[1] P. 490. [Book I, part IV., sec. II.]
What does it come to?
257. A slight scrutiny of this passage will show that it is a prolonged tautology. The difference is merely verbal between the processes by which the ideas of number and unity are severally supposed to be given, except that in the former process it is the moment of surveying the times that is supposed to be one, while the times themselves are many; in the latter it is the object that is supposed to be one, but the times many. According to the second version of the former process—that according to which the different times surveyed together are said to give the idea of number ‘by their object’—even this difference disappears. The only remaining distinction is that in the one case the object is supposed to be given as one, ‘without interruption or variation,’ but to become multiple as conceived to exist in different moments; in the other the objects are supposed to be given as manifold, being ideas presented in successive times, but to become one through the imaginary restriction of the multiplicity to the times in distinction from the object. Undoubtedly any one of these verbally distinct processes will yield indifferently the ideas of number and of unity, since these ideas in strict correlativity are presupposed by each of them. ‘Two points of time surveyed at the same time’ will give us the idea of number because, being a duality in unity, they are already a number. So, too, and for the same reason, will the object, one in itself but multiple as existent at different times. Nor does the idea given by imagining ideas, successively presented, to be ‘one uninterrupted object,’ differ from the above more than many-in-one differs from one-in-many. The real questions of course are, How two times can be surveyed at one time; how a single object can be multiplied or become many; how a succession of ideas can be imagined to be an unvaried and uninterrupted object. To these questions Hume has no answer to give. His reduction of thought to feeling logically excluded an answer, and the only alternative for him was to ignore or disguise them.
Unites alone really exist: number a ‘fictitious denomination’. Yet ‘unites’ and ‘number’ are correlative; and the supposed fiction unaccountable.
258. In the passage from part II. of the Treatise, already referred to, he distinctly tells us that the unity to which existence belongs excludes multiplicity. ‘Existence itself belongs to unity, and is never applicable to number but on account of the unites of which the number is composed. Twenty men may be said to exist, but ’tis only because one, two, three, four, &c., are existent. … A unite, consisting of a number of fractions, is merely a fictitious denomination, which the mind may apply to any quantity of objects it collects together; nor can such an unity any more exist alone than number can, as being in reality a true number. But the unity which can exist alone, and whose existence is necessary to that of all number, is of another kind and must be perfectly indivisible and incapable of being resolved into any lesser unity’. [1] What then is the ‘unity which can exist alone’? The answer, according to Hume, must be that it is an impression separately felt and not resoluble into any other impressions. But then the question arises, how a succession of such impressions can form a number or sum; and if they cannot, how the so-called real unity or separate impression can in any sense be a unite, since a unite is only so as one of a sum. To put the question otherwise, Is it not the case that a unite has no more meaning without number than number without unites, and that every number is not only just such a ‘fictitious denomination,’ as Hume pronounces a ‘unite consisting of a number of fractions’ to be, but a fiction impossible for our consciousness according to Hume’s account of it? It will not do to say that such a question touches only the fiction of ‘abstract number,’ but not the existence of numbered objects; that (to take Hume’s instance) twenty men exist with the existence of each individual man, each real unit, of the lot. It is precisely the numerability of objects—not indeed their existence, if that only means their successive appearance, but their existence as a sum—that is in question. If such numerability is possible for such a consciousness as Hume makes ours to be; in other words, if he can explain the fact that we count; ‘abstract number’ may no doubt be left to take care of itself. Is it then possible? ‘Separate impressions’ mean impressions felt at different times, which accordingly can no more co-exist than, to use Hume’s expression, ‘the year 1737 can concur with the year 1738;’ whereas the constituents of a sum must, as such, co-exist. Thus when we are told that ‘twenty may be said to exist because one, two, three, &c., are existent,’ the alleged reason, understood as Hume was bound to understand it, is incompatible with the supposed consequence. The existence of an object would, to him, mean no more than the occurrence of an impression; but that one impression should occur, and then another and then another, is the exact opposite of their coexistence as a sum of impressions, and it is such co-existence that is implied when the impressions are counted and pronounced so many. Thus when Hume tells us that a single object, by being ‘multiplied in order to be conceived at once as existent in different points of time,’ gives us the idea of number, we are forced to ask him what precisely it is which thus, being one, can become manifold. Is it a ‘unite that can exist alone’? That, having no parts, cannot become manifold by resolution. ‘But it may by repetition?’ No, for it is a separate impression, and the repetition of an impression cannot co-exist, so as to form one sum, with its former occurrence. ‘But it may be thought of as doing so?’ No, for that, according to Hume, could only mean that feelings might concur in a fainter stage though they could not in a livelier. Is the single object then a unite which already consists of parts? But that is a ‘fictitious denomination,’ and presupposes the very idea of number that has to be accounted for.
[1] P. 338. [Book I, part II., sec. II.]
Idea of time even more unaccountable on Hume’s principles.
259. The impossibility of getting number, as a many-in-one, out of the succession of feelings, so long as the self is treated as only another name for that succession, is less easy to disguise when the supposed units are not merely given in succession, but are actually the moments of the succession; in other words, when time is the many-in-one to be accounted for. How can a multitude of feelings of which no two are present together, undetermined by relation to anything other than the feelings, be at the same time a consciousness of the relation between the moments in which the feelings are given, or of a sum which these moments form? How can there be a relation between ‘objects’ of which one has ceased before the other has begun to exist? ‘For the same reason,’ says Hume, ‘that the year 1737 cannot concur with the present year 1738, every moment must be distinct from, and posterior or antecedent to, another’. [1] How then can the present moment form one sum with all past moments, the present year with all past years; the sum which we indicate by the number 1738? The answer of common sense of course will be that, though the feeling of one moment is really past before that of another begins, yet thought retains the former, and combining it with the latter, gets the idea of time both as a relation and as a sum. Such an answer, however, implies that the retaining and combining thought is other than the succession of the feelings, and while it takes this succession to be the reality, imports into it that determination by the relations of past and present which it can only derive from the retaining and combining thought opposed to it. It is thus both inconsistent with Hume’s doctrine, which allows no such distinction between thought, i.e. the succession of ideas, and the succession of impressions, and inconsistent with itself. Yet Hume by disguising both inconsistencies contrives to avail himself of it. By tacitly assuming that a conception of ‘the manner in which impressions appear to the mind’ is given in and with the occurrence of the impressions, he imports the consciousness of time, both as relation and as numerable quantity, into the sequence of impressions. He thus gains the advantage of being able to speak of this sequence indifferently under predicates which properly exclude each other. He can make it now a consciousness in time, now a consciousness of itself as in time; now a series that cannot be summed, now a conception of the sum of the series. The sequence of feelings, then, having been so dealt with as to make it appear in effect that time can be felt, that it should be thought of can involve no further difficulty. The conception, smuggled into sensitive experience as an ‘impression,’ can be extracted from it again as ‘idea,’ without ostensible departure from the principle that the idea is only the weaker impression.
[1] P. 338. [Book I, part II., sec. II.]
His ostensible explanation of it.