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