But to return to the antinomy of infinite divisibility, [{57}] on which most of Zeno's arguments rest, you will perhaps expect me to say something of the different solutions which have been offered. In the first place, we must not forget Zeno's own solution. He did not propound this contradiction for its own sake, but to support the thesis of Parmenides. His solution is that as multiplicity and motion contain these contradictions, therefore multiplicity and motion cannot be real. Therefore, there is, as Parmenides said, only one Being, with no multiplicity in it, and excludent of all motion and becoming. The solution given by Kant in modern times is essentially similar. According to Kant, these contradictions are immanent in our conceptions of space and time, and since time and space involve these contradictions it follows that they are not real beings, but appearances, mere phenomena. Space and time do not belong to things as they are in themselves, but rather to our way of looking at things. They are forms of our perception. It is our minds which impose space and time upon objects, and not objects which impose space and time upon our minds. Further, Kant drew from these contradictions the conclusion that to comprehend the infinite is beyond the capacity of human reason. He attempted to show that, wherever we try to think the infinite, whether the infinitely large or the infinitely small, we fall into irreconcilable contradictions. Therefore, he concluded that human faculties are incapable of apprehending infinity. As might be expected, many thinkers have attempted to solve the problem by denying one or other side of the contradiction, by saying that one or other side does not follow from the premises, that one is true and the other false. David Hume, for example, [{58}] denied the infinite divisibility of space and time, and declared that they are composed of indivisible units having magnitude. But the difficulty that it is impossible to conceive of units having magnitude which are yet indivisible is not satisfactorily explained by Hume. And in general, it seems that any solution which is to be satisfactory must somehow make room for both sides of the contradiction. It will not do to deny one side or the other, to say that one is false and the other true. A true solution is only possible by rising above the level of the two antagonistic principles and taking them both up to the level of a higher conception, in which both opposites are reconciled.
This was the procedure followed by Hegel in his solution of the problem. Unfortunately his solution cannot be fully understood without some knowledge of his general philosophical principles, on which it wholly depends. I will, however, try to make it as plain as possible. In the first place, Hegel did not go out of his way to solve these antinomies. They appear as mere incidents in the development of his thought. He did not regard them as isolated cases of contradiction which occur in thought, as exceptions to a general rule, which therefore need special explanation. On the contrary, he regarded them, not as exceptions to, but as examples of, the essential character of reason. All thought, all reason, for Hegel, contains immanent contradictions which it first posits and then reconciles in a higher unity, and this particular contradiction of infinite divisibility is reconciled in the higher notion of quantity. The notion of quantity contains two factors, namely the one and the many. Quantity means precisely a many in [{59}] one, or a one in many. If, for example, we consider a quantity of anything, say a heap of wheat, this is, in the first place, one; it is one whole. Secondly, it is many; for it is composed of many parts. As one it is continuous; as many it is discrete. Now the true notion of quantity is not one, apart from many, nor many apart from one. It is the synthesis of both. It is a many in one. The antinomy we are considering arises from considering one side of the truth in a false abstraction from the other. To conceive unity as not being in itself multiplicity, or multiplicity as not being unity, is a false abstraction. The thought of the one involves the thought of the many, and the thought of the many involves the thought of the one. You cannot have a many without a one, any more than you can have one end of a stick without the other. Now, if we consider anything which is quantitatively measured, such as a straight line, we may consider it, in the first place, as one. In that case it is a continuous indivisible unit. Next we may regard it as many, in which case it falls into parts. Now each of these parts may again be regarded as one, and as such is an indivisible unit; and again each part may be regarded as many, in which case it falls into further parts; and this alternating process may go on for ever. This is the view of the matter which gives rise to the contradictions we have been considering. But it is a false view. It involves the false abstraction of first regarding the many as something that has reality apart from the one, and then regarding the one as something that has reality apart from the many. If you persist in saying that the line is simply one and not many, then there arises the theory of indivisible units. If you [{60}] persist in saying it is simply many and not one, then it is divisible ad infinitum. But the truth is that it is neither simply many nor simply one; it is a many in one, that is, it is a quantity. Both sides of the contradiction are, therefore, in one sense true, for each is a factor of the truth. But both sides are also false, if and in so far as, each sets itself up as the whole truth.
