but ‘playing with sounds.’ It may serve to remind an opponent of a definition which he has made but is forgetting, but ‘carries no knowledge with it but of the signification of a word, however certain it be.’ (Book IV. chap. viii. secs. 5 & 9.) Yet there is a real gold, outside the mind, of which the complex idea of gold in the mind must needs try to be a copy, though the conditions of real existence are such that no ‘complex idea in the mind’ can possibly be a copy of it. Thus the verbal truth, which general propositions concerning substances express, is under a perpetual doom of being really untrue. The exemption of mathematical and moral knowledge from this doom remains an unexplained mercy. Because merely mental, such knowledge is real--there being no reality for it to _mis_represent--and yet not trifling. The proposition that ‘the external angle of all triangles is bigger than either of the opposite internal angles,’ has that general certainty which is never to be found but in our ideas, yet ‘conveys instructive real knowledge,’ the predicate being ‘a necessary consequence of precise complex idea’ which forms the subject, yet ‘not contained in it.’ (Book IV. chap. viii. sec. 8.) [3] The same might be said apparently, according to Locke’s judgment (though he is not so explicit about this), of a proposition in morals, such as ‘God is to be feared and obeyed by man.’ (Book IV. chap. xi. sec. 13.) [4] But how are such propositions, at once abstract and real, general and instructive, to be accounted for? There is no ‘workmanship of the mind’ recognised by Locke but that which consists in compounding and abstracting (_i.e._, separating) ideas of which ‘it cannot originate one.’ The ‘abstract ideas’ of mathematics, the ‘mixed modes’ of morals, just as much as the ideas of substances, must be derived by such mental artifice from a material given in simple feeling, and ‘real’ because so given. Yet, while this derivation renders ideas of substances unreal in contrast with their real ‘originals,’ and general propositions about them ‘trifling,’ because, while ‘intimating an existence,’ they tell nothing about it, on the other hand it actually constitutes the reality of moral and mathematical ideas. Their relation to an original disappears; they are themselves archetypes, from which the mind, by its own act, can elicit other ideas not already involved in the meaning of their names. But this can only mean that the mind has some other function than that of uniting what it has ‘found’ in separation, and separating again what it has thus united--that it can itself originate. [1] See above, paragraph 25. [2] Book IV. chap. xi. sec. 13, xii. 9, &c. [3] Just as according to Kant such a proposition expresses a judgment ‘synthetical,’ yet ‘á-priori.’ [4] Cf. Book IV. chap. iii. sec. 18, and Book III. chap, xi. sec. 16. Significance of this doctrine.