procedure must not be analogous to what it was before; we must not try to picture to our minds the absence of space, as though that were in itself a something that could be pictured; we must turn our attention to other relations, such as time relations, and ask whether it is not conceivable that such should be the only relations obtaining within a given system.

Those who insist upon the fact that we cannot but conceive space as infinite employ a very similar argument to prove their point. They set us a self-contradictory task, and regard our failure to accomplish it as proof of their position. Thus, Sir William Hamilton (1788-1856) argues: "We are altogether unable to conceive space as bounded—as finite; that is, as a whole beyond which there is no further space." And Herbert Spencer echoes approvingly: "We find ourselves totally unable to imagine bounds beyond which there is no space."

Now, whatever one may be inclined to think about the infinity of space, it is clear that this argument is an absurd one. Let me write it out more at length: "We are altogether unable to conceive space as bounded—as finite; that is, as a whole in the space beyond which there is no further space." "We find ourselves totally unable to imagine bounds, in the space beyond which there is no further space." The words which I have added were already present implicitly. What can the word "beyond" mean if it does not signify space beyond? What Sir William and Mr. Spencer have asked us to do is to imagine a limited space with a beyond and yet no beyond.

There is undoubtedly some reason why men are so ready to affirm that space is infinite, even while they admit that they do not know that the world of material things is infinite. To this we shall come back again later. But if one wishes to affirm it, it is better to do so without giving a reason than it is to present such arguments as the above.

25. SPACE AS INFINITELY DIVISIBLE.—For more than two thousand years men have been aware that certain very grave difficulties seem to attach to the idea of motion, when we once admit that space is infinitely divisible. To maintain that we can divide any portion of space up into ultimate elements which are not themselves spaces, and which have no extension, seems repugnant to the idea we all have of space. And if we refuse to admit this possibility there seems to be nothing left to us but to hold that every space, however small, may theoretically be divided up into smaller spaces, and that there is no limit whatever to the possible subdivision of spaces. Nevertheless, if we take this most natural position, we appear to find ourselves plunged into the most hopeless of labyrinths, every turn of which brings us face to face with a flat self-contradiction.

To bring the difficulties referred to clearly before our minds, let us suppose a point to move uniformly over a line an inch long, and to accomplish its journey in a second. At first glance, there appears to be nothing abnormal about this proceeding. But if we admit that this line is infinitely divisible, and reflect upon this property of the line, the ground seems to sink from beneath our feet at once.

For it is possible to argue that, under the conditions given, the point must move over one half of the line in half a second; over one half of the remainder, or one fourth of the line, in one fourth of a second; over one eighth of the line, in one eighth of a second, etc. Thus the portions of line moved over successively by the point may be represented by the descending series:

1/2, 1/4, 1/8, 1/16, . . . [Greek omicron symbol]

Now, it is quite true that the motion of the point can be described in a number of different ways; but the important thing to remark here is that, if the motion really is uniform, and if the line really is infinitely divisible, this series must, as satisfactorily as any other, describe the motion of the point. And it would be absurd to maintain that a part of the series can describe the whole motion. We cannot say, for example, that, when the point has moved over one half, one fourth, and one eighth of the line, it has completed its motion. If even a single member of the series is left out, the whole line has not been passed over; and this is equally true whether the omitted member represent a large bit of line or a small one.

The whole series, then, represents the whole line, as definite parts of the series represent definite parts of the line. The line can only be completed when the series is completed. But when and how can this series be completed? In general, a series is completed when we reach the final term, but here there appears to be no final term. We cannot make zero the final term, for it does not belong to the series at all. It does not obey the law of the series, for it is not one half as large as the term preceding it—what space is so small that dividing it by 2 gives us [omicron]? On the other hand, some term just before zero cannot be the final term; for if it really represents a little bit of the line, however small, it must, by hypothesis, be made up of lesser bits, and a smaller term must be conceivable. There can, then, be no last term to the series; i.e. what the point is doing at the very last is absolutely indescribable; it is inconceivable that there should be a very last.

