260. ‘The idea of time is not derived from a particular impression mixed up with others and plainly distinguishable from them, but arises altogether from the manner in which impressions appear to the mind, without making one of the number. Five notes played on the flute give us the impression and idea of time, though time be not a sixth impression which presents itself to the hearing or any other of the senses. Nor is it a sixth impression which the mind by reflection finds in itself. These five sounds, making their appearance in this particular manner, excite no emotion or affection in the mind, which being observed by it can give rise to a new idea. For that is necessary to produce a new idea of reflection; nor can the mind, by revolving over a thousand times all its ideas of sensation, ever extract from them any new original idea, unless nature has so framed its faculties that it feels some new original impression arise from such a contemplation. But here it only takes notice of the manner in which the different sounds make their appearance, and that it may afterwards consider without considering these particular sounds, but may conjoin it with any other objects. The ideas of some objects it certainly must have, nor is it possible for it without these ever to arrive at any conception of time; which, since it appears not as any primary distinct impression, can plainly be nothing but different ideas or impressions or objects disposed in a certain manner, i.e. succeeding each other. [1]

[1] P. 343. [Book I, part II., sec. III.]

It turns upon equivocation between feeling and conception of relations between felt things.

261. In this passage the equivocation between ‘impression’ as feeling, and ‘impression’ as conception of the manner in which feelings occur, is less successfully disguised than is the like equivocation in the account of extension—not indeed from any failure in Hume’s power of statement, but from the nature of the case. In truth the mere reproduction of impressions can as little account for the one conception as for the other. Just as, in order to account for the ‘impression’ from which the abstract idea of space may be derived, we have to suppose first that the feeling of colour, through being presented by the self-conscious subject to itself, becomes a coloured thing, and next, that this thing is viewed as a whole of parts limiting each other; so, in order to account for the ‘impression’ from which the idea of time may be abstracted, we have to suppose the presentation of the succession of feelings to a consciousness not in succession, and the consequent view of such presented succession as a sum of numerable parts. It is a relation only possible for a thinking consciousness—a relation, in Hume’s language, not depending on the nature of the impressions related—that has in each case to be introduced into experience in order to be extracted from it again by ‘consideration:’ but there is this difference, that in one case the relation is not really between feelings at all, but between things or parts of a thing; while in the other it is just that relation between feelings, the introduction of which excludes the possibility that any feeling should be the consciousness of the relation. Thus to speak of a feeling of extension does not involve so direct a contradiction as to speak in the same way of time. The reader gives Hume the benefit of a way of thinking which Hume’s own theory excludes. Himself distinguishing between feeling and felt thing, and regarding extension as a relation between parts of a thing, he does not reflect that for Hume there is no such distinction; that a ‘feeling of extension’ means that feeling is extended, which again means that it has co-existent parts; and that what is thus said of feeling as extended is incompatible with what is said of it as feeling. But when it comes to a ‘feeling of time’—a feeling of the successiveness of all feelings—the incompatibility between what is said of feeling as the object and what is implied of it as the subject is less easy to disguise. In like manner because we cannot really think of extension as being that which yet according to Hume it is, it does not strike us, when he speaks of it as coloured or of colour as extended, that he is making one feeling a quality of another. But it would be otherwise if any specific feeling were taken as a quality of what is ostensibly a relation between all feelings. There is thus no ‘sensible quality’ with which time can be said to be ‘endowed,’ as extension with ‘colour and solidity;’ none that can be made to do the same duty in regard to it as these do in regard to extension, ‘giving the idea’ of it without actually being it.

He fails to assign any impression or compound of impressions from which idea of time is copied.

262. Hence, as the passage last quoted shows, in the case of time the alternative between ascribing it to a sixth sense, and confessing that it is not an impression at all, is very hard to avoid. It would seem that there is an impression of ‘the manner in which impressions appear to the mind,’ which yet is no ‘distinct impression.’ What, then, is it? It cannot be any one of the impressions of sense, for then it would be a distinct impression. It cannot be a ‘compound impression,’ for such composition is incompatible with that successiveness of all feelings to each other which is the object of the supposed impression. It cannot be any ‘new original impression’ arising from the contemplation of other impressions, for then, according to Hume, it would be ‘an affection or emotion.’ But after the exclusion of impressions of sense, compound impressions, and impressions of reflection, Hume’s inventory of the possible sources of ideas is exhausted. To have been consistent, he ought to have dealt with the relation of time as he afterwards does with that of cause and effect, and, in default of an impression from which it could be derived, have reduced it to a figure of speech. But since the possibility of accounting for the propensities to feign, which our language about cause and effect according to him represents, required the consciousness of relation in time, this course could not be taken. Accordingly after the possibility of time being an impression has been excluded as plainly as it can be by anything short of a direct negation, by a device singularly naïf it is made to appear as an impression after all. On being told that the consciousness of time is not a ‘new original impression of reflection,’ since in that case it would be an emotion or affection, but ‘only the notice which the mind takes of the manner in which impressions appear to it,’ the reader must be supposed to forget the previous admission that it is no distinct impression at all, and to interpret this ‘notice which the mind takes,’ because it is not an impression of reflection, as an impression of sense. To make such interpretation easier, the account given of time earlier in the paragraph quoted is judiciously altered at its close, so that instead of having to ascribe to feeling a consciousness of ‘the manner in which impressions appear to the mind,’ we have only to ascribe to it the impressions so appearing. But this alteration admitted, what becomes of the ‘abstractness’ of the idea of time, i.e. of the possibility of its being ‘conjoined with any objects’ indifferently? It is the essential condition of such indifferent conjunction, as Hume puts it, that time should be only the manner of appearance as distinct from the impressions themselves. If time is the impressions, it must have the specific sensuous character which belongs to these. It must be a multitude of sounds, a multitude of tastes, a multitude of smells—these one after the other in endless series. How then can such a series of impressions become such an idea, i.e. so grow fainter as to be ‘conjoined’ indifferently ‘with any impressions whatever’?

