GENERAL INTRODUCTION TO VOL. I. (continued 7)

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.

Quantity made up of impressions, and there must be a least possible impression.

265. The essence of his doctrine is contained in the following passages: ‘’Tis certain that the imagination reaches a minimum, and may raise up to itself an idea, of which it cannot conceive any subdivision, and which cannot be diminished without a total annihilation. When you tell me of the thousandth and ten thousandth part of a grain of sand, I have a distinct idea of these numbers and of their several proportions, but the images which I form in my mind to represent the things themselves are nothing different from each other nor inferior to that image by which I represent the grain of sand itself, which is supposed so vastly to exceed them. What consists of parts is distinguishable into them, and what is distinguishable is separable. But whatever we may imagine of the thing, the idea of a grain of sand is not distinguishable nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas. ’Tis the same case with the impressions of the senses as with the ideas of the imagination. Put a spot of ink upon paper, fix your eye upon that spot, and retire to such a distance that at last you lose sight of it; ’tis plain that the moment before it vanished the image or impression was perfectly indivisible. ’Tis not for want of rays of light striking on our eyes that the minute parts of distant bodies convey not any sensible impression; but because they are removed beyond that distance at which their impressions were reduced to a minimum, and were incapable of any further diminution. A microscope or telescope, which renders them visible, produces not any new rays of light, but only spreads those which always flowed from them; and by that means both gives parts to impressions, which to the naked eye appear simple and uncompounded, and advances to a minimum what was formerly imperceptible.’ [1]

[1] P. 335, Part II. § 1.

Yet it is admitted that there is an idea of number not made up of impressions. A finite division into impressions no more possible than an infinite one.

266. In this passage it will be seen that Hume virtually yields the point as regards number. When he is told of the thousandth or ten thousandth part of a grain of sand he has ‘a distinct idea of these numbers and of their different proportions,’ though to this idea no distinct ‘image’ corresponds; in other words, though the idea is not a copy of any impression. It is of such parts as parts of the grain of sand—as parts of a ‘compound impression’—that he can form no idea, and for the reason given in the sequel, that they are less than any possible impression, less than the ‘minimum visibile.’ This, it would seem, is a fixed quantity. That which is the least possible impression once is so always. Telescopes and microscopes do not alter it, but present it under conditions under which it could not be presented to the naked eye. Their effect, according to Hume, could not be to render that visible which existed unseen before, nor to reveal parts in that which previously had, though it seemed not to have, them—that would imply that an impression was ‘an image of something distinct and external’—but either to present a simple impression of sight where previously there was none or to substitute a compound impression for one that was simple. [1] It is then because all divisibility is supposed to be into impressions, i.e. into feelings, and because there are conditions under which every feeling disappears, that an infinite divisibility is pronounced impossible. But the question is whether a finite divisibility into feelings is not just as impossible as an infinite one. Just as for the reasons stated above [2] a ‘compound feeling’ is impossible, so is the division of a compound into feelings. Undoubtedly if the ‘minimum visibile’ were a feeling it would not be divisible, but for the same reason it would not be a quantity. But if it is not a quantity, with what meaning is it called a minimum, and how can a quantity be supposed to be made up of such ‘visibilia’ as have themselves no quantity? In truth the ‘minimum visibile’ is not a feeling at all but a felt thing, conceived under attributes of quantity; in particular, as the term ‘minimum’ implies, under a relation of proportion to other quantities of which, if expressed numerically, Hume himself, according to the admission above noticed, would have to confess there was an idea which was an image of no impression. That which thought thus presents to itself as a thing doubtless has been a feeling; but, as thus presented, it is already other than and independent of feeling. With a step backward or a turn of the head, the feeling may cease, ‘the spot of ink may vanish;’ but the thing does not therefore cease to be a thing or to have quantity, which implies the possibility of continuous division.

[1] It will be noticed that in the last sentence of the passage quoted, Hume assumes the convenient privilege of ‘speaking with the vulgar,’ and treats the ‘minimum visibile’ presented by telescope or microscope as representing something other than itself, which previously existed, though it was imperceptible.

[2] See above, §§ 241 & 246.

In Hume’s instances it is not really a feeling, but a conceived thing, that appears as finitely divisible.

267. It is thus the confusion between feeling and conception that is at the bottom of the difficulty about divisibility. For a consciousness formed merely by the succession of feelings, as there would be no thing at all, so there would be no parts of a thing—no addibility or divisibility. But Hume is forced by the exigencies of his theory to hold together, as best he may, the reduction of all consciousness to feeling and the existence for it of divisible objects. The consequence is his supposition of ‘compound impressions’ or feelings having parts, divisible into separate impressions but divisible no further when these separate impressions have been reached. We find, however, that in all the instances he gives it is not really a feeling that is divided into feelings, but a thing into other things. It is the heap of sand, for instance, that is divided into grains, not the feeling which, by intellectual interpretation, represents to me a heap of sand that is divided into lesser feelings. I may feel the heap and feel the grain, but it is not a feeling that is the heap nor a feeling that is the grain. Hume would not offend common sense by saying that it was so, but his theory really required that he should, for the supposition that the grain is no further divisible when there are no separate impressions into which it may be divided, implies that in that case it is itself a separate impression, even as the heap is a compound one. But what difference, it may be asked, does it make to say that the heap and the grain are not feelings, but things conceived of, if it is admitted, as since Berkeley it must be, that the thing is nothing outside or independent of consciousness? Do we not by such a statement merely change names and invite the question how a thought can have parts, in place of the question how a feeling can have them?

Upon true notion of quantity infinite divisibility follows of course.

268. If thought were no more than Hume takes feeling to be, this objection would be valid. But if by thought we understand the self-conscious principle which, present to all feelings, forms out of them a world of mutually related objects, permanent with its own permanence, we shall also understand that the relations by which thought qualifies its object are not qualities of itself—that, in thinking of its object as made up of parts, it does not become itself a quantum. We shall also be on the way to understand how thought, detaching that relation of simple distinctness by which it has qualified its objects, finds before it a multitude of units of which each, as combining in itself distinctions from all the other units, is at the same time itself a multitude; in other words, finds a quantum of which each part, being the same in kind with the whole and all other parts, is also a quantum; i.e. which is infinitely divisible. When once it is understood, in short, that quantity is simply the most elementary of the relations by which thought constitutes the real world, as detached from this world and presented by thought to itself as a separate object, then infinite divisibility becomes a matter of course. It is real just in so far as quantity, of which it is a necessary attribute, is real. If quantity, though not feeling, is yet real, that its parts should not be feelings can be nothing against their reality. This once admitted, the objections to infinite divisibility disappear; but so likewise does that mysterious dignity supposed to attach to it, or to its correlative, the infinitely addible, as implying an infinite capacity in the mind. From Hume’s point of view, the mind being ‘a bundle of impressions’—though how impressions, being successive, should form a bundle is not explained—its capacity must mean the number of its impressions, and, all divisibility being into impressions, it follows that infinite divisibility means an infinite capacity in the mind. This notion however arises, as we have shown, from a confusion between a felt division of an impossible ‘compound feeling,’ and that conceived divisibility of an object which constitutes but a single attribute of the object and represents a single relation of the mind towards it. There may be a sense in which all conception implies infinity in the conceiving mind, but so far from this doing so in any special way, it arises, as we have seen, from the presentation of objects under that very condition of endless, unremoved, distinction which constitutes the true limitation of our thought.

