=204.= But can we agree in regarding empty space, the "infinite given whole," as really given? Must we not, in spite of Kant's argument, regard it as wholly conceptual? It is not required, in the first place, by the argument of the first half of this chapter, which required only that every _This_ of sense-perception should be resolvable into _Thises_, and thus involved only an order among _Thises_, not anything given originally without reference to them at all. In the second place, Kant's two arguments[198] designed to prove that empty space is not conceptual, are inadequate to their purpose. The argument that the parts of space are not contained _under_ it, but _in_ it, proves certainly that space is not a general conception, of which spatial figures are the instances; but it by no means follows that empty space is not a conception. Empty space is undifferentiated and homogeneous; parts of space, or spatial figures, arise only by reference to some differentiating matter, and thus belong rather to spatial order than to empty space. If empty space be the pre-condition of spatial order, we cannot expect it to be connected with spatial relations as genus with species. But empty space may nevertheless be a universal conception; it may be related to spatial order as the state to the citizens. These are not instances of the state, but are contained in it; they also, in a sense, presuppose it, for a man can only become a citizen by being related to other citizens in a state[199]. The uniqueness of space, again, seems hardly a valid argument for its intuitional nature; to regard it as an argument implies, indeed, that all conceptions are abstracted from a series of instances--a view which has been criticized in Chapter II. (§ 77), and need not be further discussed here[200]. There is no ground, therefore, in Kant's two arguments for the intuitional nature of empty space, which can be maintained against criticism. =205.= 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.