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.
But our experience does not present us only with objects in space relations; it presents us with a succession of changes in those objects. And if we will reason about those changes as we have reasoned about space relations, many of our difficulties regarding the nature of time may, as it seems, be made to disappear.
Thus we may recognize that we are directly conscious of duration, of succession, and may yet hold that this crude and immediate experience of duration is not what we mean by real time. Every one distinguishes between apparent time and real time now and then. We all know that a sermon may _seem _long and not be long; that the ten years that we live over in a dream are not ten real years; that the swallowing of certain drugs may be followed by the illusion of the lapse of vast spaces of time, when really very little time has elapsed. What is this real time?
It is nothing else than the order of the changes which take place or may take place in real things. In the last chapter I spoke of space as the "form" of the real world; it would be better to call it a "form" of the real world, and to give the same name also to time.
It is very clear that, when we inquire concerning the real time of any occurrence, or ask how long a series of such lasted, we always look for our answer to something that has happened in the external world. The passage of a star over the meridian, the position of the sun above the horizon, the arc which the moon has described since our last observation, the movement of the hands of a clock, the amount of sand which has fallen in the hourglass, these things and such as these are the indicators of real time. There may be indicators of a different sort; we may decide that it is noon because we are hungry, or midnight because we are tired; we may argue that the preacher must have spoken more than an hour because he quite wore out the patience of the congregation. These are more or less uncertain signs of the lapse of time, but they cannot be regarded as experiences of the passing of time either apparent or real.
Thus, we see that real space and real time are the plan of the world system. They are not things of any sort, and they should not be mistaken for things. They are not known independently of things, though, when we have once had an experience of things and their changes, we can by abstraction from the things themselves fix our attention upon their arrangement and upon the order of their changes. We can divide and subdivide spaces and times without much reference to the things. But we should never forget that it would never have occurred to us to do this, indeed, that the whole procedure would be absolutely meaningless to us, were not a real world revealed in our experience as it is.
He who has attained to this insight into the nature of time is in a position to offer what seem to be satisfactory solutions to the problems which have been brought forward above.
(1) He can see, thus, why it is absurd to speak of any portion of time as becoming nonexistent. Time is nothing else than an order, a great system of relations. One cannot drop out certain of these and leave the rest unchanged, for the latter imply the former. Day-after-to-morrow would not be day-after-to-morrow, if to-morrow did not lie between it and to-day. To speak of dropping out to-morrow and leaving it the time it was conceived to be is mere nonsense.
(2) He can see why it does not indicate a measureless conceit for a man to be willing to say that time is infinite. One who says this need not be supposed to be acquainted with the whole past and future history of the real world, of which time is an aspect. We constantly abstract from things, and consider only the order of their changes, and in this order itself there is no reason why one should set a limit at some point; indeed, to set such a limit seems a gratuitous absurdity. He who says that time is infinite does not say much; he is not affirming the existence of some sort of a thing; he is merely affirming a theoretical possibility, and is it not a theoretical possibility that there may be an endless succession of real changes in a real world?
(3) It is evident, furthermore, that, when one has grasped firmly the significance of the distinction between apparent time and real time, one may with a clear conscience speak of time as infinitely divisible. Of course, the time directly given in any single experience, the minute or the second of which we are conscious as it passes, cannot be regarded as composed of an infinite number of parts. We are not directly conscious of these subdivisions, and it is a monstrous assumption to maintain that they must be present in the minute or second as perceived.
But no such single experience of duration constitutes what we mean by real time. We have seen that real time is the time occupied by the changes in real things, and the question is, How far can one go in the subdivision of this time?
Now, the touch thing which usually is for us in common life the real thing is not the real thing for science; it is the appearance under which the real world of atoms and molecules reveals itself. The atom is not directly perceivable, and we may assign to its motions a space so small that no one could possibly perceive it as space, as a something with part out of part, a something with a here and a there. But, as has been before pointed out (section 26), this does not prevent us from believing the atom and the space in which it moves to be real, and we can represent them to ourselves as we can the things and the spaces with which we have to do in common life.