What are the ultimate elements of extension? If not extended, what are they?

269. When, as with Hume, it is only in its application to space and time that the question of infinite divisibility is treated, its true nature is more easily disguised, for the reason already indicated, that space and time are not necessarily considered as quanta. When Hume, indeed, speaks of space as a ‘composition of parts’ or ‘made up of points,’ he is of course treating it as a quantum; but we shall find that in seeking to avoid the necessary consequence of its being a quantum—the consequence, namely, that it is infinitely divisible—he can take advantage of the possibility of treating it as the simple, unquantified, relation of externality. We have already spoken of the dexterity with which, having shown that all divisibility, because into impressions, is into simple parts, he turns this into an argument in favour of the composition of space by impressions. ‘Our idea of space is compounded of parts which are indivisible.’ Let us take one of these parts, then, and ask what sort of idea it is: ‘let us form a judgment of its nature and qualities.’ ‘’Tis plain it is not an idea of extension: for the idea of extension consists of parts; and this idea, according to the supposition, is perfectly simple and indivisible. Is it therefore nothing? That is impossible,’ for it would imply that a real idea was composed of nonentities. The way out of the difficulty is to ‘endow the simple parts with colour and solidity.’ In words already quoted, ‘that compound impression, which represents extension, consists of several lesser impressions, that are indivisible to the eye or feeling, and may be called impressions of atoms or corpuscles endowed with colour and solidity.’ (Part II. § 3, near the end.)

Colours or coloured points? What is the difference?

270. It is very plain that in this passage Hume is riding two horses at once. He is trying so to combine the notion of the constitution of space by impressions with that of its constitution by points, as to disguise the real meaning of each. In what lies the difference between the feelings of colour, of which we have shown that they cannot without contradiction be supposed to ‘make up extension,’ and ‘coloured points or corpuscles’? Unless the points, as points, mean something, the substitution of coloured points for colours means nothing. But according to Hume the point is nothing except as an impression of sight or touch. If then we refuse his words the benefit of an interpretation which his doctrine excludes, we find that there remains simply the impossible supposition that space consists of feelings. This result cannot be avoided, unless in speaking of space as composed of points, we understand by the point that which is definitely other than an impression. Thus the question which Hume puts—If extension is made up of parts, and these, being indivisible, are unextended, what are they?—really remains untouched by his ostensible answer. Such a question indeed to a philosophy like Locke’s, which, ignoring the constitution of reality by relations, supposed real things to be first found and then relations to be superinduced by the mind—much more to one like Hume’s, which left no mind to superinduce them—was necessarily unanswerable.

True way of dealing with the question.

271. In truth, extension is the relation of mutual externality. The constituents of this relation have not, as such, any nature but what is given by the relation. If in Hume’s language we ‘separate each from the others and, considering it apart, form a judgment of its nature and qualities,’ by the very way we put the problem we render it insoluble or, more properly, destroy it; for, thus separated, they have no nature. It is this that we express by the proposition which would otherwise be tautological, that extension is a relation between extended points. The ‘points’ are the simplest expression for those coefficients to the relation of mutual externality, which, as determined by that relation and no otherwise, have themselves the attribute of being extended and that only. If it is asked whether the points, being extended, are therefore divisible, the answer must be twofold. Separately they are not divisible, for separately they are nothing. Whether, as determined by mutual relation, they are divisible or no, depends on whether they are treated as forming a quantum or no. If they are not so treated, we cannot with propriety pronounce them to be either further divisible or not so, for the question of divisibility has no application to them. But being perfectly homogeneous with each other and with that which together they constitute, they are susceptible of being so treated, and are so treated when, with Hume in the passage before us, we speak of them as the parts of which extended matter consists. Thus considered as parts of a quantum and therefore themselves quanta, the infinite divisibility which belongs to all quantity belongs also to them.

‘If the point were divisible, it would be no termination of a line.’ Answer to this.

272. In this lies the answer to the most really cogent argument which Hume offers against infinite divisibility ‘A surface terminates a solid; a line terminates a surface; a point terminates a line: but I assert that if the ideas of a point, line, or surface were not indivisible, ’tis impossible we should ever conceive these terminations. For let these ideas be supposed infinitely divisible, and then let the fancy endeavour to fix itself on the idea of the last surface, line, or point, it immediately finds this idea to break into parts; and upon its seizing the last of these parts it loses its hold by a new division, and so on ad infinitum, without any possibility of its arriving at a concluding idea’. [1] If ‘point,’ ‘line,’ or ‘surface’ were really names for ‘ideas’ either in Hume’s sense, as feelings grown fainter, or in Locke’s, as definite imprints made by outward things, this passage would be perplexing. In truth they represent objects determined by certain conceived relations, and the relation under which the object is considered may vary without a corresponding variation in the name. When a ‘point’ is considered simply as the ‘termination of a line,’ it is not considered as a quantum. It represents the abstraction of the relation of externality, as existing between two lines. It is these lines, not the point, that in this case are the constituents of the relation, and thus it is they alone that are for the time considered as extended, therefore as quanta, therefore as divisible. So when the line in turn is considered as the ‘termination of a surface.’ It then represents the relation of externality as between surfaces, and for the time it is the surfaces, not the line, that are considered to have extension and its consequences. The same applies to the view of a surface as the termination of a solid. Just as the line, though not a quantum when considered simply as a relation between surfaces, becomes so when considered in relation to another line, so the point, though it ‘has no magnitude’ when considered as the termination of a line, yet acquires parts, or becomes divisible, so soon as it is considered in relation to other points as a constituent of extended matter; and it is thus that Hume considers it, ἑκὼν ἢ ἄκων [2], when he talks of extension as ‘made up of coloured points.’

[1] P. 345. [Book I, part II., sec. IV.]

[2] [Greek ἑκὼν ἢ ἄκων (hekon e akon) = like it or not. Tr.]

What becomes of the exactness of mathematics according to Hume?

