354 So far, then, as geometry is concerned, Hume s opinion is perfectly definite. It is an experimental or observational science, founded on primary or immediate judgments (in his phraseology, perceptions), of relation between facts of intuition ; its conclusions are hypo thetical only in so far as they do not imply the existence at the moment of corresponding real experience ; and its propositions have no exact truth. With respect to arithmetic and algebra, the science of numbers, he expresses an equally definite opinion, but unfortu nately it is quite impossible to state in any satisfactory fashion the grounds for it or even its full bearing. He nowhere explains the origin of the notions of unity and number, but merely asserts that through their means we can have absolutely exact arithmetical pro positions (Works, i. 97, 98). Upon the nature of the reasoning by which in mathematical science we pass from data to conclusions, Hume gives no explicit statement. If we were to say that on his view the essential step must be the establishment of identities or equi valences, we should probably be doing justice to his doctrine of numerical reasoning, but should have some difficulty in showing the application of the method to geometrical reasoning. For in the latter case we possess, according to Hume, no standard of equiva lence other than that supplied by immediate observation, and con sequently transition from one premise to another byway of reason ing must be, in geometrical matters, a purely verbal process. Taken as a whole, the theory is perhaps the only consistent development from the psychological principle with which Hume had started, and its incompleteness, even incoherence, points to the gravest defects of that principle. Hume has not offered even a plausible explanation of the mode by which it becomes possible for a consciousness made up of isolated momentary impressions and ideas to be aware of coexistence and number, or succession. The relations of ideas are accepted as facts of immediate observation, as being themselves perceptions or individual elements of conscious experience, and to all appearance they are regarded by Hume as being in a sense analytical, because the formal criterion of identity is applicable to them. It is applicable, however, not because the predicate is contained in the subject, but because, such judgments of relation being thought as immediate facts of conscious experience, the supposition of their non-existence is a contradiction in terms. The ambiguity in his criterion, however, seems entirely to have escaped Hume s attention. A somewhat detailed consideration of Hume s doctrine with regard to mathematical science has been given for the reason that this por tion of his theory has been very generally overlooked or misinter preted. It does not seem necessary to endeavour to follow his minute examination of the principle of real cognition with the same fulness. It will probably be sufficient to indicate the problem as conceived by Hume, and the relation of the method he adopts for solving it to the fundamental doctrine of his theory of knowledge. Real cognition, as Hume points out, implies transition from the present impression or feeling to something connected with it. As this thing can only be an impression or perception, and is not itself present, it is represented by its copy or idea. Now the supreme, all-comprehensive link of connexion between present feeling or im pression and either past or future experience is that of causation. The idea in question is, therefore, the idea of something connected with the present impression as its cause or effect. But this is ex plicitly the idea of the said thing as having had or as about to have existence, in other words, belief in the existence of some matter of fact. What, for a conscious experience so constituted as Hume will admit, is the precise significance of such belief in real existence ? Clearly the real existence of a fact is not demonstrable. For whatever is may he conceived not to be. " No negation of a fact can involve a contradiction." Existence of any fact, not present as a perception, can only be proved by arguments from cause or effect. But as each perception is in consciousness only as a contin gent fact, which might not be or might be other than it is, we must admit that the mind can conceive no necessary relations or con nexions among the several portions of its experience. If, therefore, a present perception leads us to assert the existence of some other, this can only be interpreted as meaning that in some natural, i.e., psychological, manner the idea of this other perception is excited, and that the idea is viewed by the mind in some peculiar fashion. The .natural link of connexion Hume finds in the simi larities presented by experience. One fact or perception is discovered by experience to be uniformly or generally accompanied by another, and its occurrence therefore naturally excites the idea of that other. But when an idea is so roused up by a present im pression, and when this idea, being a consequence of inemory, has an itself a certain vivacity or liveliness, we regard it with a peculiar indefinable feeling, and in this feeling consists the immense differ ence between mere imagination and belief. The mind is led easily and rapidly from the present impression to the ideas of impressions found by experience to be the usual accompaniments of the present fact. Theease andrapidity of the mental transition is the sole ground for the supposed necessity of the causal connexion betweeii portions of experience. We mistake the subjective transition