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 construction from elements that were true, then it might be derived only for our knowledge, and be original in fact. But so long as its attempted derivation is in part obscure and in part illusory, it is better to regard this whole question as irrelevant.

Let us then, taking space or extension simply as it is, enquire whether it contradicts itself. The reader will be acquainted with the difficulties that have arisen from the continuity and the discreteness of space. These necessitate the conclusion that space is endless, while an end is essential to its being. Space cannot come to a final limit, either within itself or on the outside. And yet, so long as it remains something always passing away, internally or beyond itself, it is not space at all. This dilemma has been met often by the ignoring of one aspect, but it has never been, and it will never be, confronted and resolved. And naturally, while it stands, it is the condemnation of space.

I am going to state it here in the form which exhibits, I think, most plainly the root of the contradiction, and also its insolubility. Space is a relation—which it cannot be; and it is a quality or substance—which again it cannot be. It is a peculiar form of the problem which we discussed in the last chapter, and is a special attempt to combine the irreconcilable. I will set out this puzzle antithetically.

1. Space is not a mere relation. For any space must consist of extended parts, and these parts clearly are spaces. So that, even if we could take our space as a collection, it would be a collection of solids. The relation would join spaces which would not be mere relations. And hence the collection, if taken as a mere inter-relation, would not be space. We should be brought to the proposition that space is nothing but a relation of spaces. And this proposition contradicts itself.

Again, from the other side, if any space is taken