mposed 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 o