It was pointed out many centuries ago that it is equally inconceivable that there should be a very first. How can a point even begin to move along an infinitely divisible line? Must it not before it can move over any distance, however short, first move over half that distance? And before it can move over that half, must it not move over the half of that? Can it find something to move over that has no halves? And if not, how shall it even start to move? To move at all, it must begin somewhere; it cannot begin with what has no halves, for then it is not moving over any part of the line, as all parts have halves; and it cannot begin with what has halves, for that is not the beginning. What does the point do first? that is the question. Those who tell us about points and lines usually leave us to call upon gentle echo for an answer.

The perplexities of this moving point seem to grow worse and worse the longer one reflects upon them. They do not harass it merely at the beginning and at the end of its journey. This is admirably brought out by Professor W. K. Clifford (1845-1879), an excellent mathematician, who never had the faintest intention of denying the possibility of motion, and who did not desire to magnify the perplexities in the path of a moving point. He writes:—

"When a point moves along a line, we know that between any two positions of it there is an infinite number . . . of intermediate positions. That is because the motion is continuous. Each of those positions is where the point was at some instant or other. Between the two end positions on the line, the point where the motion began and the point where it stopped, there is no point of the line which does not belong to that series. We have thus an infinite series of successive positions of a continuously moving point, and in that series are included all the points of a certain piece of line-room." [1]

Thus, we are told that, when a point moves along a line, between any two positions of it there is an infinite number of intermediate positions. Clifford does not play with the word "infinite"; he takes it seriously and tells us that it means without any end: "Infinite; it is a dreadful word, I know, until you find out that you are familiar with the thing which it expresses. In this place it means that between any two positions there is some intermediate position; between that and either of the others, again, there is some other intermediate; and so on without any end. Infinite means without any end."

But really, if the case is as stated, the point in question must be at a desperate pass. I beg the reader to consider the following, and ask himself whether he would like to change places with it:—

(1) If the series of positions is really endless, the point must complete one by one the members of an endless series, and reach a nonexistent final term, for a really endless series cannot have a final term.

(2) The series of positions is supposed to be "an infinite series of successive positions." The moving point must take them one after another. But how can it? Between any two positions of the point there is an infinite number of intermediate positions. That is to say, no two of these successive positions must be regarded as next to each other; every position is separated from every other by an infinite number of intermediate ones. How, then, shall the point move? It cannot possibly move from one position to the next, for there is no next. Shall it move first to some position that is not the next? Or shall it in despair refuse to move at all?

Evidently there is either something wrong with this doctrine of the infinite divisibility of space, or there is something wrong with our understanding of it, if such absurdities as these refuse to be cleared away. Let us see where the trouble lies.

26. WHAT IS REAL SPACE?—It is plain that men are willing to make a number of statements about space, the ground for making which is not at once apparent. It is a bold man who will undertake to say that the universe of matter is infinite in extent. We feel that we have the right to ask him how he knows that it is. But most men are ready enough to affirm that space is and must be infinite. How do they know that it is? They certainly do not directly perceive all space, and such arguments as the one offered by Hamilton and Spencer are easily seen to be poor proofs.

Men are equally ready to affirm that space is infinitely divisible. Has any man ever looked upon a line and perceived directly that it has an infinite number of parts? Did any one ever succeed in dividing a space up infinitely? When we try to make clear to ourselves how a point moves along an infinitely divisible line, do we not seem to land in sheer absurdities? On what sort of evidence does a man base his statements regarding space? They are certainly very bold statements.

A careful reflection reveals the fact that men do not speak as they do about space for no reason at all. When they are properly understood, their statements can be seen to be justified, and it can be seen also that the difficulties which we have been considering can be avoided. The subject is a deep one, and it can scarcely be discussed exhaustively in an introductory volume of this sort, but one can, at least, indicate the direction in which it seems most reasonable to look for an answer to the questions which have been raised. How do we come to a knowledge of space, and what do we mean by space? This is the problem to solve; and if we can solve this, we have the key which will unlock many doors.

Now, we saw in the last chapter that we have reason to believe that we know what the real external world is. It is a world of things which we perceive, or can perceive, or, not arbitrarily but as a result of careful observation and deductions therefrom, conceive as though we did perceive it—a world, say, of atoms and molecules. It is not an Unknowable behind or beyond everything that we perceive, or can perceive, or conceive in the manner stated.