It is with time just as it is with space. We can perceive an inch to have parts; we cannot perceive a thousandth of an inch to have parts, if we can perceive it at all; but we can represent it to ourselves as extended, that is, we can let an experience which is extended stand for it, and can dwell upon the parts of that. We can perceive a second to have duration; we cannot perceive a thousandth of a second to have duration; but we can conceive it as having duration, i.e. we can let some experience of duration stand for it and serve as its representative.
It is, then, reasonable to speak of the space covered by the vibration of an atom, and it is equally reasonable to speak of the time taken up by its vibration. It is not necessary to believe that the duration that we actually experience as a second must itself be capable of being divided up into the number of parts indicated by the denominator of the fraction that we use in indicating such a time, and that each of these parts must be perceived as duration.
There is, then, a sense in which we may affirm that time is infinitely divisible. But we must remember that apparent time—the time presented in any single experience of duration—is never infinitely divisible; and that real time, in any save a relative sense of the word, is not a single experience of duration at all. It is a recognition of the fact that experiences of duration may be substituted for each other without assignable limit.
(4) But what shall we say to the last problem—to the question how we can be conscious of time at all, when the parts of time are all successive? How can we even have a consciousness of "crude" time, of apparent time, of duration in any sense of the word, when duration must be made up of moments no two of which can exist together and no one of which alone can constitute time? The past is not now, the future is not yet, the present is a mere point, as we are told, and cannot have parts. If we are conscious of time as past, present, and future, must we not be conscious of a series as a series when every member of it save one is nonexistent? Can a man be conscious of the nonexistent?
The difficulty does seem a serious one, and yet I venture to affirm that, if we examine it carefully, we shall see that it is a difficulty of our own devising. The argument quietly makes an assumption—and makes it gratuitously—with which any consciousness of duration is incompatible, and then asks us how there can be such a thing as a consciousness of duration.
The assumption is that we can be conscious only of the existent, and this, written out a little more at length, reads as follows: we can be conscious only of the now existent, or, in other words of the present. Of course, this determines from the outset that we cannot be conscious of the past and the future, of duration.
The past and the future are, to be sure, nonexistent from the point of view of the present; but it should be remarked as well that the present is nonexistent from the point of view of the past or the future. If we are talking of time at all we are talking of that no two parts of which are simultaneous; it would be absurd to speak of a past that existed simultaneously with the present, just as it would be absurd to speak of a present existing simultaneously with the past. But we should not deny to past, present, and future, respectively, their appropriate existence; nor is it by any means self-evident that there cannot be a consciousness of past, present, and future as such.
We fall in with the assumption, it seems, because we know very well that we are not directly conscious of a remote past and a remote future. We represent these to ourselves by means of some proxy—we have present memories of times long past and present anticipations of what will be in the time to come. Moreover, we use the word "present" very loosely; we say the present year, the present day, the present hour, the present minute, or the present second. When we use the word thus loosely, there seems no reason for believing that there should be such a thing as a direct consciousness that extends beyond the present. It appears reasonable to say: No one can be conscious save of the present.
It should be remembered, however, that the generous present of common discourse is by no means identical with the ideal point between past and future dealt with in the argument under discussion. We all say: I now see that the cloud is moving; I now see that the snow is falling. But there can be no moving, no falling, no change, in the timeless "now" with which we have been concerned. Is there any evidence whatever that we are shut up, for all our immediate knowledge, to such a "now"? There is none whatever.
The fact is that this timeless "now" is a product of reflective thought and not a something of which we are directly conscious. It is an ideal point in the real time of which this chapter has treated, the time that is in a certain sense infinitely divisible. It is first cousin to the ideal mathematical point, the mere limit between two lines, a something not perceptible to any sense. We have a tendency to carry over to it what we recognize to be true of the very different present of common discourse, a present which we distinguish from past and future in a somewhat loose way, but a present in which there certainly is the consciousness of change, of duration. And when we do this, we dig for ourselves a pit into which we proceed to fall.
