122. The ambiguity of his position will become clearer if we resort to his favourite ‘instances in gold.’ The proposition, ‘all gold is soluble in aqua regia,’ is certainly true, if such solubility is included in the complex idea which the word ‘gold’ stands for, and if such inclusion is all that the proposition purports to state. It is equally certain and equally trifling with the proposition, ‘a centaur is four-footed.’ But, in fact, as a proposition concerning substance, it purports to state more than this, viz. that a ‘body whose complex idea is made up of yellow, very weighty, ductile, fusible, and fixed,’ is always soluble in aqua regia. In other words, it states the invariable co-existence in a body of the complex idea, ‘solubility in aqua regia,’ with the group of ideas indicated by ‘gold.’ Thus understood—as instructive or synthetical—it has not the certainty which would belong to it if it were ‘trifling,’ or analytical, ‘since we can never, from the consideration of the ideas themselves, with certainty affirm’ their co-existence (Book IV. chap. vi. sec 9). If we see the solution actually going on, or can recall the sight of it by memory, we can affirm its co-existence with the ideas in question in that ‘bare instance;’ and thus, on the principle that ‘whatever ideas have once been united in nature may be so united again’ (Book IV. chap. iv. sec. 12), infer a capacity of co-existence between the ideas, but that is all. ‘Constant observation may assist our judgments in guessing’ an invariable actual co-existence (Book IV. chap. viii. sec. 9); but beyond guessing we cannot get. If our instructive proposition concerning co-existence is to be general it must remain problematical. It is otherwise with mathematical propositions. ‘If the three angles of a triangle were once equal to two right angles, it is certain that they always will be so;’ but only because such a proposition concerns merely ‘the habitudes and relations of ideas.’ ‘If the perception that the same ideas will eternally have the same habitudes and relations be not a sufficient ground of knowledge, there could be no knowledge of general propositions in mathematics; for no mathematical demonstration could be other than particular: and when a man had demonstrated any proposition concerning one triangle and circle, his knowledge would not reach beyond that particular diagram’ (Book IV. chap. i. sec. 9).
Not the knowledge which is now supposed to be got by induction. Yet more than Locke was entitled to suppose it could give.
123. To a reader, fresh from our popular treatises on Logic, such language would probably at first present no difficulty. He would merely lament that Locke, as a successor of Bacon, was not better acquainted with the ‘Inductive methods,’ and thus did not understand how an observation of co-existence in the bare instance, if the instance be of the right sort, may warrant a universal affirmation. Or he may take the other side, and regard Locke’s restriction upon general certainty as conveying, not any doubt as to the validity of the inference from an observed case to all cases where the conditions are ascertainably the same, but a true sense of the difficulty of ascertaining in any other case that the conditions are the same. On looking closer, however, he will see that, so far from Locke’s doctrine legitimately allowing of such an adaptation to the exigencies of science, it is inconsistent with itself in admitting the reality of most of the conditions in the case supposed to be observed, and thus in allowing the real truth even of the singular proposition. This purports to state, according to Locke’s terminology, that certain ‘ideas’ do now or did once co-exist in a body. But the ideas, thus stated to co-exist, according to Locke’s doctrine that real existence is only testified to by actual present sensation, differ from each other as that which really exists from that which does not. In the particular experiment of gold being solved in aqua regia, from the complex idea of solubility an indefinite deduction would have to be made for qualification by ideas retained in the understanding before we could reach the present sensation; and not only so, but the group of ideas indicated by ‘gold,’ to whose co-existence with solubility the experiment is said to testify, as Locke himself says, form merely a nominal essence, while the body to which we ascribe this essence is something which we ‘accustom ourselves to suppose,’ not any ‘parcel of matter’ having a real existence in nature. [1] In asserting the co-existence of the ideas forming such a nominal essence with the actual sensation supposed to be given in the experiment, we change the meaning of ‘existence,’ between the beginning and end of the assertion, from that according to which all ideas exist to that according to which existence has no ‘connexion with any other of our ideas but those of ourselves and God,’ but is testified to by present sensation. [2] This paralogism escapes Locke just as his equivocal use of the term ‘idea’ escapes him. The distinction, fixed in Hume’s terminology as that between impression and idea, forces itself upon him, as we have seen, in the Fourth book of the Essay, where the whole doctrine of real existence turns upon it, but alongside of it survives the notion that ideas, though ‘in the mind’ and forming a nominal essence, are yet, if rightly taken from things, ectypes of reality. Thus he does not see that the co-existence of ideas, to which the particular 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 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. In his Fourth Book he so far departs from the doctrine implied in his chapters on the reality and adequacy of ideas and on the names of substances, as to treat the notion of several single subjects in which ideas co-exist (which he still holds to be the proper notion of substances), as a fiction of thought. There are no such single subjects. What we deem so are really ‘retainers to other parts of nature.’ ‘Their observable qualities, actions, and powers are owing to something without them; and there is not so complete and perfect a part that we know of nature, which does not owe the being it has, and the excellencies of it, to its neighbours’ (Book IV. chap. vi. sec. 11). As thus conceived of, the ‘objective order’ which our experience represents is doubtless other than that collection of fixed separate ‘things,’ implied in the language about substances which Locke found in vogue, but it remains an objective order still—an order of ‘qualities, actions, and powers’ which no multitude of sensible events could constitute, but apart from which no sensible event could have such significance as to render even a singular proposition of real truth possible.