273. It is the necessity then, according to his theory, of making space an impression that throughout underlies Hume’s argument against its infinite divisibility; and, as we have seen, the same theory which excludes its infinite divisibility logically extinguishes it as a quantity, divisible and measurable, altogether. He of course does not recognize this consequence. He is obliged indeed to admit that in regard to the proportions of ‘greater, equal and less,’ and the relations of different parts of space to each other, no judgments of universality or exactness are possible. We may judge of them, however, he holds, with various approximations to exactness, whereas upon the supposition of infinite divisibility, as he ingeniously makes out, we could not judge of them at all. He ‘asks the mathematicians, what they mean when they say that one line or surface is equal to, or greater or less than, another.’ If they ‘maintain the composition of extension by indivisible points,’ their answer, he supposes, will be that ‘lines or surfaces are equal when the numbers of points in each are equal.’ This answer he reckons ‘just,’ but the standard of equality given is entirely useless. ‘For as the points which enter into the composition of any line or surface, whether perceived by the sight or touch, are so minute and so confounded with each other that ’tis utterly impossible for the mind to compute their number, such a computation will never afford us a standard by which we may judge of proportions.’ The opposite sect of mathematicians, however, are in worse case, having no standard of equality whatever to assign. ‘For since, according to their hypothesis, the least as well as greatest figures contain an infinite number of parts, and since infinite numbers, properly speaking, can neither be equal nor unequal with respect to each other, the equality or inequality of any portion of space can never depend on any proportion in the number of their parts.’ His own doctrine is ‘that the only useful notion of equality or inequality is derived from the whole united appearance, and the comparison of, particular objects.’ The judgments thus derived are in many cases certain and infallible. ‘When the measure of a yard and that of a foot are presented, the mind can no more question that the first is longer than the second than it can doubt of those principles which are most clear and self-evident.’ Such judgments, however, though ‘sometimes infallible, are not always so.’ Upon a ‘review and reflection’ we often ‘pronounce those objects equal which at first we esteemed unequal,’ and vice versâ. Often also ‘we discover our error by a juxtaposition of the objects; or, where that is impracticable, by the use of some common and invariable measure which, being successively applied to each, informs us of their different proportions. And even this correction is susceptible of a new correction, and of different degrees of exactness, according to the nature of the instrument by which we measure the bodies, and the care which we employ in the comparison.’ [1]

[1] Pp. 351-53. [Book I, part II., sec. IV.]

The universal propositions of geometry either untrue or unmeaning.

274. Such indefinite approach to exactness is all that Hume can allow to the mathematician. But it is undoubtedly another and an absolute sort of exactness that the mathematician himself supposes when he pronounces all right angles equal. Such perfect equality ‘beyond what we have instruments and art’ to ascertain, Hume boldly calls a ‘mere fiction of the mind, useless as well as incomprehensible’. [1] Thus when the mathematician talks of certain angles as always equal, of certain lines as never meeting, he is either making statements that are untrue or speaking of nonentities. If his ‘lines’ and ‘angles’ mean ideas that we can possibly have, his universal propositions are untrue; if they do not, according to Hume they can mean nothing. He says, for instance, that ‘two right lines cannot have a common segment;’ but of such ideas of right lines as we can possibly have this is only true ‘where the right lines incline upon each other with a sensible angle.’ [2] It is not true when they ‘approach at the rate of an inch in 20 leagues.’ According to the ‘original standard of a right line,’ which is ‘nothing but a certain general appearance, ’tis evident right lines may be made to concur with each other’. [3] Any other standard is a ‘useless and incomprehensible fiction.’ Strictly speaking, according to Hume, we have it not, but only a tendency to suppose that we have it arising from the progressive correction of our actual measurements. [4]

[1] P. 353. [Book I, part II., sec. IV.]

[2] Cf. Aristotle, Metaph. 998a, on a corresponding view ascribed to Protagoras.

[3] P. 356. [Book I, part II., sec. IV.]

[4] P. 354. [Book I, part II., sec. IV.]

Distinction between Hume’s doctrine and that of the hypothetical nature of mathematics.

275. Now it is obvious that what Hume accounts for by means of this tendency to feign, even if the tendency did not presuppose conditions incompatible with his theory, is not mathematical science as it exists. It has even less appearance of being so than (to anticipate) has that which is accounted for by those propensities to feign, which he substitutes for the ideas of cause and substance, of being natural science as it exists. In the latter case, when the idea of necessary connexion has been disposed of, an impression of reflection can with some plausibility be made to do duty instead; but there is no impression of reflection in Hume’s sense of the word, no ‘propensity,’ that can be the subject of mathematical reasoning. He speaks, indeed, of our supposing some imaginary standard—of our having ‘an obscure and implicit notion’—of perfect equality, but such language is only a way of saving appearances; for according to him, a ‘supposition’ or ‘notion’ which is neither impression nor idea, cannot be anything. A hasty reader, catching at the term ‘supposition,’ may find his statement plausible with all the plausibility of the modern doctrine, which accounts for the universality and exactness of mathematical truths as ‘hypothetical’—the doctrine that we suppose figures exactly corresponding to our definitions, though such do not really exist. With those who take this view, however, it is always understood that the definitions represent ideas, though not ideas to which real objects can be found exactly answering. Perhaps, if pressed about their distinction between idea and reality, they might find it hard consistently to maintain it, but it is by this practically that they keep their theory afloat. Hume can admit no such distinction. The real with him is the impression, and the idea the fainter impression. There can be no idea of a straight line, a curve, a circle, a right angle, a plane, other than the impression, other than the ‘appearance to the eye,’ and there are no appearances exactly answering to the mathematical definitions. If they do not exactly answer, they might as well for the purposes of mathematical demonstration not answer at all. The Geometrician, having found that the angles at the base of this isosceles triangle are equal to each other, at once takes the equality to be true of all isosceles triangles, as being exactly like the original one, and on the strength of this establishes many other propositions. But, according to Hume, no idea that we could have would be one of which the sides were precisely equal. The Fifth Proposition of Euclid then is not precisely true of the particular idea that we have before us when we follow the demonstration. Much less can it be true of the ideas, i.e. the several appearances of colour, indefinitely varying from this, which we have before us when we follow the other demonstrations in which the equality of the angles at the base of an isosceles is taken for granted.

The admission that no relations of quantity are data of sense removes difficulty as to general propositions about them.

276. Here, as elsewhere, what we have to lament is not that Hume ‘pushed his doctrine too far,’ so far as to exclude ideas of those exact proportions in space with which geometry purports to deal, but that he did not carry it far enough to see that it excluded all ideas of quantitative relations whatever. He thus pays the penalty for his equivocation between a feeling of colour and a disposition of coloured points. Even alongside of his admission that ‘relations of space and time’ are independent of the nature of the ideas so related, which amounts to the admission that of space and time there are no ideas at all in his sense of the word, he allows himself to treat ‘proportions between spaces’ as depending entirely on our ideas of the spaces—depending on ideas which in the context he by implication admits that we have not. [1] If, instead of thus equivocating, he had asked himself how sensations of colour and touch could be added or divided, how one could serve as a measure of the size of another, he might have seen that only in virtue of that in the ‘general appearance’ of objects which, in his own language, is ‘independent of the nature of the ideas themselves’—i.e. which does not belong to them as feelings, but is added by the comparing and combining thought—are the proportions of greater, less, and equal predicable of them at all; that what thought has thus added, viz. limitation by mutual externality, it can abstract; and that by such abstraction of the limit it obtains those several terminations, as Hume well calls them—the surface terminating bodies, the line terminating surfaces, the point terminating lines—from which it constructs the world of pure space: that thus the same action of thought in sense, which alone renders appearances measurable, gives an object matter which, because the pure construction of thought, we can measure exactly and with the certainty that the judgment based on a comparison of magnitudes in a single case is true of all possible cases, because in none of these can any other conditions be present than those which we have consciously put there.

