A Critical History of Greek Philosophy, W. T. Stace [best books to read for students txt] 📗

flying arrow. At any moment of its flight, says Zeno, it must be in one place, because it cannot be in two places at the same moment. This depends upon the view of time as being infinitely divisible. It is only in an infinitesimal moment, an absolute moment having no duration, that the arrow is at rest. This, however, is not the only antinomy which we find in our conceptions of space and time. Every mathematician is acquainted with the contradictions immanent in our ideas of infinity. For example, the familiar proposition that parallel straight lines meet at infinity, is a contradiction. Again, a decreasing geometrical progression can be added up to infinity, the infinite number of its terms adding up in the sum-total to a finite number. The idea of infinite space itself is a contradiction. You can say of it exactly what Zeno said of the many. There must be in existence as much space as there is, no more. But this means that there must be a definite and limited amount of space. Therefore space is finite. On the other hand, it is impossible to conceive a limit to space. Beyond the limit there must be more space. Therefore space is infinite. Zeno himself gave expression to this antinomy in the form of an argument which I have not so far mentioned. He said that everything which exists is in space. Space itself exists, therefore space must be in space. That space must be in another space and so ad infinitum. This of course is merely a quaint way of saying that to conceive a limit to space is impossible.

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