And the space with which we are concerned is real space, the space in which real things exist and move about, the real things which we can directly know or of which we can definitely know something. In some sense it must be given in our experience, if the things which are in it, and are known to be in it, are given in our experience. How must we think of this real space?

Suppose we look at a tree at a distance. We are conscious of a certain complex of color. We can distinguish the kind of color; in this case, we call it blue. But the quality of the color is not the only thing that we can distinguish in the experience. In two experiences of color the quality may be the same, and yet the experiences may be different from each other. In the one case we may have more of the same color—we may, so to speak, be conscious of a larger patch; but even if there is not actually more of it, there may be such a difference that we can know from the visual experience alone that the touch object before us is, in the one case, of the one shape, and, in the other case, of another. Thus we may distinguish between the stuff given in our experience and the arrangement of that stuff. This is the distinction which philosophers have marked as that between "matter" and "form." It is, of course, understood that both of these words, so used, have a special sense not to be confounded with their usual one.

This distinction between "matter" and "form" obtains in all our experiences. I have spoken just above of the shape of the touch object for which our visual experiences stand as signs. What do we mean by its shape? To the plain man real things are the touch things of which he has experience, and these touch things are very clearly distinguishable from one another in shape, in size, in position, nor are the different parts of the things to be confounded with each other. Suppose that, as we pass our hand over a table, all the sensations of touch and movement which we experience fused into an undistinguishable mass. Would we have any notion of size or shape? It is because our experiences of touch and movement do not fuse, but remain distinguishable from each other, and we are conscious of them as arranged, as constituting a system, that we can distinguish between this part of a thing and that, this thing and that.

This arrangement, this order, of what is revealed by touch and movement, we may call the "form" of the touch world. Leaving out of consideration, for the present, time relations, we may say that the "form" of the touch world is the whole system of actual and possible relations of arrangement between the elements which make it up. It is because there is such a system of relations that we can speak of things as of this shape or of that, as great or small, as near or far, as here or there.

Now, I ask, is there any reason to believe that, when the plain man speaks of space, the word means to him anything more than this system of actual and possible relations of arrangement among the touch things that constitute his real world? He may talk sometimes as though space were some kind of a thing, but he does not really think of it as a thing.

This is evident from the mere fact that he is so ready to make about it affirmations that he would not venture to make about things. It does not strike him as inconceivable that a given material object should be annihilated; it does strike him as inconceivable that a portion of space should be blotted out of existence. Why this difference? Is it not explained when we recognize that space is but a name for all the actual and possible relations of arrangement in which things in the touch world may stand? We cannot drop out some of these relations and yet keep space, i.e. the system of relations which we had before. That this is what space means, the plain man may not recognize explicitly, but he certainly seems to recognize it implicitly in what he says about space. Men are rarely inclined to admit that space is a thing of any kind, nor are they much more inclined to regard it as a quality of a thing. Of what could it be the quality?

And if space really were a thing of any sort, would it not be the height of presumption for a man, in the absence of any direct evidence from observation, to say how much there is of it—to declare it infinite? Men do not hesitate to say that space must be infinite. But when we realize that we do not mean by space merely the actual relations which exist between the touch things that make up the world, but also the possible relations, i.e. that we mean the whole plan of the world system, we can see that it is not unreasonable to speak of space as infinite.

The material universe may, for aught we know, be limited in extent. The actual space relations in which things stand to each other may not be limitless. But these actual space relations taken alone do not constitute space. Men have often asked themselves whether they should conceive of the universe as limited and surrounded by void space. It is not nonsense to speak of such a state of things. It would, indeed, appear to be nonsense to say that, if the universe is limited, it does not lie in void space. What can we mean by void space but the system of possible relations in which things, if they exist, must stand? To say that, beyond a certain point, no further relations are possible, seems absurd.

Hence, when a man has come to understand what we have a right to mean by space, it does not imply a boundless conceit on his part to hazard the statement that space is infinite. When he has said this, he has said very little. What shall we say to the statement that space is infinitely divisible?

To understand the significance of this statement we must come back to the distinction between appearances and the real things for which they stand as signs, the distinction discussed at length in the last chapter.