We may, then, conclude that we are directly conscious of more than the present, in the sense in which Augustine used the word. We are conscious of time, of "crude" time, and from this we can pass to a knowledge of real time, and can determine its parts with precision.
[1] Book XI, Chapters 14 and 15.
III. PROBLEMS TOUCHING THE MIND
CHAPTER VIII
WHAT IS THE MIND?
30. PRIMITIVE NOTIONS OF MIND.—The soul or mind, that something to which we refer sensations and ideas of all sorts, is an object that men do not seem to know very clearly and definitely, though they feel so sure of its existence that they regard it as the height of folly to call it in question. That he has a mind, no man doubts; what his mind is, he may be quite unable to say.
We have seen (section 7) that children, when quite young, can hardly be said to recognize that they have minds at all. This does not mean that what is mental is not given in their experience. They know that they must open their eyes to see things, and must lay their hands upon them to feel them; they have had pains and pleasures, memories and fancies. In short, they have within their reach all the materials needed in framing a conception of the mind, and in drawing clearly the distinction between their minds and external things. Nevertheless, they are incapable of using these materials; their attention is engrossed with what is physical,—with their own bodies and the bodies of others, with the things that they can eat, with the toys with which they can play, and the like. It is only later that there emerges even a tolerably clear conception of a self or mind different from the physical and contrasted with it.
Primitive man is almost as material in his thinking as is the young child. Of this we have traces in many of the words which have come to be applied to the mind. Our word "spirit" is from the Latin spiritus, originally a breeze. The Latin word for the soul, the word used by the great philosophers all through the Middle Ages, anima (Greek, anemos), has the same significance. In the Greek New Testament, the word used for spirit (pneuma) carries a similar suggestion. When we are told in the Book of Genesis that "man became a living soul," we may read the word literally "a breath."
What more natural than that the man who is just awakening to a consciousness of that elusive entity the mind should confuse it with that breath which is the most striking outward and visible sign that distinguishes a living man from a dead one?
That those who first tried to give some scientific account of the soul or mind conceived it as a material thing, and that it was sufficiently common to identify it with the breath, we know from direct evidence. A glance at the Greek philosophy, to which we owe so much that is of value in our intellectual life, is sufficient to disclose how difficult it was for thinking men to attain to a higher conception.
Thus, Anaximenes of Miletus, who lived in the sixth century before Christ, says that "our soul, which is air, rules us." A little later, Heraclitus, a man much admired for the depth of his reflections, maintains that the soul is a fiery vapor, evidently identifying it with the warm breath of the living creature. In the fifth century, B.C., Anaxagoras, who accounts for the ordering of the elements into a system of things by referring to the activity of Mind or Reason, calls mind "the finest of things," and it seems clear that he did not conceive of it as very different in nature from the other elements which enter into the constitution of the world.
Democritus of Abdera (between 460 and 360 B.C.), that great investigator of nature and brilliant writer, developed a materialistic doctrine that admits the existence of nothing save atoms and empty space. He conceived the soul to consist of fine, smooth, round atoms, which are also atoms of fire. These atoms are distributed through the whole body, but function differently in different places—in the brain they give us thought, in the heart, anger, and in the liver, desire. Life lasts just so long as we breathe in and breathe out such atoms.
The doctrine of Democritus was taken up by Epicurus, who founded his school three hundred years before Christ—a school which lived and prospered for a very long time. Those who are interested in seeing how a materialistic psychology can be carried out in detail by an ingenious mind should read the curious account of the mind presented in his great poem, "On Nature," by the Roman poet Lucretius, an ardent Epicurean, who wrote in the first century B.C.
The school which we commonly think of contrasting with the Epicurean, and one which was founded at about the same time, is that of the Stoics. Certainly the Stoics differed in many things from the Epicureans; their view of the world, and of the life of man, was a much nobler one; but they were uncompromising materialists, nevertheless, and identified the soul with the warm breath that animates man.