Critical Remarks on Eleaticism.
The consideration of the meaning of Zeno's doctrine will give us an insight into the essentials of the position of the Eleatics. Zeno said that motion and multiplicity are not real. Now what does this mean? Did Zeno mean to say that when he walked about the streets of Elea, it was not true that he walked about? Did he mean that it was not a fact that he moved from place to place? When I move my arms, did he mean that I am not moving my arms, but that they really remain at rest all the time? If so, we might justly conclude that this philosophy is a mere craze of speculation run mad, or else a joke. But this is not what is meant. The Eleatic position is that though the world of sense, of which multiplicity and motion are essential features, may exist, yet that outward world is not the true Being. They do not deny that the world exists. They do not deny that motion exists or that multiplicity exists. These things no sane man can deny. The existence of motion and multiplicity is, as Hegel says, as sensuously certain as the existence of elephants. Zeno, then, does not deny the existence of the world. What he denies is the truth of existence. What he means is: certainly there is motion and multiplicity; certainly the world is here, is present to our senses, but it is not the true world. It is [{61}] not reality. It is mere appearance, illusion, an outward show and sham, a hollow mask which hides the real being of things. You may ask what is meant by this distinction between appearance and reality. Is not even an appearance real? It appears. It exists. Even a delusion exists, and is therefore a real thing. So is not the distinction between appearance and reality itself meaningless? Now all this is perfectly true, but it does not comprehend quite what is meant by the distinction. What is meant is that the objects around us have existence, but not self-existence, not self-substantiality. That is to say, their being is not in themselves, their existence is not grounded in themselves but is grounded in another, and flows from that other. They exist, but they are not independent existences. They are rather beings whose being flows into them from another, which itself is self-existent and self-substantial. They are, therefore, mere appearances of that other, which is the reality. Of course the Eleatics did not speak of appearance and reality in these terms. But this is what they were groping for, and dimly saw.
If we now look back upon the road on which we have travelled from the beginning of Greek philosophy, we shall be able to characterize the direction in which we have been moving. The earliest Greek philosophers, the Ionics, propounded the question, "what is the ultimate principle of things?" and answered it by declaring that the first principle of things is matter. The second Greek School, the Pythagoreans, answered the same question by declaring numbers to be the first principle. The third school, the Eleatics, answered the question by asserting that the first principle of things is Being. [{62}] Now the universe, as we know it, is both quantitative and qualitative. Quantity and quality are characteristics of every sense-object. These are not, indeed, the only characteristics of the world, but they are the only characteristics which have so far come to light. Now the position of the Ionics was that the ultimate reality is both quantitative and qualitative, that is to say, it is matter, for matter is just what has both quantity and quality. The Pythagoreans abstracted from the quality of things. They stripped off the qualitative aspect from things, and were accordingly left with only quantity as ultimate reality. Quantity is the same as number. Hence the Pythagorean position that the world is made of numbers. The Eleatic philosophy, proceeding one step further in the same direction, abstracted from quantity as well as quality. Whereas the Pythagoreans had denied the qualitative aspect of things, leaving themselves only with the quantitative, the Eleatics denied both quantity and quality, for in denying multiplicity they denied quantity. Therefore they are left with the total abstraction of mere Being which has in it neither dividedness (quantity), nor positive character (quality). The rise from the Ionic to the Eleatic philosophy is therefore essentially a rise from sensuous to pure thinking. The Eleatic Being is a pure abstract thought. The position of the Pythagoreans on the other hand is that of semi-sensuous thought. They form the stepping-stone from the Ionics to the Eleatics.