How can he adjust the exact sciences to his theory of space and time?

263. The case then between Hume and the conceptions which the exact sciences presuppose, as we have so far examined it, stands thus. Of the idea of quantity, as such, he gives no account whatever. We are told, indeed, that there are ‘unites which can exist alone,’ i.e. can be felt separately, and which are indivisible; but how such unites, being separate impressions, can form a sum or number, or what meaning a unite can have except as one of a number—how again a sum formed of separate unites can be a continuous whole or magnitude—we are not told at all. Of the ideas of space and time we do find an account. They are said to be given in impressions, but, to justify this account of them, each impression has to be taken to be at the same time a consciousness of the manner of its own existence, as determined by relation to other impressions not felt along with it and as interpreted in a way that presupposes the unexplained idea of quantity. With this supposed origin of the ideas the sciences resting on them have to be adjusted. They may take the relations of number and magnitude, time and space, for granted, as ‘qualities of perceptions,’ and no question will be asked as to how the perceptions come to assume qualities confessed to be ‘independent of their own nature.’ It is only when they treat them in a way incompatible not merely with their being feelings—that must always be the case—but with their being relations between felt things, that they are supposed to cross the line which separates experimental knowledge from metaphysical jargon. So long then as space is considered merely as the relation of externality between objects of the ‘outer,’ time as that of succession between objects of the ‘inner,’ sense—in other words, so long as they remain what they are to the earliest self-consciousness and do not become the subject matter of any science of quantity—if we sink the difference between feelings and relations of felt things, and ask no questions about the origin of the distinction between outer and inner sense, they may be taken as data of sensitive experience. It is otherwise when they are treated as quantities, and it is their susceptibility of being so treated that, rightly understood, brings out their true character as the intelligible element in sensitive experience. But Hume contrives at once to treat them as quantities, thus seeming to give the exact sciences their due, and yet to appeal to their supposed origin in sense as evidence of their not having properties which, if they are quantities, they certainly must have. Having thus seemingly disposed of the purely intelligible character of quantity in its application to space and time, he can more safely ignore what he could not so plausibly dispose of—its pure intelligibility as number.

In order to seem to do so, he must get rid of ‘Infinite Divisibility’.

264. The condition of such a method being acquiesced in is, that quantity in all its forms should be found reducible to ultimate unites or indivisible parts in the shape of separate impressions. Should it be found so, the whole question indeed, how ideas of relation are possible for a merely feeling consciousness, would still remain, but mathematics would stand on the same footing with the experimental sciences, as a science of relations between impressions. Upon this reducibility, then, we find Hume constantly insisting. In regard to number indeed he could not ignore the fact that the science which deals with it recognizes no ultimate unite, but only such a one as ‘is itself a true number.’ But he passes lightly over this difficulty with the remark that the divisible unite of actual arithmetic is a ‘fictitious denomination’—leaving his reader to guess how the fiction can be possible if the real unite is a separate indivisible impression—and proceeds with the more hopeful task of resolving space into such impressions. He is well aware that the constitution of space by impressions and its constitution by indivisible parts stand or fall together. If space is a compound impression, it is made up of indivisible parts, for there is a ‘minimum visibile’ and by consequence a minimum of imagination; and conversely, if its parts are indivisible, they can be nothing but impressions; for, being indivisible, they cannot be extended, and, not being extended, they must be either simple impressions or nothing. With that instinct of literary strategy which never fails him, Hume feels that the case against infinite divisibility, from its apparent implication of an infinite capacity in the mind, is more effective than that in favour of space being a compound impression, and accordingly puts that to the front in the Second Part of the Treatise, in order, having found credit for establishing it, to argue back to the constitution of space by impressions. In fact, however, it is on the supposed composition of all quantity from separate impressions that his argument against its infinite divisibility rests.