CHAPTER IV. PHILOSOPHICAL CONSEQUENCES. 180. What is the relation to experience of a form of externality in general? 178 181. This form is the class-conception, containing every possible intuition of externality; and some such intuition is necessary to experience 178 182. What relation does this view bear to Kant's? 179 183. It is less psychological, since it does not discuss whether space is given in sensation, 180 184. And maintains that not only space, but any form of externality which renders experience possible, must be given in sense-perception 181 185. Externality should mean, not externality to the Self, but the mutual externality of presented things 181 186. Would this be unknowable without a given form of externality? 182 187. Bradley has proved that space and time preclude the existence of mere particulars, 182 188. And that knowledge requires the This to be neither simple nor self-subsistent 183 189. To prove that experience requires a form of externality, I assume that all knowledge requires the recognition of identity in difference 184 190. Such recognition involves time 184 191. And some other form giving simultaneous diversity 185 192. The above argument has not deduced sense-perception from the categories, but has shown the former, unless it contains a certain element, to be unintelligible to the latter 186 193. How to account for the realization of this element, is a question for metaphysics 187 [xvi] 194. What are we to do with the contradictions in space? 188 195. Three contradictions will be discussed in what follows 188 196. (1) The antinomy of the Point proves the relativity of space, 189 197. And shows that Geometry must have some reference to matter, 190 198. By which means it is made to refer to spatial order, not to empty space 191 199. The causal properties of matter are irrelevant to Geometry, which must regard it as composed of unextended atoms, by which points are replaced 191 200. (2) The circle in defining straight lines and planes is overcome by the same reference to matter 192 201. (3) The antinomy that space is relational and yet more than relational, 193 202. Seems to depend on the confusion of empty space with spatial order 193 203. Kant regarded empty space as the subject-matter of Geometry, 194 204. But the arguments of the Aesthetic are inconclusive on this point, 195 205. And are upset by the mathematical antinomies, which prove that spatial order should be the subject-matter of Geometry 196 206. The apparent thinghood of space is a psychological illusion, due to the fact that spatial relations are immediately given 196 207. The apparent divisibility of spatial relations is either an illusion, arising out of empty space, or the expression of the possibility of quantitatively different spatial relations 197 208. Externality is not a relation, but an aspect of relations. Spatial order, owing to its reference to matter, is a real relation 198