When I see a tree from a distance, the visual experience which I have is, as we have seen, not an indivisible unit, but is a complex experience; it has parts, and these parts are related to each other; in other words, it has both "matter" and "form." It is, however, one thing to say that this experience has parts, and it is another to say that it has an infinite number of parts. No man is conscious of perceiving an infinite number of parts in the patch of color which represents to him a tree at a distance; to say that it is constituted of such strikes us in our moments of sober reflection as a monstrous statement.

Now, this visual experience is to us the sign of the reality, the real tree; it is not taken as the tree itself. When we speak of the size, the shape, the number of parts, of the tree, we do not have in mind the size, the shape, the number of parts, of just this experience. We pass from the sign to the thing signified, and we may lay our hand upon this thing, thus gaining a direct experience of the size and shape of the touch object.

We must recognize, however, that just as no man is conscious of an infinite number of parts in what he sees, so no man is conscious of an infinite number of parts in what he touches. He who tells me that, when I pass my finger along my paper cutter, what I perceive has an infinite number of parts, tells me what seems palpably untrue. When an object is very small, I can see it, and I cannot see that it is composed of parts; similarly, when an object is very small, I can feel it with my finger, but I cannot distinguish its parts by the sense of touch. There seem to be limits beyond which I cannot go in either case.

Nevertheless, men often speak of thousandths of an inch, or of millionths of an inch, or of distances even shorter. Have such fractions of the magnitudes that we do know and can perceive any real existence? The touch world of real things as it is revealed in our experience does not appear to be divisible into such; it does not appear to be divisible even so far, and much less does it appear to be infinitely divisible.

But have we not seen that the touch world given in our experience must be taken by the thoughtful man as itself the sign or appearance of a reality more ultimate? The speck which appears to the naked eye to have no parts is seen under the microscope to have parts; that is to say, an experience apparently not extended has become the sign of something that is seen to have part out of part. We have as yet invented no instrument that will make directly perceptible to the finger tip an atom of hydrogen or of oxygen, but the man of science conceives of these little things as though they could be perceived. They and the space in which they move—the system of actual and possible relations between them—seem to be related to the world revealed in touch very much as the space revealed in the field of the microscope is related to the space of the speck looked at with the naked eye.

Thus, when the thoughtful man speaks of real space, he cannot mean by the word only the actual and possible relations of arrangement among the things and the parts of things directly revealed to his sense of touch. He may speak of real things too small to be thus perceived, and of their motion as through spaces too small to be perceptible at all. What limit shall he set to the possible subdivision of real things? Unless he can find an ultimate reality which cannot in its turn become the appearance or sign of a further reality, it seems absurd to speak of a limit at all.

We may, then, say that real space is infinitely divisible. By this statement we should mean that certain experiences may be represented by others, and that we may carry on our division in the case of the latter, when a further subdivision of the former seems out of the question. But it should not mean that any single experience furnished us by any sense, or anything that we can represent in the imagination, is composed of an infinite number of parts.

When we realize this, do we not free ourselves from the difficulties which seemed to make the motion of a point over a line an impossible absurdity? The line as revealed in a single experience either of sight or of touch is not composed of an infinite number of parts. It is composed of points seen or touched—least experiences of sight or touch, minima sensibilia. These are next to each other, and the point, in moving, takes them one by one.

But such a single experience is not what we call a line. It is but one experience of a line. Though the experience is not infinitely divisible, the line may be. This only means that the visual or tactual point of the single experience may stand for, may represent, what is not a mere point but has parts, and is, hence, divisible. Who can set a limit to such possible substitutions? in other words, who can set a limit to the divisibility of a real line?

It is only when we confuse the single experience with the real line that we fall into absurdities. What the mathematician tells us about real points and real lines has no bearing on the constitution of the single experience and its parts. Thus, when he tells us that between any two points on a line there are an infinite number of other points, he only means that we may expand the line indefinitely by the system of substitutions described above. We do this for ourselves within limits every time that we approach from a distance a line drawn on a blackboard. The mathematician has generalized our experience for us, and that is all he has done. We should try to get at his real meaning, and not quote him as supporting an absurdity.

[1] "Seeing and Thinking," p. 149.



