those of substances, to be taken from real existence; but though, like these, inadequate to its complexity, to be saved from the necessary infirmities which attach to ideas of substances because not considered as so taken, but merely as in the mind. There is language about mathematics in Locke that may be interpreted in this direction, though his most explicit statements are on the other side. It is not our business to adjust them, but merely to point out the opposite tendencies between which a clear-sighted operator on the material given by Locke would find that he had to choose. Two lines of thought in Locke, between which a follower would have to choose. 125. On the one hand there is the identification of real existence with the momentary sensible event. This view, of which the proper result is the exclusion of predication concerning real existence altogether, appears in Locke’s restriction of such predication to the singular proposition, and in his converse assertion that propositions of mathematical certainty ‘concern not existence’ (Book IV. chap. iv. sec. 8). The embarrassment resulting from such a doctrine is that it leads round to the admission of the originativeness of thought and of the reality of its originations, with the denial of which it starts. [1] It leads Locke himself along a track, which his later followers scarcely seem to have noticed, when he treats the ‘never enough to be admired discoveries of Mr. Newton’ as having to do merely with the relations of ideas in distinction from things, and looks for a true extension of knowledge--neither in syllogism which can yield no instructive, nor in experiment which can yield no general, certainty--but only in a further process of ‘singling out and laying in order intermediate ideas,’ which are ‘real as well as nominal essences of their species,’ because they have no reference to archetypes elsewhere than in the mind (Book IV. chap. vii. sec. 11, and Book IV. chap. xii. sec. 7). On the other hand there is the notion that ideas, without distinction between ‘actual sensation’ and ‘idea in the mind,’ are taken from permanent things, and are real if correctly so taken. From this it results that propositions, universally true as representing a necessary relation between ideas of primary qualities, are true also of real existence; and that an extension of such real certainty through the discovery of a necessary connexion between ideas of primary and those of secondary qualities, though scarcely to be hoped for, has no inherent impossibility. It is this notion, again, that unwittingly gives even that limited significance to the particular experiment which Locke assigns to it, as indicating a co-existence between ideas present as sensations and those which can only be regarded as in the mind. Nor is it the intrinsic import so much as the expression of this notion that is altered when Locke substitutes an order of nature for substance as that in which the ideas co-exist.