Now let us consider what of worth there is in this Eleatic principle, and what its defects are. In the first place, it is necessary for us to understand that the Eleatic philosophy is the first monism. A monistic philosophy [{63}] is a philosophy which attempts to explain the entire universe from one single principle. The opposite of monism is therefore pluralism, which is that kind of philosophy which seeks to explain the universe from many ultimate and equally underived principles. But more particularly and more frequently we speak of the opposite of monism as being dualism, that is to say, the position that there are two ultimate principles of explanation. If, for example, we say that all the good in the universe arises from one source which is good, and that all the evil arises from another source which is evil, and that these sources of good and evil cannot be subordinated one to the other, and that one does not arise out of the other, but both are co-ordinate and equally primeval and independent, that position would be a dualism. All philosophy, which is worthy of the name, seeks, in some sense, a monistic explanation of the universe, and when we find that a system of philosophy breaks down and fails, then we may nearly always be sure its defect will reveal itself as an unreconciled dualism. Such a philosophy will begin with a monistic principle, and will attempt to derive or deduce the entire universe from it, but somewhere or other it comes across something in the world which it cannot bring under that principle. Then it is left with two equally ultimate existences, neither of which can be derived from the other. Thus it breaks out into dualism.
Now the search for a monistic explanation of things is a universal tendency of human thought. Wherever we look in the world of thought, we find that this monistic tendency appears. I have already said that it appears throughout the history of philosophy. It reveals itself, [{64}] too, very clearly in the history of religion. Religion begins in polytheism, the belief in many gods. From that it passes on to monotheism, the belief in one God, who is the sole author and creator of the universe. In Hindu thought we find the same thing. Hindu thought is based upon the principle that "All is one." Everything in the world is derived from one ultimate being, Brahman. But not only is this monistic tendency traceable in religion and philosophy; it is also traceable in science. The progress of scientific explanation is essentially a progress towards monism. In the first place, the explanation of isolated facts consists always in assigning causes for them. Suppose there is a strange noise in your room at night. You say it is explained when you find that it is due to the falling of a book or the scuttling of a rat across the floor. The noise is thus explained by assigning a cause for it. But this simply means that you have robbed it of its isolated and exceptional position, and reduced it to the position of an example of a general law. When the water freezes in your jug, you say that the cause of this is the cold. It is an example of the law that whenever the cold reaches a certain degree, then, other things being equal, water solidifies. But to assign causes in this way is not really to explain anything. It does not give any reason for an event happening. You cannot see any reason why water should solidify in the cold. It merely tells us that the event is not exceptional, but is an example of what always happens. It reduces the isolated event to a case of a general law, which "explains," not merely this one event, but possibly millions of events. It is not merely that cold solidifies the water in your jug. [{65}] It equally solidifies the water in everybody's jug. The same law "explains" all these, and likewise "explains" icebergs and the polar caps on the earth and the planet Mars. In fact scientific explanation means the reduction of millions of facts to one principle. But science does not stop here. It seeks further to explain the laws themselves, and its method is to reduce the many laws to one higher and more general law. A familiar example of this is the explanation of Kepler's laws of the planetary motions. Kepler laid down three such laws. The first was that planets move in elliptical orbits with the sun in one focus. The second was that planets describe equal areas in equal times. The third was a rather more complicated law. Kepler knew these laws from observation, but he could not explain them. They were explained by Newton's discovery of the law of gravitation. Newton proved that Kepler's three laws could be mathematically deduced from the law of gravitation. In that way Kepler's laws were explained, and not only Kepler's laws, but many other astronomical laws and facts. Thus the explanation of the many isolated facts consists in their reduction to the one law, and the explanation of the many laws consists in their reduction to the one more general law. As knowledge advances, the phenomena of the universe come to be explained by fewer and fewer, and wider and wider, general principles. Obviously the ultimate goal would be the explanation of all things by one principle. I do not mean to say that scientific men have this end consciously in view. But the point is that the monistic tendency is there. What is meant by the explanation is the reduction of all things to one principle.
