experiment, as he describes it, testifies, is nothing else than the co-existence of an event with a conception--of that which is in a particular time, and (according to him) only for that reason real, with that which is not in time at all but is an unreal abstraction of the mind’s making. [3] The reality given in the actual sensation cannot, as a matter of fact, be discovered to have a necessary connexion with the ideas that form the nominal essence, and therefore cannot be asserted universally to co-exist with them; but with better faculties, he thinks, the discovery might be made (Book IV. chap. iii. sec. 16). It does not to him imply such a contradiction as it must have done if he had steadily kept in view his doctrine that of particular (_i.e._ real) existence our ‘knowledge’ is not properly knowledge at all, but simply sensation--such a contradiction as was to Hume involved in the notion of deducing a matter of fact. [1] See above, paragraphs 35, 94, &c. [2] See above, paragraph 30 and the following. [3] See above, paragraphs 45, 80, 85, 97. With Locke mathematical truths, though ideal, true also of nature. 124. It results that those followers of Locke, who hold the distinction between propositions of mathematical certainty and those concerning real existence to be one rather of degree than of kind, though they have the express words of their master against them, can find much in his way of thinking on their side. This, however, does not mean that he in any case drops the antithesis between matters of fact and relations of ideas in favour of matters of fact, so as to admit that mathematical propositions concern matters of fact, but that he sometimes drops it in favour of relations of ideas, so as to represent real existence as consisting in such relations. If the matter of fact, or real existence, is to be found only in the event constituted or reported by present feeling, such a relation of ideas, by no manner of means reducible to an event, as the mathematical proposition states, can have no sort of connection with it. But if real existence is such that the relations of ideas, called primary qualities of matter, constitute it, and the qualities included in our nominal essences are its copies or effects, then, as on the one side our complex ideas of substances only fail of reality through want of fulness, or through mistakes in the process by which they are ‘taken from things,’ so, on the other side, the mental truth of mathematical propositions need only fail to be real because the ideas, whose relations they state, are considered in abstraction from conditions which qualify them in real existence. ‘If it is true of the idea of a triangle that its three angles equal two right ones, it is true also of a triangle, wherever it really exists’ (Book IV. chap. iv. sec. 6). There is, then, no incompatibility between the idea and real existence. Mathematical ideas might fairly be reckoned, like