[1] Part III. § 1, sub init.

Hume does virtually admit this in regard to numbers.

277. To have arrived at this conclusion Hume had only to extend to proportions in space the principle upon which the impossibility of sensualizing arithmetic compels him to deal with proportions in number. ‘We are possessed,’ he says, ‘of a precise standard by which we can judge of the equality and proportion of numbers; and according as they correspond or not to that standard we determine their relations without any possibility of error. When two numbers are so combined, as that the one has always an unite answering to every unite of the other, we pronounce them equal’. [1] Now what are the unites here spoken of? If they were those single impressions which he elsewhere [2] seems to regard as alone properly unites, the point of the passage would be gone, for combinations of such unites could at any rate only yield those ‘general appearances’ of whose proportions we have been previously told there can be no precise standard. They can be no other than those unites which, not being impressions, he has to call ‘fictitious denominations’—unites which are nothing except in relation to each other and of which each, being in turn divisible, is itself a true number. We can easily retort upon Hume, then, when he argues that the supposition of infinite divisibility is incompatible with any comparison of quantities because with any unite of measurement, that, according to his own virtual admission, in the only case where such comparison is exact the ultimate unite of measurement is still itself divisible; which, indeed, is no more than saying that whatever measures quantity must itself be a quantity, and that therefore quantity is infinitely divisible. If Hume, instead of slurring over this characteristic of the science of number, had set himself to explain it, he would have found that the only possible explanation of it was one equally applicable to the science of space—that what is true of the unite, as the abstraction of distinctness, is true also of the abstraction of externality. As the unite, because constituted by relation to other unites, so soon as considered breaks into multiplicity, and only for that reason is a quantity by which other quantities can be measured; so is it also with the limit in whatever form abstracted, whether as point, line, or surface. If the fact that number can have no least part since each part is itself a number or nothing, so far from being incompatible with the finiteness of number, is the consequence of that finiteness, neither can the like attribute in spaces be incompatible with their being definite magnitudes, that can be compared with and measured by each other. The real difference, which is also the rationale of Hume’s different procedure in the two cases, is that the conception of space is more easily confused than that of number with the feelings to which it is applied, and which through such application become sensible spaces. Hence the liability to the supposition, which is at bottom Hume’s, that the last feeling in the process of diminution before such sensible space disappears (being the ‘minimum visibile’) is the least possible portion of space.

[1] P. 374. [Book I, part III., sec. I.]

[2] Above, par. 258.

With Hume idea of vacuum impossible, but logically not more so than that of space.

278. Just as that reduction of consciousness to feeling, which really excludes the idea of quantity altogether, is by Hume only recognised as incompatible with its infinite divisibility, so it is not recognised as extinguishing space altogether, but only space as a vacuum. If it be true, he says, ‘that the idea of space is nothing but the idea of visible or tangible points distributed in a certain order, it follows that we can form no idea of vacuum, or space where there is nothing visible or tangible’. [1] Here as elsewhere the acceptability of his statement lies in its being taken in a sense which according to his principles cannot properly belong to it. It is one doctrine that the ideas of space and body are essentially correlative, and quite another that the idea of space is equivalent to a feeling of sight or touch. It is of the latter doctrine that Hume’s denial of a vacuum is the corollary; but it is the former that gains acceptance for this denial in the mind of his reader. Space we have already spoken of as the relation of externality. If, abstracting this relation from the world of which it is the uniform but most elementary determination, we regard it as a relation between objects having no other determination, these become spaces and nothing but spaces—space pure and simple, vacuum. But we have known the world in confused fulness before we detach its constituent relations in the clearness of unreal abstraction. We have known bodies συγκεχυμένος [2], before we think their limits apart and out of these construct a world of pure space. It is thus in a sense true that in the development of our consciousness an idea of body precedes that of space, though the abstraction of space—the detachment of the relation so-called from the real complex of relations—precedes that of body; and it is this fact that, in the face of geometry, strengthens common sense in its position that an idea of vacuum is impossible. It is not, however, the inseparability of space from body whether in reality or for our consciousness, but its identity with a certain sort of feeling, that is implied in Hume’s exclusion of the idea of vacuum. ‘Body,’ as other than feeling, is with him as much a fiction as vacuum. That there can be no idea of vacuum, is thus in fact merely his negative way of putting that proposition of which the positive form is, that space is a compound impression of sight and touch. Having examined that proposition in the positive, we need not examine it again in the negative form. It will be more to the purpose to enquire whether the ‘tendency to suppose’ or ‘propensity to feign’ by which, in the absence of any such idea, our language about ‘pure space’ has to be accounted for, does not according to Hume’s own showing presuppose such an idea.

[1] P. 358. [Book I, part II., sec. V.]

[2] [Greek συγκεχυμένος (synkechymenos) = confused or jumbled-up. Tr.]

How it is that we talk as if we had idea of vacuum according to Hume.

279. By vacuum he understands invisible and intangible extension. If an idea of vacuum, then, is possible at all, he argues, it must be possible for darkness and mere motion to convey it. That they cannot do so alone is clear from the consideration that darkness is ‘no positive idea’ and that an ‘invariable motion,’ such as that of a ‘man supported in the air and softly conveyed along by some invisible power,’ gives no idea at all. Neither can they do so when ‘attended with visible and tangible objects.’ ‘When two bodies present themselves where there was formerly an entire darkness, the only change that is discoverable is in the appearance of these two objects: all the rest continues to be, as before, a perfect negation of light and of every coloured or tangible object’. [1] ‘Such dark and indistinguishable distance between two bodies can never produce the idea of extension,’ any more than blindness can. Neither can a like ‘imaginary distance between tangible and solid bodies.’ ‘Suppose two cases, viz. that of a man supported in the air, and moving his limbs to and fro without meeting anything tangible; and that of a man who, feeling something tangible, leaves it, and after a motion of which he is sensible perceives another tangible object. Wherein consists the difference between these two cases? No one will scruple to affirm that it consists merely in the perceiving those objects, and that the sensation which arises from the motion is in both cases the same; and as that sensation is not capable of conveying to us an idea of extension, when unaccompanied with some other perception, it can no more give us that idea, when mixed with the impressions of tangible objects, since that mixture produces no alteration upon it’. [2] But though a ‘distance not filled with any coloured or solid object’ cannot give us an idea of vacuum, it is the cause why we falsely imagine that we can form such an idea. There are ‘three relations’—natural relations according to Hume’s phraseology [3]—between it and that distance which really ‘conveys the idea of extension.’ ‘The distant objects affect the senses in the same manner, whether separated by the one distance or the other; the former species of distance is found capable of receiving the latter; and they both equally diminish the force of every quality. These relations betwixt the two kinds of distance will afford us an easy reason why the one has so often been taken for the other, and why we imagine we have an idea of extension without the idea of any object either of the sight or feeling’. [4]

[1] P. 362. [Book I, part II., sec. V.]

