Note 205 — Introductory material

Another ground for condemning empty space is to be found in the mathematical antinomies. For it is no solution, as Lotze points out (Metaphysik, Bk. II. Chap. I., § 106), to regard empty space as purely subjective: contradictions in a necessary subjective intuition form as great a difficulty as in anything else. But these antinomies arise only in connection with empty space, not with spatial order as an aggregate of relations. For only when space is regarded as possessed of some thinghood, can a whole or a true element be demanded. This we have seen already in connection with the Point. When space is regarded, so far as it is valid, as only spatial order, unbounded extension and infinite divisibility both disappear. What is divided is not spatial relations, but matter; and if matter, as we have seen that Geometry requires, consists of unextended atoms with spatial relations, there is no reason to regard matter either as infinitely divisible, or as consisting of atoms of finite extension.