Inference then can give no new knowledge.
333. Thus inference, according to Hume’s account of it as originating in habit, suffers from a weakness quite as fatal as that which he supposes to attach to it if accounted for as the work of reason. ‘The work of reason’ to a follower of Locke meant either the mediate perception of likeness between ideas, which the discovery of cause or effect cannot be; or else syllogism, of which Locke had shown once for all that it could yield no ‘instructive propositions.’ But if an idea arrived at by that process could be neither new nor real—not new, because we must have been familiar with it before we put it into the compound idea from which we ‘deduce’ it; not real, because it has not the liveliness either of sensation or of memory—the idea inferred according to Hume’s process, however real with the reality of liveliness, is certainly not new. ‘If this means’ (the modern logician may perhaps reply), ‘that according to Hume no new phenomenon can be given by inference, he was quite right in thinking so. If the object of inference were a separate phenomenon, it would be quite true that it must have been repeatedly perceived before it could be inferred, and that thus inference would be nugatory. But inference is in fact not to such an object, but to a uniform relation of certain phenomena in the way of co-existence and sequence; and what Hume may be presumed to mean is not that every such relation must have been perceived before it can be inferred, much less that it must have been perceived so constantly that an appearance of the one phenomenon causes instinctive expectation of the other, but (a) that the phenomena themselves must have been given by immediate perception, and (b) that the conception of a law of causation, in virtue of which a uniformity of relation between them is inferred from a single instance of it, is itself the result of an “inductio per enumerationem simplicem,” of the accumulated experience of generations that the same sequents follow the same antecedents.’
Nor does this merely mean that it cannot constitute new phenomena, while it can prove relations, previously unknown, between phenomena. Such a distinction inadmissible with Hume.
334. At the point which our discussion has reached, few words should be wanted to show that thus to interpret Hume is to read into him an essentially alien theory, which has doubtless grown out of his, but only by a process of adaptation which it needs a principle the opposite of his to justify. Hume, according to his own profession, knows of no objects but impressions and ideas—feelings stronger or more faint—of no reality which it needs thought, as distinct from feeling, to constitute. But a uniform relation between phenomena is neither impression nor idea, and can only exist for thought. He could not therefore admit inference to such relation as to a real existence, without a double contradiction, nor does he ever explicitly do so. He never allows that inference is other than a transition to a certain sort of feeling, or that it is other than the work of imagination, the weakened sense, as enlivened by custom to a degree that puts it almost on a level with sense; which implies that in every case of inference the inferred object is not a uniform relation—for how can there be an image of uniform relation?—and that it is something which has been repeatedly and without exception perceived to follow another before it can be inferred. Even when in violation of his principle he has admitted a ‘system of memory’—a system of things which have been felt, but which are not feelings, stronger or fainter, and which are what they are only through relation—he still in effect, as we have seen, makes the ‘system of judgment,’ which he speaks of as inferred from it, only the double of it. To suppose that, on the strength of a general inference, itself the result of habit, in regard to the uniformity of nature, particular inferences may be made which shall be other than repetitions of a sequence already habitually repeated, is, if there can be degrees of contradiction, even more incompatible with Hume’s principles than to suppose such inferences without it. If a uniformity of relation between particular phenomena is neither impression nor idea, even less so is the system of all relations.
His distinction of probability of causes from that of chances might seem to imply conception of nature, as determining inference.
335. There is language, however, in the chapters on ‘Probability of Chances and of Causes,’ which at first sight might seem to warrant the ascription of such a supposition to Hume. According to the distinction which he inherited from Locke all inference to or from causes or effects, since it does not consist in any comparison of the related ideas, should be merely probable. And as such he often speaks of it. His originality lies in his effort to explain what Locke had named; in his treating that ‘something not joined on both sides to, and so not showing the agreement or disagreement of, the ideas under consideration’ which yet ‘makes me believe’, [1] definitely as Habit. But ‘in common discourse,’ as he remarks, ‘we readily affirm that many arguments from causation exceed probability’; [2] the explanation being that in these cases the habit which determines the transition from impression to idea is ‘full and perfect.’ There has been enough past experience of the immediate sequence of the one ‘perception’ on the other to form the habit, and there has been no exception to it. In these cases the ‘assurance,’ though distinct from knowledge, may be fitly styled ‘proof,’ the term ‘probability’ being confined to those in which the assurance is not complete. Hume thus comes to use ‘probability’ as equivalent to incompleteness of assurance, and in this sense speaks of it as ‘derived either from imperfect experience, or from contrary causes, or from analogy’. [3] It is derived from analogy when the present impression, which is needed to give vivacity to the ‘related idea,’ is not perfectly like the impressions with which the idea has been previously found united; ‘from contrary causes,’ when there have been exceptions to the immediate sequence or antecedence of the one perception to the other; ‘from imperfect experience’ when, though there have been no exceptions, there has not been enough experience of the sequence to form a ‘full and perfect habit of transition.’ Of this last ‘species of probability,’ Hume says that it is a kind which, ‘though it naturally takes place before any entire proof can exist, yet no one who is arrived at the age of maturity can any longer be acquainted with. ’Tis true, nothing is more common than for people of the most advanced knowledge to have attained only an imperfect experience of many particular events; which naturally produces only an imperfect habit and transition; but then we must consider that the mind, having formed another observation concerning the connexion of causes and effects, gives new force to its reasoning from that observation; and by means of it can build an argument on one single experiment, when duly prepared and examined. What we have found once to follow from any object we conclude will for ever follow from it; and if this maxim be not always built upon as certain, ’tis not for want of a sufficient number of experiments, but because we frequently meet with instances to the contrary’—which give rise to the other sort of weakened assurance or probability, that from ‘contrary causes’. [4]
[1] Locke, 4, 15, 3.
[2] P. 423. [Book I, part III., sec. XI.]
[3] P. 439. [Book I, part III., sec. XIII.]
[4] Pp. 429 & 430. [Book I, part III., sec. XII.]