resting upon custom or past experience for an objective connexion independent of special feelings. All reasoning about matters of fact is therefore a species of feeling, and belongs to the sensitive rather than to the cogitative side of our nature. While it is evident that some such conclusion must follow from the attempt to regard the cognitive consciousness as made.up of dis connected feelings, it is equally clear, not only that the result is self-contradictory, but that it involves certain assumptions not in any way deducible from the fundamental view with which Hume starts. For in the problem of real cognition he is brought face to face with the characteristic feature of knowledge, distinction of self from matters known, and reference of transitory states to perma nent objects or relations. Deferring his criticism of the significance of self and object, Hume yet makes use of both to aid his explana tion of the belief attaching to reality. The reference of an idea to past experience has no meaning, unless we assume an identity in the object referred to. For a past impression is purely transitory, and, as Hume occasionally points out, can have no connexion of fact with the present consciousness. His exposition has thus a certain plausibility, which would not belong to it had the final view of the permanent object been already given. The final problem of Hume s theory of knowledge, the discussion of the real significance of the two factors of cognition, self and external things, is handled in the Treatise with great fulness and dialectical subtlety. As in the case of the previous problem, it is unnecessary to follow the steps of his analysis, which are, for the 7nost part, attempts to substitute qualities of feeling for the relations of thought which appear to be involved. The results follow with the utmost ease from his original postulate. If there is nothing in conscious experience save what observation can disclose, while each act of observation is itself an isolated feeling (an impression or idea), it is manifest that a permanent identical thing can never be an object of experience. Whatever permanence or identity is ascribed to an impression or idea is the result of association, is one of those "pro pensities to feign" which are due to natural connexions among ideas. We regard as successive presentations of one thing the resembling feelings which are experienced in succession. Identity, then, whether of self or object, there is none, and the supposition of objects, distinct from impressions, is but a further consequence of our " propensity to feign." Hume s explanation of the belief in external things by reference to association is well deserving of care ful study and of comparison with the more recent analysis of the same problem by J. S. Mill. At the close of his presentation of the empirical theory of cog nition, Hume gives one of those comprehensive reviews of its sig nificance and its difficulties which mark the rare acuteness of his intellect. He has done what was possible to manufacture cognition out of the isolated, disconnected states of mental experience. He has endeavoured to contemplate conscious experience ab extra, as itself an object of experience, and to admit nothing which was not capable of being presented in the fashion of an immediate fact of experience. And as the result of the whole he has to confess that his laboriously constructed theory of cognition is but a rope of sand, that no ingenuity can conjure coherence into elements assumed from, the outset as incoherent, that the attempt to regard cognition of a fact as being merely one isolated state leads to hope less confusion. The passage in which, with the utmost frankness, he expresses his opinion on the sum total of his speculative analysis is so remarkable, both in reference to his own work and in reference to later developments of philosophy, that it is well to quote it in full. In the Appendix to the Treatise, he gives a brief resume of what he clearly recognized to be the crux in his theory, the ex planation of belief, a cognition which involves the relation among themselves of the parts of experience, and then goes on to say : " If perceptions are distinct existences, they form a whole only by being connected together. But no connexions among distinct existences are ever discoverable by human understanding. We only feel a connexion or determination of the thought to pass from one object to another. It follows, therefore, that the thought alone feels personal identity, when, reflecting on the train of past percep tions that coTnpose a mind, the ideas of them are felt to be connected together and naturally introduce each other. " However extraordinary this conclusion may seem, it need not surprise us. Modern philosophers seem inclined to think that per sonal identity arises from consciousness, and consciousness is nothing but a reflected thought or perception. The present philosophy, there fore, has a promising aspect. But all my hopes vanish when I come to explain the principles that unite our successive perceptions in our thought or consciousness. I cannot discover any theory which gives me satisfaction on this head "In short, there are two principles which I cannot render con sistent, nor is it in my power to renounce either of them ; viz., that all our distinct perceptions are distinct existences, and that the mind never perceives any real connexion among distinct existences. Pid our perceptions either inhere in something simple or indi vidual, or did the mind perceive some real connexion among them,
there would be no difficulty in the case " (ii. p. 551).
