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 s.p.a.ce. 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 circ.u.mstances, 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 a.n.a.lysis, material which is given us in sensation. The various senses furnish us with different cla.s.ses 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 pa.s.s 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 a.s.sumption more perfectly useless and purposeless than the a.s.sumption 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 s.p.a.ce; 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 circ.u.mstances, the mountain _ought_ to be robed in its azure hue, and, under certain circ.u.mstances, it _ought not_.
The circ.u.mstances in each case are open to investigation.
Now, let us subst.i.tute for the real world of touch things, which furnishes the explanation of given visual experiences, that philosophic fiction, that pseudo-real nonent.i.ty, 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 s.p.a.ce, 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 s.p.a.cE
23. WHAT ARE WE SUPPOSED TO KNOW ABOUT IT.--The plain man may admit that he is not ready to hazard a definition of s.p.a.ce, but he is certainly not willing to admit that he is wholly ignorant of s.p.a.ce 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 circ.u.mstance of its position, every part of s.p.a.ce is exactly like every other part, and that, although objects may move about in s.p.a.ce, it is incredible that the s.p.a.ces 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 s.p.a.ce 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 s.p.a.ce is _necessary_. We can think of objects in s.p.a.ce as annihilated, but we cannot conceive s.p.a.ce to be annihilated. We can clear s.p.a.ce of things, but we cannot clear away s.p.a.ce itself, even in thought.
(2) s.p.a.ce must be _infinite_. We cannot conceive that we should come to the end of s.p.a.ce.
(3) Every s.p.a.ce, however small, is _infinitely divisible_. That is to say, even the most minute s.p.a.ce must be composed of s.p.a.ces. 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 s.p.a.ce. Its annihilation would not leave a gap, for a gap means a bit of empty s.p.a.ce; nor could it bring the surrounding s.p.a.ces into juxtaposition, for one cannot shift s.p.a.ces, and, in any case, a shifting that is not a shifting through s.p.a.ce is an absurdity.
Again, he cannot conceive of any journey that would bring him to the end of s.p.a.ce. There is no more reason for stopping at one point than at another; why not go on? What could end s.p.a.ce?
As to the infinite divisibility of s.p.a.ce, 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. s.p.a.cE AS NECESSARY AND s.p.a.cE AS INFINITE.--That these statements about s.p.a.ce contain truth one should not be in haste to deny. It seems silly to say that s.p.a.ce 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 s.p.a.ce is necessary and cannot be "thought away."
As we have seen above, it is manifestly impossible to annihilate in thought a certain portion of s.p.a.ce 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 s.p.a.ce as a whole as nonexistent?
I do not say, be it observed, can we conceive of something as attacking and annihilating s.p.a.ce? Whatever s.p.a.ce 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 s.p.a.ce relations have no part? May we not conceive such to be possible?
It should be remarked that s.p.a.ce 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 s.p.a.ce and contemplate another aspect of the system of things. s.p.a.ce is not such a necessity of thought that we must keep thinking of s.p.a.ce 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 s.p.a.ce, of course), characterized by time relations and perhaps other relations, but not by s.p.a.ce relations?
It goes without saying that we cannot go on thinking of s.p.a.ce and at the same time not think of s.p.a.ce. Those who keep insisting upon s.p.a.ce 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 s.p.a.ce," says the German philosopher Kant (1724-1804), "although we can easily conceive that there are no objects in s.p.a.ce."
It would, perhaps, be fairer to translate the first half of this sentence as follows: "We can never picture to ourselves the nonexistence of s.p.a.ce." 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 s.p.a.ce? Does not one first clear s.p.a.ce of objects, and then try to clear s.p.a.ce of s.p.a.ce in much the same way? We try to "think s.p.a.ce 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 s.p.a.ce, _i.e._ to imagine the s.p.a.ce 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 s.p.a.ce. But if we are to think of s.p.a.ce as nonexistent, what shall we call before our minds? Our procedure must not be a.n.a.logous to what it was before; we must not try to picture to our minds _the absence of s.p.a.ce_, 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 s.p.a.ce 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 s.p.a.ce as bounded--as finite; that is, as a whole beyond which there is no further s.p.a.ce."
And Herbert Spencer echoes approvingly: "We find ourselves totally unable to imagine bounds beyond which there is no s.p.a.ce."
Now, whatever one may be inclined to think about the infinity of s.p.a.ce, it is clear that this argument is an absurd one. Let me write it out more at length: "We are altogether unable to conceive s.p.a.ce as bounded--as finite; that is, as a whole _in the s.p.a.ce_ beyond which there is no further s.p.a.ce." "We find ourselves totally unable to imagine bounds, _in the s.p.a.ce_ beyond which there is no further s.p.a.ce."
The words which I have added were already present implicitly. What can the word "beyond" mean if it does not signify s.p.a.ce beyond? What Sir William and Mr. Spencer have asked us to do is to imagine a limited s.p.a.ce with a _beyond_ and yet _no beyond_.
There is undoubtedly some reason why men are so ready to affirm that s.p.a.ce 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. s.p.a.cE 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 s.p.a.ce is infinitely divisible. To maintain that we can divide any portion of s.p.a.ce up into ultimate elements which are not themselves s.p.a.ces, and which have no extension, seems repugnant to the idea we all have of s.p.a.ce. And if we refuse to admit this possibility there seems to be nothing left to us but to hold that every s.p.a.ce, however small, may theoretically be divided up into smaller s.p.a.ces, and that there is no limit whatever to the possible subdivision of s.p.a.ces. 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: