'different resemblances and relations,' without such explanation as Hume cannot consistently give, is in fact a contradiction in terms. The true explanation is that the 'impression' has a different meaning, when figure and colour are said to be inseparable in the impression, from that which it has when spoken of as a subject of different resemblances and relations. In the former sense it is the feeling pure and simple-one as presented singly in time, after another and before a third. In this sense it is doubtless insusceptible of distinction into qualities of figure and colour, because (for reasons already stated) it can have no qualities at all. But the simplicity in which many different resemblances and relations may be contained' is quite other than this singleness. It is the unity of an object thought of under manifold relations-a unity of which Hume, reducing all consciousness to impression' and impression to feeling, has no consistent account to give. Failing such an account, the unity of the intelligible object, and the singleness of the feeling in time, are simply confused with each other. It is only an object as thought of, not a feeling as felt, that can properly be said to have qualities at all; while it is only because it is still regarded as a feeling that qualities of it, which cannot be referred to separate impressions, are pronounced the same and indistinguishable. If the idea of space is other than a feeling grown fainter, the sole reason for regarding it as originally an impression of colour disappears; if it is such a feeling, it cannot contain such different resemblances and relations' as render it representative of objects not only coloured in every possible way, but not coloured at all.

yet avoids appearance

of doing so,

by treating

ation' of

253. It is thus by playing fast and loose with the difference between feeling and conception that Hume is able, when the character of extension as an intelligible relation is urged, to reply that it is the same with the feeling of colour; and on the other hand, when asked how there then the rela can be an abstract idea of it, to reply that this does not tions of a mean a separate idea, but coloured objects considered under felt thing as if it a certain relation, viz. under that which consists in the were itself the feeldisposition of their parts. The most effective way of meeting. ing him on his own ground is to ask him how it is, since 'consideration' can only mean a succession of ideas, and ideas are fainter impressions, that extension, being one and the same impression with colour, can by any consideration'

Summary of contra

dictions in

his account

of exteneion.

become so different from it as to constitute a resemblance to objects that are not coloured at all. The true explanation, according to his own terminology, would be that the resemblance between the white globe and all other globes, being a resemblance not of impressions but of such relations between impressions as do not depend on the nature of the impressions' related, is unaffected by the presence or absence of colour or any other sensation. Of such relations, however, there can properly, if ideas are fainter impressions, be no ideas at all. In regard to those of cause and identity Hume virtually admits this; but the propensities to feign,' by which in the case of these latter relations he tries to account for the appearance of there being ideas of them, cannot plausibly be applied to relations in space and time, of which, as we shall see, ideas must be assumed in order to account for the fictions' of body and necessary connexion. Since then they cannot be derived from any separate impression without the introduction in effect of a sixth sense, and since all constitutive action of thought as distinct from feeling is denied by Hume, the only way to save appearances is to treat the order in which a multitude of impressions present themselves as the same with each impression, even though immediately afterwards it may have to be confessed, that it is so independent of the nature of any or all of the impressions as to be the foundation of an abstract idea, which is representative of other impressions having nothing whatever in common with them but the order of appearance. This once allowed-an abstract idea having been somehow arrived at which is not really the copy of any impression-it is easy to argue back from the abstract idea to an impression, and because there is an idea of the composition of points to substitute a 'composition of coloured points' for colour as the original impression. From such impression, being already extension, the idea of extension can undoubtedly be abstracted.

