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

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

209. Conclusion 199