[2] P. 363. [Book I, part II., sec. V.]

[3] Above, § 206.

[4] P. 364. [Book I, part II., sec. V.]

His explanation implies that we have an idea virtually the same.

280. It appears then that we have an idea of ‘distance unfilled with any coloured or solid object.’ To speak of this distance as ‘imaginary’ or fictitious can according to Hume’s principles make no difference, so long as he admits, which he is obliged to do, that we actually have an idea of it; for every idea, being derived from an impression, is as much or as little imaginary as every other. And not only have we such an idea, but Hume’s account of the ‘relations’ between it and the idea of extension implies that, as ideas of distance, they do not differ at all. But the idea of ‘distance unfilled with any coloured or solid object’ is the idea of vacuum. It follows that the idea of extension does not differ from that of vacuum, except so far as it is other than the idea of distance. But it is from the consideration of distance that Hume himself expressly derives it; [1] and so derived, it can no more differ from distance than an idea from a corresponding impression. Thus, after all, he has to all intents and purposes to admit the idea of vacuum, but saves appearances by refusing to call it extension—the sole reason for such refusal being the supposition that every idea, and therefore the idea of extension, must be a datum of sense, which the admission of an idea of ‘invisible and intangible distance’ already contradicts.

[1] Part II. § 3, sub. inst.

By a like device that he is able to explain the appearance of our having such ideas as Causation and Identity.

281. We now know the nature of that preliminary manipulation which ‘impressions and ideas’ have to undergo, if their association is to yield the result which Hume requires—if through it the succession of feelings is to become a knowledge of things and their relations. Such a result was required as the only means of maintaining together the two characteristic positions of Locke’s philosophy; that, namely, the only world we can know is the world of ‘ideas,’ and that thought cannot originate ideas. Those relations, which Locke had inconsistently treated at once as intellectual superinductions and as ultimate conditions of reality, must be dealt with by one of two methods. They must be reduced to impressions where that could plausibly be done: where it could not, it must be admitted that we have no ideas of them, but only ‘tendencies to suppose’ that we have such, arising from the association, through ‘natural relations,’ of the ideas that we have. So dexterously does Hume work the former method that, of all the ‘philosophical relations’ which he recognizes, only Identity and Causation remain to be disposed of by the latter; and if the other relations—resemblance, time and space, proportion in quantity and degree in quality—could really be admitted as data of sense, there would at least be a possible basis for those ‘tendencies to suppose’ which, in the absence of any corresponding ideas, the terms ‘Identity’ and ‘Causation’ must be taken to represent. But, as we have shown, they can only be claimed for sense, if sense is so far one with thought—one not by conversion of thought into sense but by taking of sense into thought—as that Hume’s favourite appeals to sense against the reality of intelligible relations become unmeaning. They may be ‘impressions,’ there may be ‘impressions of them,’ but only if we deny of the impression what Hume asserts of it, and assert of it what he denies—only if we understand by ‘impression’ not an ‘internal and perishing existence;’ not that which, if other than taste, colour, sound, smell or touch, must be a ‘passion or emotion ‘; not that which carries no reference to an object other than itself, and which must either be single or compound; but something permanent and constituted by permanently coexisting parts; something that may ‘be conjoined with’ any feeling, because it is none; that always carries with it a reference to a subject which it is not but of which it is a quality; and that is both many and one, since ‘in its simplicity it contains many different resemblances and relations.’

282. In the account just adduced of vacuum, the effect of that double dealing with ‘impressions,’ which we shall have to trace at large in Hume’s explanation of our language about Causation and Identity, is already exhibited in little. Just as, after the idea of pure space has been excluded because not a copy of any possible impression, we yet find an ‘idea,’ only differing from it in name, introduced as the basis of that tendency to suppose which is to take the place of the excluded idea, so we shall find ideas of relation in the way of Identity and Causation—ideas which according to Hume we have not—presupposed as the source of those ‘propensities to feign’ which he accounts for the appearance of our having them.

Knowledge of relation in way of Identity and Causation excluded by Locke’s definition of knowledge.

283. The primary characteristic of these relations according to Hume, which they share with those of space and time, and which in fact vitiates that definition of ‘philosophical relation,’ as depending on comparison, which he adopts, is that they ‘depend not on the ideas compared together, but may be changed without any change in the ideas’. [1] It follows that they are not objects of knowledge, according to the definition of knowledge which Hume inherited, as ‘the perception of agreement or disagreement between ideas.’ A partial recognition of this consequence in regard to cause and effect we found in Locke’s suspicion that a science of nature was impossible—impossible because, however often a certain ‘idea of quality and substance’ may have followed or accompanied another, such sequence or accompaniment never amounts to agreement or ‘necessary connexion’ between the ideas, and therefore never can warrant a general assertion, but only the particular one, that the ideas in question have so many times occurred in such an order. ‘Matters of fact,’ however, which no more consist in agreement of ideas than does causation, are by Locke treated without scruple as matter of knowledge when they can be regarded as relations between present sensations. Thus the ‘particular experiment’ in Physics constitutes knowledge—the knowledge, for instance, that a piece of gold is now dissolved in aqua regia; and when ‘I myself see a man walk on the ice, it is knowledge.’ In such cases it does not occur to him to ask, either what are the ideas that agree or how much of the experiment is a present sensation. [2] Nor does Hume commonly carry his analysis further. After admitting that the relations called ‘identity and situation in time and place’ do not depend on the nature of the ideas related, he proceeds: ‘When both the objects are present to the senses along with the relation, we call this perception rather than reasoning; nor is there in this case any exercise of the thought or any action, properly speaking, but a mere passive admission of the impressions through the organs of sensation. According to this way of thinking, we ought not to receive as reasoning any of the observations we may make concerning identity and the relations of time and place; since in none of them the mind can go beyond what is immediately present to the senses, either to discover the real existence or the relations of objects’. [3]

[1] P. 372. [Book I, part III., sec. I.]

[2] Above, §§ 122 & 123.

[3] P. 376. [Book I, part III., sec. II.]

Inference a transition from an object perceived or remembered to one that is not so.