CHAPTER VII

OF TIME

27. TIME AS NECESSARY, INFINITE, AND INFINITELY DIVISIBLE.—Of course, we all know something about time; we know it as past, present, and future; we know it as divisible into parts, all of which are successive; we know that whatever happens must happen in time. Those who have thought a good deal about the matter are apt to tell us that time is a necessity of thought, we cannot but think it; that time is and must be infinite; and that it is infinitely divisible.

These are the same statements that were made regarding space, and, as they have to be criticised in just the same way, it is not necessary to dwell upon them at great length. However, we must not pass them over altogether.

As to the statement that time is a necessary idea, we may freely admit that we cannot in thought annihilate time, or think it away. It does not seem to mean anything to attempt such a task. Whatever time may be, it does not appear to be a something of such a nature that we can demolish it or clear it away from something else. But is it necessarily absurd to speak of a system of things—not, of course, a system of things in which there is change, succession, an earlier and a later, but still a system of things of some sort—in which there obtain no time relations? The problem is, to be sure, one of theoretical interest merely, for such a system of things is not the world we know.

And as for the infinity of time, may we not ask on what ground any one ventures to assert that time is infinite? No man can say that infinite time is directly given in his experience. If one does not directly perceive it to be infinite, must one not seek for some proof of the fact? The only proof which appears to be offered us is contained in the statement that we cannot conceive of a time before which there was no time, nor of a time after which there will be no time; a proof which is no proof, for written out at length it reads as follows: we cannot conceive of a time in the time before which there was no time, nor of a time in the time after which there will be no time. As well say: We cannot conceive of a number the number before which was no number, nor of a number the number after which will be no number. Whatever may be said for the conclusion arrived at, the argument is a very poor one.

When we turn to the consideration of time as infinitely divisible, we seem to find ourselves confronted with the same difficulties which presented themselves when we thought of space as infinitely divisible. Certainly no man was immediately conscious of an infinite number of parts in the minute which just slipped by. Shall he assert that it did, nevertheless, contain an infinite number of parts? Then how did it succeed in passing? how did it even begin to pass away? It is infinitely divisible, that is, there is no end to the number of parts into which it may be divided; those parts and parts of parts are all successive, no two can pass at once, they must all do it in a certain order, one after the other.

Thus, something must pass first. What can it be? If that something has parts, is divisible, the whole of it cannot pass first. It must itself pass bit by bit, as must the whole minute; and if it is infinitely divisible we have precisely the problem that we had at the outset. Whatever passes first cannot, then, have parts.

Let us assume that it has no parts, and bid it Godspeed! Has the minute begun? Our minute is, by hypothesis, infinitely divisible; it is composed of parts, and those parts of other parts, and so on without end. We cannot by subdivision come to any part which is itself not composed of smaller parts. The partless thing that passed, then, is no part of the minute. That is all still waiting at the gate, and no member of its troop can prove that it has a right to lead the rest. In the same outer darkness is waiting the point on the line that misbehaved itself in the last chapter.

28. THE PROBLEM OF PAST, PRESENT, AND FUTURE.—It seems bad enough to have on our hands a minute which must pass away in successive bits, and to discover that no bit of it can possibly pass first. But if we follow with approval the reflections of certain thinkers, we may find ourselves at such a pass that we would be glad to be able to prove that we may have on our hands a minute of any sort. Men sometimes are so bold as to maintain that they know time to be infinite; would it not be well for them to prove first that they can know time at all?

The trouble is this; as was pointed out long ago by Saint Augustine (354-430) in his famous "Confessions," [1] the parts of time are successive, and of the three divisions, past, present, and future, only one can be regarded as existing: "Those two times, past and future, how can they be, when the past is not now, and the future is not yet?" The present is, it seems, the only existent; how long is the present?

"Even a single hour passes in fleeting moments; as much of it as has taken flight is past, what remains is future. If we can comprehend any time that is divisible into no parts at all, or perhaps into the minutest parts of moments, this alone let us call present; yet this speeds so hurriedly from the future to the past that it does not endure even for a little space. If it has duration, it is divided into a past and a future; but the present has no duration.

