Its annihilation would not leave a gap, for a gap means a bit of empty space; nor could it bring the surrounding spaces into juxtaposition, for one cannot shift spaces, and, in any case, a shifting that is not a shifting through space is an absurdity.
Again, he cannot conceive of any journey that would bring him to the end of space.

There is no more reason for stopping at one point than at another; why not go on?
What could end space?
As to the infinite divisibility of space, 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.

SPACE AS NECESSARY AND SPACE AS INFINITE .-- That these statements about space contain truth one should not be in haste to deny.

It seems silly to say that space 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 space is necessary and cannot be "thought away." As we have seen above, it is manifestly impossible to annihilate in thought a certain portion of space and leave the other portions intact.
There are many things in the same case.