284. This passage points out the way which Hume’s doctrine of causation was to follow. That in any case ‘the mind should go beyond a present feeling, either to discover the real existence or the relations of objects’ other than present feelings, was what he could not consistently admit. In the judgment of causation, however, it seems to do so. ‘From the existence or action of one object,’ seen or remembered, it seems to be assured of the existence or action of another, not seen or remembered, on the ground of a necessary connection between the two. [1] It is such assurance that is reckoned to constitute reasoning in the distinctive sense of the term, as different at once from the analysis of complex ideas and the simple succession of ideas—such reasoning as, in the language of a later philosophy, can yield synthetic propositions. What Hume has to do, then, is to explain this ‘assurance’ away by showing that it is not essentially different from that judgment of relation in time and place which, because the related objects are ‘present to the senses along with the relation,’ is called ‘perception rather than reasoning,’ and to which no ‘exercise of the thought’ is necessary, but a ‘mere passive admission of impressions through the organs of sensation.’ Nor, for the assimilation of reasoning to perception, is anything further needed than a reference to the connection of ideas with impressions and of the ideas of imagination with those of memory, as originally stated by Hume. When both of the objects compared are present to the senses, we call the comparison perception; when neither, or only one, is so present, we call it reasoning. But the difference between the object that is present to sense, and that which is not, is merely the difference between impression and idea, which again is merely the difference between the more and the less lively feeling. [2] To feeling, whether with more or with less vivacity, every object, whether of perception or reasoning, must alike be present. Is it then a sufficient account of the matter, according to Hume, to say that when we are conscious of contiguity and succession between objects of which both are impressions we call it perception; but that when both objects are ideas, or one an impression and the other an idea, we call it reasoning? Not quite so. Suppose that I ‘have seen that species of object we call flame, and have afterwards felt that species of sensation we call heat.’ If I afterwards remembered the succession of the feeling upon the sight, both objects (according to Hume’s original usage of terms [3]) would be ideas as distinct from the impressions; or, if upon seeing the flame I remembered the previous experience of heat, one object would be an idea; but we should not reckon it a case of reasoning. ‘In all cases wherein we reason concerning objects, there is only one either perceived or remembered, and the other is supplied in conformity to our past experience’—supplied by the only other faculty than memory that can ‘supply an idea,’ viz. imagination. [4]

[1] Pp. 376, 384. [Book I, part III., secs. II. and IV.]

[2] Pp. 327, 375. [Book I, part I., sec. VII. and part III., sec. III.]

[3] Above, par. 195.

[4] Pp. 384, 388. [Book I, part III., secs. IV. and V.]

Relation of cause and effect the same as this transition.

285. This being the only account of ‘inference from the known to the unknown,’ which Hume could consistently admit, his view of the relation of cause and effect must be adjusted to it. It could not be other than a relation either between impression and impression, or between impression and idea, or between idea and idea; and all these relations are equally between feelings that we experience. Thus, instead of being the ‘objective basis’ on which inference from the known to the unknown rests, it is itself the inference; or, more properly, it and the inference alike disappear into a particular sort of transition from feeling to feeling. The problem, then, is to account for its seeming to be other than this. ‘There is nothing in any objects to persuade us that they are always remote or always contiguous; and when from experience and observation we discover that the relation in this particular is invariable, we always conclude that there is some secret cause which separates or unites them’. [1] It would seem, then, that the relation of cause and effect is something which we infer from experience, from the connection of impressions and ideas, but which is not itself impression or idea. And it would seem further, that, as we infer such an unexperienced relation, so likewise we make inferences from it. In regard to identity ‘we readily suppose an object may continue individually the same, though several times absent from and present to the senses; and ascribe to it an identity, notwithstanding the interruption of the perception, whenever we conclude that if we had kept our hand or eye constantly upon it, it would have conveyed an invariable and uninterrupted perception. But this conclusion beyond the impressions of our senses can be founded only on the connection of cause and effect; nor can we otherwise have any security that the object is not changed upon us, however much the new object may resemble that which was formerly present to the senses.’

[1] P. 376. [Book I, part III., sec. II.]

Yet seems other than this. How this appearance is to be explained.

286. This relation which, going beyond our actual experience, we seem to infer as the explanation of invariable contiguity in place or time of certain impressions, and from which again we seem to infer the identity of an object of which the perception has been interrupted, is what we call necessary connection. It is their supposed necessary connection which distinguishes objects related as cause and effect from those related merely in the way of contiguity and succession, [1] and it is a like supposition that leads us to infer what we do not see or remember from what we do. If then the reduction of thought and the intelligible world to feeling was to be made good, this supposition, not being an impression of sense or a copy of such, must be shown to be an ‘impression of reflection,’ according to Hume’s sense of the term, i.e. a tendency of the soul, analogous to desire and aversion, hope and fear, derived from impressions of sense but not copied from them; [2] and the inference which it determines must be shown to be the work of imagination, as affected by such impression of reflection. This in brief is the purport of Hume’s doctrine of causation.

[1] P. 376. [Book I, part III., sec. II.]

[2] Above, par. 195.

Inference, resting on supposition of necessary connection, to be explained before that connection.

287. After his manner, however, he will go about with his reader. The supposed ‘objective basis’ of knowledge is to be made to disappear, but in such a way that no one shall miss it. So dexterously, indeed, is this done, that perhaps to this day the ordinary student of Hume is scarcely conscious of the disappearance. Hume merely announces to begin with that he will ‘postpone the direct survey of this question concerning the nature of necessary connection,’ and deal first with these other two questions, viz. (1) ‘For what reason we pronounce it necessary that everything whose existence has a beginning, should also have a cause?’ and (2) ‘Why we conclude that such particular causes must necessarily have such particular effects; and what is the nature of that inference we draw from the one to the other, and of the belief we repose in it?’ That is to say, he will consider the inference from cause or effect, before he considers cause and effect as a relation between objects, on which the inference is supposed to depend. Meanwhile necessary connection, as a relation between objects, is naturally supposed in some sense or other to survive. In what sense, the reader expects to find when these two preliminary questions have been answered. But when they have been answered, necessary connection, as a relation between objects, turns out to have vanished.

Account of the inference given by Locke and Clarke rejected.

288. With the first of the above questions Hume only concerns himself so far as to show that we cannot know either intuitively or demonstratively, in Locke’s sense of the words, that ‘everything whose existence has a beginning also has a cause.’ Locke’s own argument for the necessity of causation—that ‘something cannot be produced by nothing’—as well as Clarke’s—that ‘if anything wanted a cause it would produce itself, i.e. exist before it existed’—are merely different ways, as Hume shows, of assuming the point in question. ‘If everything must have a cause, it follows that upon exclusion of other causes we must accept of the object itself, or of nothing, as causes. But ’tis the very point in question, whether everything must have a cause or not’. [1] On that point, according to Locke’s own showing, there can be no certainty, intuitive or demonstrative; for between the idea of beginning to exist and the idea of cause there is clearly no agreement, mediate or immediate. They are not similar feelings, they are not quantities that can be measured against each other, and to these alone can the definition of knowledge and reasoning, which Hume retained, apply. There thus disappears that last remnant of ‘knowledge’ in regard to nature which Locke had allowed to survive—the knowledge that there is a necessary connection, though one which we cannot find out. [2]

[1] P. 382. [Book I, part III., sec. III.]

[2] cf. Locke IV. 3, 29, and Introduc, par. 121.

Three points to be explained in the inference according to Hume.

289. Having thus shown, as he conceives, what the true answer to the first of the above questions is not, Hume proceeds to show what it is by answering the second. ‘Since it is not from knowledge or any scientific reasoning that we derive the opinion of the necessity of a cause to every new production,’ it must be from experience; [1] and every general opinion derived from experience is merely the summary of a multitude of particular ones. Accordingly when it has been explained why we infer particular causes from particular effects (and vice versâ), the inference from every event to a cause will have explained itself. Now ‘all our arguments concerning causes and effects consist both of an impression of the memory or senses, and of the idea of that existence which produces the object of the impression or is produced by it. Here, therefore, we have three things to explain, viz. first, the original impression; secondly, the transition to the idea of the connected cause or effect; thirdly, the nature and qualities of that idea.’ [2]

[1] P. 383. [Book I, part III., sec. III.]