254. We now know what becomes of extended matter' when the doctrine, which has only to be stated to find acceptance, that we cannot 'look for anything anywhere but in our ideas in other words that for us there is no world but consciousness-is fairly carried out. Its position must become more and more equivocal, as the assumption, that consciousness reveals to us an alien matter, has in one after

6

another of its details to be rejected, until a principle of synthesis within consciousness is found to explain it. In default of this, the feeling consciousness has to be made to take its place as best it may; which means that what is said of it as feeling has to be unsaid of it as extended, and vice versa. As feeling, it carries no reference to anything other than itself, to an object of which it is a quality; as extended, it is a qualified object. As extended again, its qualities are relations of coexistent parts; as feeling, it is an unlimited succession, and therefore, not being a possible whole, can have no parts at all. Finally as feeling, it must in each moment of existence either be on the same footing' with pain and pleasure or else a distinction between impressions of sensation and reflection being unwarrantably admitted-be a colour, a taste, a sound, a smell, or tangibility;' as extended, it is an 'order of appearance' or 'disposition of corpuscles,' which, being predicable indifferently at any rate of two of these sensations, can no more be the same with either than either can be the same with the other. It is not the fault of Hume but his merit that, in undertaking to maintain more strictly than others the identification of extension with feeling, he brought its impossibility more clearly into view. The pity is that having carried his speculative enterprise so far before he was thirty, he allowed literary vanity to interfere with its consistent pursuit, caring only to think out the philosophy which he inherited so far as it enabled him to pose with advantage against Mystics and Dogmatists, but not to that further issue which is the entrance to the philosophy of Kant.

255. As it was, he never came fairly to ask himself the fruitful question, How the sciences of quantity 'continuous and discreet,' which undoubtedly do exist, are possible to a merely feeling consciousness, because, while professedly reducing all consciousness to this form, he still allowed himself to interpret it in the terms of these sciences and, having done so, could easily account for their apparent 'abstraction' from it. If colour is already for feeling a magnitude, as is implied in calling it a composition of coloured points,' the question, how a knowledge of magnitude is possible, is of course superfluous. It only remains to deal, as Hume professes to do, with the apparent abstraction

He gives

no account of quantity as such.

His ac

count of the relation between

Time and
Number.

What does

in mathematics of magnitude from colour and the consequent suppositions of pure space and infinite divisibility. Any ulterior problem he ignores. That magnitude is not any the more a feeling for being endowed with colour' he shows no suspicion. He pursues his sensationalism' in short, in its bearing on mathematics, just as far as Berkeley did and no further. The question at issue, as he conceived it, was not as to the possibility of magnitude altogether, but only as to the existence of a vacuum; not as to the possibility of number altogether, but only as to the infinity of its parts. Just as he takes magnitude for granted as found in extension, and extension as equivalent to the feeling of colour, so he takes number for granted, without indeed any explicit account of the impression in which it is to be found, but apparently as found in time, which again is identified with the succession of impressions. In the second part of the Treatise, though the idea of number is assumed and an account is given of it which is supposed to be fatal to the infinite divisibility of extension, we are told nothing of the impression or impressions from which it is derived. In the Fourth Part, however, there is a passage in which a certain consideration of time is spoken of as its source.

256. In the latter passage, in order to account for the idea of identity, he is supposing a single object placed before us and surveyed for any time without our discovering in it any variation or interruption.' 'When we consider any two points of this time,' he proceeds, we may place them in different lights. We may either survey them at the very same instant; in which case they give us the idea of number, both by themselves and by the object, which must be multiplied in order to be conceived at once, as existent in these two different points of time: or, on the other hand, we may trace the succession of time by a like succession of ideas, and conceiving first one moment, along with the object then existent, imagine afterwards a change in the time without any variation or interruption in the object; in which case it gives us the idea of unity.''

257. A slight scrutiny of this passage will show that it is it come to? a prolonged tautology. The difference is merely verbal between the processes by which the ideas of number and unity

1 P. 490.

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.

258. In the passage from part II. of the Treatise, already Unites referred to, he distinctly tells us that the unity to which alone really existence belongs excludes multiplicity. Existence itself exist: belongs to unity, and is never applicable to number but on number a account of the unites of which the number is composed. denomina Twenty men may be said to exist, but 'tis only because one, tion.'" two, three, four, &c., are existent.

A unite, con

sisting of a number of fractions, is merely a fictitious de

nomination, which the mind may apply to any quantity of

'fictitious