[2] P. 372 [Book I, part III., sec. I.], ‘Philosophical relations may be divided into two classes: into such as depend entirely on the ideas which we compare together; and such as may be changed without any change in the ideas. ... The relations of contiguity and distance between two objects may be changed without any change in the objects themselves or their ideas.’ [3] P. 480. [Book I, part IV., sec. II.] ‘When we doubt whether sensations present themselves as distinct objects or as mere impressions, the difficulty is not concerning their nature, but concerning their relations and situation.’ [4] P. 481. [Book I, part IV., sec. II.] In there showing that the senses alone cannot convince us of the external existence of body, he remarks that ‘sounds, tastes, and smells appear not to have any existence in extension;’ and (p. 483) [ibid] ‘as far as the senses are judges, all perceptions are the same in the manner of their existence.’ Therefore perceptions of sight cannot have ‘an existence in extension’ any more than ‘sounds, tastes, and smells;’ and if so, how can ‘existence in extension’ be a perception? [5] Above, paragraphs 235 and 244. No logical alternative between identifying space with colour, and admitting an idea not copied from an impression. 251. To have plainly admitted that it was not an impression must have compelled Hume either to discard the ‘abstract idea’ with which geometry deals, or to admit the possibility of ideas other than ‘fainter impressions.’ It is a principle on which he insists with much emphasis and repetition, that whatever ‘objects,’ ‘impressions,’ or ‘ideas’ are distinguishable are also separable. [1] Now if there is an abstract idea of extension, it can scarcely be other than distinguishable, and consequently (according to Hume’s account of the relation of idea to impression) derived from a distinguishable and therefore separable impression. It would seem then that Hume cannot escape conviction of one of two inconsistencies; either that of supposing a separate impression of extension, which yet is not of the nature of any assignable sensation; or that of supposing an abstract idea of it in the absence of any such impression. We shall find that he does not directly face either horn of the dilemma, but evades both of them. He admits that ‘the ideas of space and time are no separate and distinct ideas, but merely those of the manner or order in which objects’ (_sc._ impressions) ‘exist’. [2] In the Fourth Book, where the equivalence of impression to feeling is more consistently carried out, the fact that what is commonly reckoned an impression is really a judgment about the ‘manner of existence,’ as opposed to the ‘nature,’ of impressions, is taken as sufficient proof that it is no impression at all; and if not an impression, therefore not an idea. [3] He thus involuntarily recognized the true difference between feeling and thought, between the mere occurrence of feelings