262. He fails to assign any impression or compound of impressions from which idea of time is copied. 263. How can he adjust the exact sciences to his theory of space and time? 264. In order to seem to do so, he must get rid of ‘Infinite Divisibility’. 265. Quantity made up of impressions, and there must be a least possible impression. 266. Yet it is admitted that there is an idea of number not made up of impressions. A finite division into impressions no more possible than an infinite one. 267. In Hume’s instances it is not really a feeling, but a conceived thing, that appears as finitely divisible. 268. Upon true notion of quantity infinite divisibility follows of course. 269. What are the ultimate elements of extension? If not extended, what are they? 270. Colours or coloured points? What is the difference? 271. True way of dealing with the question. 272. ‘If the point were divisible, it would be no termination of a line.’ Answer to this. 273. What becomes of the exactness of mathematics according to Hume? 274. The universal propositions of geometry either untrue or unmeaning. 275. Distinction between Hume’s doctrine and that of the hypothetical nature of mathematics. 276. The admission that no relations of quantity are data of sense removes difficulty as to general propositions about them. 277. Hume does virtually admit this in regard to numbers. 278. With Hume idea of vacuum impossible, but logically not more so than that of space. 279. How it is that we talk as if we had idea of vacuum according to Hume. 280. His explanation implies that we have an idea virtually the same. 281. By a like device that he is able to explain the appearance of our having such ideas as Causation and Identity. 283. Knowledge of relation in way of Identity and Causation excluded by Locke’s definition of knowledge. 284. Inference a transition from an object perceived or remembered to one that is not so. 285. Relation of cause and effect the same as this transition. 286. Yet seems other than this. How this appearance is to be explained. 287. Inference, resting on supposition of necessary connection, to be explained before that connection. 288. Account of the inference given by Locke and Clarke rejected. 289. Three points to be explained in the inference according to Hume. 290. _a_. The original impression from which the transition is made _b_. The transition to inferred idea 291. _c_. The qualities of this idea. 292. It results that necessary connection is an impression of reflection, _i.e._, a propensity to the transition described. 293. The transition not to anything beyond sense. 294. Nor determined by any objective relation. 295. Definitions of cause: _a_. As a ‘philosophical’ relation. 296. Is Hume entitled to retain ‘philosophical’ relations as distinct from ‘natural’? 297. Examination of Hume’s language about them. 298. Philosophical relation consists in a comparison, but no comparison between cause and effect.