In philosophy, in religion, and in science, then, we find this monistic tendency of thought. But it might be asked how we know that this universal tendency is right? How do we know that it is not merely a universal error? Is there no logical or philosophical basis for the belief that the ultimate explanation of things must be one? Now this is a subject which takes us far afield from Greek philosophy. The philosophical basis of monism was never thought out till the time of Spinoza. So we cannot go into it at length here. But, quite shortly, the question is--Is there any reason for believing that the ultimate explanation of things must be one? Now if we are to explain the universe, two conditions must be fulfilled. In the first place, the ultimate reality by which we attempt to explain everything must explain all the other things in the world. It must be possible to deduce the whole world from it. Secondly, the first principle must explain itself. It cannot be a principle which itself still requires explanation by something else. If it is itself not self-explanatory, but is an ultimate mystery, then even if we succeed in deducing the universe from it, nothing is thereby explained. This, for example, is precisely the defect of materialism. Even if we suppose it proved that all things, including mind, arise from matter, yet the objection remains that this explains nothing at all, for matter is not a self-explanatory existence. It is an unintelligible mystery. And to reduce the universe to an ultimate mystery is not to explain it. Again; some people think that the world is to be explained by what they call a "first cause." But why should any cause be the first? Why should we stop anywhere in the chain of causes? Every cause is [{67}] necessarily the effect of a prior cause. The child, who is told that God made the world, and who inquires who, in that case, made God, is asking a highly sensible question. Or suppose, in tracing back the chain of causes, we come upon one which we have reason to say is really the first, is anything explained thereby? Still we are left with an ultimate mystery. Whatever the principle of explanation is, it cannot be a principle of this kind. It must be a principle which explains itself, and does not lead to something further, such as another cause. In other words, it must be a principle which has its whole being in itself, which does not for its completeness refer us to anything beyond itself. It must be something fully comprehended in itself, without reference to anything outside it. That is to say, it must be what we call self-determined or absolute. Now any absolute principle must necessarily be one. Suppose that it were two. Suppose you attempt to explain the world by two principles, X and Y, each of which is ultimate, neither being derived from the other. Then what relation does X bear to Y? We cannot fully comprehend X without knowing its relation to Y. Part of the character and being of X is constituted by its relation to Y. Part of X's character has to be explained by Y. But that is not to be self-explained. It is to be explained by something not itself. Therefore, the ultimate explanation of things must be one.
The Eleatics, then, were perfectly correct in saying that all is one, and that the ultimate principle of the universe, Being, is one. But if we examine the way in which they carried out their monism, we shall see that it broke down in a hopeless dualism. How did they [{68}] explain the existence of the world? They propounded the principle of Being, as the ultimate reality. How then did they derive the actual world from that principle? The answer is that they neither derived it nor made any attempt to derive it. Instead of deducing the world from their first principle, they simply denied the reality of the world altogether. They attempted to solve the problem by denying the existence of the problem. The world, they said, is simply not-being. It is an illusion. Now certainly it is a great thing to know which is the true world, and which the false, but after all this is not an explanation. To call the world an illusion is not to explain it. If the world is reality, then the problem of philosophy is, how does that reality arise? If the world is illusion, then the problem is, how does that illusion arise? Call it illusion, if you like. But this is not explaining it. It is simply calling it names. This is the defect, too, of Indian philosophy in which the world is said to be Maya--delusion. Hence in the Eleatic philosophy there are two worlds brought face to face, lying side by side of each other, unreconciled--the world of Being, which is the true world, and the world of facts, which is illusion. Although the Eleatics deny the sense-world, and call it illusion, yet of this illusion they cannot rid themselves. In some sense or other, this world is here, is present. It comes back upon our senses, and demands explanation. Call it illusion, but it still stands beside the true world, and demands that it be deduced from that. So that the Eleatics have two principles, the false world and the true world, simply lying side by side, without any connecting link between them, without anything to [{69}] show how the one arises from the other. It is an utterly irreconcilable dualism.