[2] P. 385. [Book I, part III., sec. V.]

a. The original impression from which the transition is made, and b. The transition to inferred idea

290. As to the original impression we must notice that there is a certain inconsistency with Hume’s previous usage of terms in speaking of an impression of memory at all. [1] This, however, will be excused when we reflect that according to him impression and idea only differ in liveliness, and that he is consistent in claiming for the ideas of memory, not indeed the maximum, but a high degree of vivacity, superior to that which belongs to ideas of imagination. All that can be said, then, of that ‘original impression,’ whether of the memory or senses, which is necessary to any ‘reasoning from cause or effect,’ is that it is highly vivacious. That the transition from it to the ‘idea of the connected cause or effect’ is not determined by reason, has already been settled. It could only be so determined, according to the received account of reason, if there were some agreement in respect of quantity or quality between the idea of cause and that of the effect, to be ascertained by the interposition of other ideas. [2] But when we examine any particular objects that we hold to be related as cause and effect, e.g. the sight of flame and the feeling of heat, we find no such agreement. What we do find is their ‘constant conjunction’ in experience, and ‘conjunction’ is equivalent to that ‘contiguity in time and place,’ which has already been pointed out as one of those ‘natural relations’ which act as ‘principles of union’ between ideas. [3] Because the impression of flame has always been found to be followed by the impression of heat, the idea of flame always suggests the idea of heat. It is simple custom then that determines the transition from the one to the other, or renders ‘necessary’ the connection between them. In order that the transition, however, may constitute an inference from cause to effect (or vice versâ), one of the two objects thus naturally related, but not both, must be presented as an impression. If both were impressions it would be a case of ‘sensation, not reasoning;’ if both were ideas, no belief would attend the transition. This brings us to the question as to the ‘nature and qualities’ of the inferred idea.

[1] Above, par. 195.

[2] Cf. Locke IV. 17, 2.

[3] Above, par. 206.

c. The qualities of this idea.

291. ‘’Tis evident that all reasonings from causes or effects terminate in conclusions concerning matter of fact, i.e. concerning the existence of objects or of their qualities’; [1] in other words, in belief. If this meant a new idea, an idea that we have not previously had, it would follow that inference could really carry us beyond sense, that there could be an idea not copied from any prior impression. But according to Hume it does not mean this. ‘The idea of existence is the very same with the idea of what we conceive to be existent;’ [2] and not only so, ‘the belief of existence joins no new ideas to those which compose the idea of the object. When I think of God, when I think of him as existent, and when I believe him to be existent, my idea of him neither increases nor diminishes’. [3] In what then lies the difference between incredulity and belief; between an ‘idea assented to,’ or an object believed to exist, and a fictitious object or idea from which we dissent? The answer is, ‘not in the parts or composition of the idea, but in the manner of conceiving it,’ which must be understood to mean the manner of ‘feeling’ it; and this difference is further explained to lie in ‘the superior force, or vivacity, or steadiness’ with which it is felt.’ [4] We are thus brought to the further question, how it is that this ‘superior vivacity’ belongs to the inferred idea when we ‘reason’ from cause to effect or from effect to cause. The answer here is that the ‘impression of the memory or senses,’ which in virtue of a ‘natural relation’ suggests the idea, also ‘communicates to it a share of its force or vivacity.’

[1] P. 394. [Book I, part III., sec. VII.]

[2] P. 370. [Book I, part II., sec. VI.]

[3] P. 395. [Book I, part III., sec. II.]

[4] P. 398 [Book I, part III., sec. VII.]. Cf. above, par. 170, for the corresponding view in Berkeley.

It results that necessary connection is an impression of reflection, i.e., a propensity to the transition described.

292. Thus it appears that in order to the conclusion that any particular cause must have any particular effect, there is needed first the presence of an impression, and secondly the joint action of those two ‘principles of union among ideas,’ resemblance and contiguity. In virtue of the former principle the given impression calls up the image of a like impression previously experienced, which again in virtue of the latter calls up the image of its usual attendant, and the liveliness of the given impression so communicates itself to the recalled ideas as to constitute belief in their existence. If this is the true account of the matter, the question as to the nature of necessary connexion has answered itself. ‘The necessary connexion betwixt causes and effects is the foundation of our inference from one to the other. The foundation of the inference is the transition arising from the accustomed union. These are therefore the same’. [1] We may thus understand how it is that there seems to be an idea of such connexion to which no impression of the senses, or (to use an equivalent phrase of Hume’s) no ‘quality in objects’ corresponds. If the first presentation of two objects, of which one is cause, the other effect, (i.e. of which we afterwards come to consider one the cause, the other the effect) gives no idea of a connexion between them, as it clearly does not, neither can it do so however often repeated. It would not do so, unless the repetition ‘either discovered or produced something new’ in the objects; and it does neither. But it does ‘produce a new impression in the mind.’ After observing a ‘constant conjunction of the objects, and an uninterrupted resemblance of their relations of contiguity and succession, we immediately feel a determination of the mind to pass from one of the objects to its usual attendant, and to conceive it in a stronger light on account of that relation.’ It is of this ‘internal impression,’ this ‘propensity which custom produces,’ that the idea of necessary connexion is the copy. [2]

[1] P. 460. [Book I, part III., sec. XIV.]

[2] Pp. 457-460. [Book I, part III., sec. XIV.]

The transition not to anything beyond sense.

293. The sequence of ideas, which this propensity determines, clearly does not involve any inference ‘beyond sense,’ ‘from the known to the unknown,’ ‘from instances of which we have had experience, to those of which we have had none,’ any more than does any other ‘recurrence of an idea’—which, as we have seen, merely means, according to Hume, the return of a feeling at a lower level of intensity after it has been felt at a higher. The idea which we speak of as an inferred cause or effect is only an ‘instance of which we have no experience’ in the sense of being numerically different from the similar ideas, whose previous constant association with an impression like the given one, determines the ‘inference;’ but in the same sense the ‘impression’ which I now feel on putting my hand to the fire is different from the impressions previously felt under the same circumstances, and I do not for that reason speak of this impression as an instance of which I have had no experience. Thus Hume, though retaining the received phraseology in reference to the ‘conclusion from any particular cause to any particular effect’—phraseology which implies that prior to the inference the object inferred is in some sense unknown or unexperienced—yet deprives it of meaning by a doctrine which makes inference, as he himself puts it, ‘a species of sensation,’ ‘an unintelligible instinct of our souls,’ ‘more properly an act of the sensitive than of the cogitative part of our natures’ [1]—which in fact leaves no ‘part of our natures’ to be cogitative at all.

[1] Pp. 404, 475, and 471. [Book I, part III., sec. VIII., part IV. sec. I. and part III., sec. XVI.]

