202. Now for this discussion it is essential to distinguish clearly between empty space and spatial figures. Empty space, as a form of externality, is not actual relations, but the possibility of relations: if we ascribe existential import to it, as the ground, in reality, of all diversity in relation, we at once have space as something not itself relations, though giving the possibility of all relations. In this sense, space is to be distinguished from spatial order. Spatial order, it may be said, presupposes space, as that in which this order is possible. Thus Stumpf says[195]: "There is no order or relation without a positive absolute content, underlying it, and making it possible to order anything in this manner. Why and how should we otherwise distinguish one order from another?... To distinguish different orders from one another, we must everywhere recognize a particular absolute content, in relation to which the order takes place. And so space, too, is not a mere order, but just that by which the spatial order, side-by-sideness (Nebeneinander) distinguishes itself from the rest."
May we not, then, resolve the antinomy very simply, by a reference to this ambiguity of space? Bradley contends (Appearance and Reality, pp. 36–7) that, on the one hand, space has parts, and is therefore not mere relations, while on the other hand, when we try to say what these parts are, we find them after all to be mere relations. But cannot the space which has parts be regarded as empty space, Stumpf's absolute underlying content, which is not mere relations, while the parts, in so far as they turn out to be mere relations, are those relations which constitute spatial order, not empty space? If this can be maintained, the antinomy no longer exists.
But such an explanation, though I believe it to be a first step towards a solution, will, I fear, itself demand almost as much explanation as the original difficulty. For the connection of empty space with spatial order is itself a question full of difficulty, to be answered only after much labour.
203. Let us consider what this empty space is. (I speak of "empty" space without necessarily implying the absence of matter, but only to denote a space which is not a mere order of material things.) Stumpf regards it as given in sense; Kant, in the last two arguments of his metaphysical deduction, argues that it is an intuition, not a concept, and must be known before spatial order becomes possible. I wish to maintain, on the contrary, that it is wholly conceptual; that space is given only as spatial order; that spatial relations, being given, appear as more than mere relations, and so become hypostatized; that when hypostatized, the whole collection of them is regarded as contained in empty space; but that this empty space itself, if it means more than the logical possibility of space-relations, is an unnecessary and self-contradictory assumption. Let us begin by considering Kant's arguments on this point.
Leibnitz had affirmed that space was only relations, while Newton had maintained the objective reality of absolute space. Kant adopted a middle course: he asserted absolute space, but regarded it as purely subjective. The assertion of absolute space is the object of his second argument; for if space were mere relations between things, it would necessarily disappear with the disappearance of the things in it; but this the second argument denies[196]. Now spatial order obviously does disappear with matter, but absolute or empty space may be supposed to remain. It is this, then, which Kant is arguing about, and it is this which he affirms to be a pure intuition, necessarily presupposed by spatial order[197].
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.
206. But whence arises, on this view, the paradox that we cannot but regard space as having more or less thinghood, and as divisible ad infinitum? This must be explained, I think, as a psychological illusion, unavoidably arising from the fact that spatial relations are immediately presented. They thus have a peculiar psychical quality, as immediate experiences, by which quality they can be distinguished from time-relations or any other order in which things may be arranged. To Stumpf, whose problem is psychological, such a psychical quality would constitute an absolute underlying content, and would fully justify his thesis; to us, however, whose problem is epistemological, it would not do so, but would leave the meaning of the spatial element in sense-perception free from any implication of an absolute or empty space[201]. May we not, then, abandon empty space, and say: Spatial order consists of felt relations, and quâ felt has, for Psychology, an existence not wholly resolvable into relations, and unavoidably seeming to be more than mere relations. But when we examine the information, as to space, which we derive from sense-perception, we find ourselves plunged in contradictions, as soon as we allow this information to consist of more than relations. This leaves spatial order alone in the field, and reduces empty space to a mere name for the logical possibility of spatial relations.