31. THE MIND AS IMMATERIAL.—It is scarcely too much to say that the Greek philosophy as a whole impresses the modern mind as representing the thought of a people to whom it was not unnatural to think of the mind as being a breath, a fire, a collection of atoms, a something material. To be sure, we cannot accuse those twin stars that must ever remain the glory of literature and science, Plato and Aristotle, of being materialists. Plato (427-347, B.C.) distributes, it is true, the three-fold soul, which he allows man, in various parts of the human body, in a way that at least suggests the Democritean distribution of mind-atoms. The lowest soul is confined beneath the diaphragm; the one next in rank has its seat in the chest; and the highest, the rational soul, is enthroned in the head. However, he has said quite enough about this last to indicate clearly that he conceived it to be free from all taint of materiality.
As for Aristotle (384-322, B.C.), who also distinguished between the lower psychical functions and the higher, we find him sometimes speaking of soul and body in such a way as to lead men to ask themselves whether he is really speaking of two things at all; but when he specifically treats of the nous or reason, he insists upon its complete detachment from everything material. Man's reason is not subjected to the fate of the lower psychical functions, which, as the "form" of the body, perish with the body; it enters from without, and it endures after the body has passed away. It is interesting to note, however, an occasional lapse even in Aristotle. When he comes to speak of the relation to the world of the Divine Mind, the First Cause of Motion, which he conceives as pure Reason, he represents it as touching the world, although it remains itself untouched. We seem to find here just a flavor—an inconsistent one—of the material.
Such reflections as those of Plato and Aristotle bore fruit in later ages. When we come down to Plotinus the Neo-Platonist (204-269, A.D.), we have left the conception of the soul as a warm breath, or as composed of fine round atoms, far behind. It has become curiously abstract and incomprehensible. It is described as an immaterial substance This substance is, in a sense, in the body, or, at least, it is present to the body. But it is not in the body as material things are in this place or in that. It is as a whole in the whole body, and it is as a whole in every part of the body. Thus the soul may be regarded as divisible, since it is distributed throughout the body; but it must also be regarded as indivisible, since it is wholly in every part.
Let the man to whom such sentences as these mean anything rejoice in the meaning that he is able to read into them! If he can go as far as Plotinus, perhaps he can go as far as Cassiodorus (477-570, A.D.), and maintain that the soul is not merely as a whole in every part of the body, but is wholly in each of its own parts.
Upon reading such statements one's first impulse is to exclaim: How is it possible that men of sense should be led to speak in this irresponsible way? and when they do speak thus, is it conceivable that other men should seriously occupy themselves with what they say?
But if one has the historic sense, and knows something of the setting in which such doctrines come to the birth, one cannot regard it as remarkable that men of sense should urge them. No one coins them independently out of his own brain; little by little men are impelled along the path that leads to such conclusions. Plotinus was a careful student of the philosophers that preceded him. He saw that mind must be distinguished from matter, and he saw that what is given a location in space, in the usual sense of the words, is treated like a material thing. On the other hand, he had the common experience that we all have of a relation between mind and body. How do justice to this relation, and yet not materialize mind?
What he tried to do is clear, and it seems equally clear that he had good reason for trying to do it. But it appears to us now that what he actually did was to make of the mind or soul a something very like an inconsistent bit of matter, that is somehow in space, and yet not exactly in space, a something that can be in two places at once, a logical monstrosity. That his doctrine did not meet with instant rejection was due to the fact, already alluded to, that our experience of the mind is something rather dim and elusive. It is not easy for a man to say what it is, and, hence, it is not easy for a man to say what it is not.
The doctrine of Plotinus passed over to Saint Augustine, and from him it passed to the philosophers of the Middle Ages. How extremely difficult it has been for the world to get away from it at all, is made clearly evident in the writings of that remarkable man Descartes.
Descartes wrote in the seventeenth century. The long sleep of the Middle Ages was past, and the several sciences had sprung into a vigorous and independent life. It was not enough for Descartes to describe the relation of mind and body in the loose terms that had prevailed up to his time. He had made a careful study of anatomy, and he realized that the brain is a central organ to which messages are carried by the nerves from all parts of the body. He knew that an injury to the nerve might prevent the receipt of a message, i.e. he knew that a conscious sensation did not come into being until something happened in the brain.