"Where, then, is the time that we may call long? Is it future? We do not say of the future: it is long; for as yet there exists nothing to be long. We say: it will be long. But when? If while yet future it will not be long, for nothing will yet exist to be long. And if it will be long, when, from a future as yet nonexistent, it has become a present, and has begun to be, that it may be something that is long, then present time cries out in the words of the preceding paragraph that it cannot be long."

Augustine's way of presenting the difficulty is a quaint one, but the problem is as real at the beginning of the twentieth century as it was at the beginning of the fifth. Past time does not exist now, future time does not exist yet, and present time, it seems, has no duration. Can a man be said to be conscious of time as past, present, and future? Who can be conscious of the nonexistent? And the existent is not time, it has no duration, there is no before and after in a mere limiting point.

Augustine's way out of the difficulty is the suggestion that, although we cannot, strictly speaking, measure time, we can measure memory and expectation. Before he begins to repeat a psalm, his expectation extends over the whole of it. After a little a part of it must be referred to expectation and a part of it to memory. Finally, the whole psalm is "extended along" the memory. We can measure this, at least.

But how is the psalm in question "extended along" the memory or the expectation? Are the parts of it successive, or do they thus exist simultaneously? If everything in the memory image exists at once, if all belongs to the punctual present, to the mere point that divides past from future, how can a man get from it a consciousness of time, of a something whose parts cannot exist together but must follow each other?

Augustine appears to overlook the fact that on his own hypothesis, the present, the only existent, the only thing a man can be conscious of, is an indivisible instant. In such there can be no change; the man who is shut up to such cannot be aware that the past is growing and the future diminishing. Any such change as this implies at least two instants, an earlier and a later. He who has never experienced a change of any sort, who has never been conscious of the relation of earlier and later, of succession, cannot think of the varied content of memory as of that which has been present. It cannot mean to him what memory certainly means to us; he cannot be conscious of a past, a present, and a future. To extract the notion of time, of past, present, and future, from an experience which contains no element of succession, from an indivisible instant, is as hopeless a task as to extract a line from a mathematical point.

It appears, then, that, if we are to be conscious of time at all, if we are to have the least conception of it, we must have some direct experience of change. We cannot really be shut up to that punctual present, that mere point or limit between past and future, that the present has been described as being. But does this not imply that we can be directly conscious of what is not present, that we can now perceive what does not now exist? How is this possible?

It is not easy for one whose reading has been somewhat limited in any given field to see the full significance of the problems which present themselves in that field. Those who read much in the history of modern philosophy will see that this ancient difficulty touching our consciousness of time has given rise to some exceedingly curious speculations, and some strange conclusions touching the nature of the mind.

Thus, it has been argued that, since the experience of each moment is something quite distinct from the experience of the next, a something that passes away to give place to its successor, we cannot explain the consciousness of time, of a whole in which successive moments are recognized as having their appropriate place, unless we assume a something that knows each moment and knits it, so to speak, to its successor. This something is the self or consciousness, which is independent of time, and does not exist in time, as do the various experiences that fill the successive moments. It is assumed to be timelessly present at all times, and thus to connect the nonexistent past with the existent present.

I do not ask the reader to try to make clear to himself how anything can be timelessly present at all times, for I do not believe that the words can be made to represent any clear thought whatever. Nor do I ask him to try to conceive how this timeless something can join past and present. I merely wish to point out that these modern speculations, which still influence the minds of many distinguished men, have their origin in a difficulty which suggested itself early in the history of reflective thought, and are by no means to be regarded as a gratuitous and useless exercise of the ingenuity. They are serious attempts to solve a real problem, though they may be unsuccessful ones, and they are worthy of attention even from those who incline to a different solution.

29. WHAT IS REAL TIME?—From the thin air of such speculations as we have been discussing let us come back to the world of the plain man, the world in which we all habitually live. It is from this that we must start out upon all our journeys, and it is good to come back to it from time to time to make sure of our bearings.

We have seen (Chapter V) that we distinguish between the real and the apparent, and that we recognize as the real world the objects revealed to the sense of touch. These objects stand to each other in certain relations of arrangement; that is to say, they exist in space. And just as we may distinguish between the object as it appears and the object as it is, so we may distinguish between apparent space and real space, i.e. between the relations of arrangement, actual and possible, which obtain among the parts of the object as it appears, and those which obtain among the parts of the object as it really is.