Nor determined by any objective relation.

294. We are not entitled then, it would seem, to say that any inference to matter of fact, any proof of an ‘instructive proposition,’—as distinct from the conclusion of a syllogism, which is simply derived from the analysis of a proposition already conceded,—rests on the relation of cause and effect. Such language implies that the relation is other than the inference, whereas, in fact, they are one and the same, each being merely a particular sort of sequence of feeling upon feeling—that sort of which the characteristic is that, when the former feeling only has the maximum of vivacity, it still, owing to the frequency with which it has been attended by the other, imparts to it a large, though less, amount of vivacity. This is the naked result to which Hume’s doctrine leads—a result which, thus put, might have set men upon reconsidering the first principles of the Lockeian philosophy. But he wished to find acceptance, and would not so put it. A consideration of the points in which he had to sacrifice consistency to plausibility—since he was always consistent where he decently could be—will lead us to the true αἴτιον τοῦ ψευδοῦς [1], the impossibility on his principles of explaining the world of knowledge.

[1] [Greek αἴτιον τοῦ ψευδοῦς (aition tou pseudous) = the cause of the error. Tr.]

Definitions of cause: a. As a ‘philosophical’ relation.

295. As the outcome of his doctrine, he submits two definitions of the relation of cause and effect. Considering it as ‘a philosophical relation or comparison of two ideas, we may define a cause to be an object precedent and contiguous to another, and where all objects resembling the former are placed in like relations of precedency and contiguity to those objects that resemble the latter.’ Considering the relation as ‘a natural one, or as an association between ideas,’ we may say that ‘a cause is an object precedent and contiguous to another, and so united with it that the idea of one determines the mind to form the idea of the other, and the impression of the one to form a more lively idea of the other’. [1]

[1] P. 464. [Book I, part III., sec. XIV.]

Is Hume entitled to retain ‘philosophical’ relations as distinct from ‘natural’?

296. Our first enquiry must be how far these definitions are really consistent with the theory from which they are derived. At the outset, it is a surprise to find that the ‘philosophical relation’ of cause and effect, as distinct from the natural one, should still appear to survive. Such a distinction has no meaning unless it implies a conceived relation of objects other than the de facto sequence of feelings, of which one ‘naturally’ introduces the other. It is the characteristic of Locke’s doctrine of knowledge that in it this distinction is still latent. His language constantly implies that knowledge, as a perception of relations, is other than the sequence of feelings; but by confining his view chiefly to relation in the way of likeness and unlikeness—a relation that exists between feelings merely as felt, or as they are for the feeling consciousness—he avoids the necessity of deciding what the ‘ideas’ are in the connection of which knowledge and reasoning consist, whether objects constituted by conceived relations or feelings suggestive of each other. But when once attention had been fixed, as it was by Hume, on an ostensible relation between objects, like that of cause and effect, which, if it exist at all, is clearly not one in the way of resemblance between feelings, the distinction spoken of becomes patent. If the colour red had not the likeness and unlikeness which it has to the colour blue, the colours would be different feelings from what they are; but if the flame of fire and its heat were not regarded severally as cause and effect, it would make no difference to them as feelings; or, to put it conversely, it is not upon any comparison of two feelings with each other that we regard them as related in the way of cause and effect. In what sense then can the relation between flame and heat be a philosophical relation, as defined by Hume—a relation in virtue of which we compare objects, or an idea that we acquire upon comparison?

Examination of Hume’s language about them.

297. This definition, indeed, is not stated so exactly or so uniformly as might be wished. In different passages ‘philosophical relation’ appears as that in respect of which we compare any two ideas; as that of which we acquire the idea by comparing objects, [1] and finally (in the context of the passage last quoted) as itself the comparison. [2] The real source of this ambiguity lies in that impossibility of regarding an object as anything apart from its relations, which compels any theory that does not recognize it to be inconsistent with itself. It is Locke’s cardinal doctrine that real ‘objects’ are first given as simple ideas, and that their relations, unreal in contrast with the simple ideas, are superinduced by the mind—a doctrine which Hume completes by excluding all ideas that are not either copies of simple feelings or compounds of these, and by consequence ideas of relation altogether. The three statements of the nature of philosophical relation, given above, mark three stages of departure from, or approach to, consistency with this doctrine. The first, implying as it does that relation is not merely a subjective result in our minds from the comparison of ideas, but belongs to the ideas themselves, is most obviously inconsistent with it according to the form in which it is presented by Locke; but the second is equally incompatible with Hume’s completion of the doctrine, for it implies that we so compare ideas as to acquire an idea of relation other than the ideas put together—an idea at once open to Hume’s own challenge, ‘Is it a colour, sound, smell, &c.; or is it a passion or emotion?’

[1] Cf. Part I. 5.

[2] P. 464. [Book I, part III., sec. XIV.]

Philosophical relation consists in a comparison, but no comparison between cause and effect.

298. We are thus brought to the third statement, according to which philosophical relation, instead of being an idea acquired upon comparison, is itself the comparison. A comparison of ideas may seem not far removed from the simple sequence of resembling ideas; but if we examine the definition of cause, as stated above, which with Hume corresponds to the view of the relation of cause and effect as a ‘philosophical’ one, we find that the relation in question is neither a comparison of the related objects nor an idea which arises upon such comparison. According to his statement a comparison is indeed necessary to give us an idea of the relation—a comparison, however, not of the objects which we reckon severally cause and effect with each other, but (a) of each of the two objects with other like objects, and (b) of the relation of precedency and contiguity between the two objects with that previously observed between the like objects. Now, unless the idea of relation between objects in the way of cause and effect is one that consists in, or is acquired by, comparison of those objects, the fact that another sort of comparison is necessary to constitute it does not touch the question of its possibility. However we come to have it, however reducible to impressions the objects may be, it is not only other than the idea of either object taken singly; it is not, as an idea of resemblance might be supposed to be, constituted by the joint presence or immediate sequence upon each other of the objects. Here, then, is an idea which is not taken either from an impression or from a compound of impressions (if such composition be possible), and this idea is ‘the source of all our reasonings concerning matters of fact.’

The comparison is between present and past experience of succession of objects.

299. The modern followers of Hume may perhaps seek refuge in the consideration that though the relation of cause and effect between objects is not one in the way of resemblance or one of which the idea is given by comparison of the objects, it yet results from comparisons, which may be supposed to act like chemical substances whose combination produces a substance with properties quite different from those of the combined substances, whether taken separately or together. Some anticipation of such a solution, it may be said, we find in Hume himself, who is aware that from the repetition of impressions of sense and their ideas new, heterogeneous, impressions—those of ‘reflection’—are formed. Of this more will be said when we come to Hume’s treatment of cause and effect as a ‘natural relation.’ For the present we have to enquire what exactly is implied in the comparisons from which this heterogeneous idea of relation is derived. If we look closely we shall find that they presuppose a consciousness of relations as little reducible to resemblance, i.e. as little the result of comparison, as that of cause and effect itself. It has been already noticed how Hume treats the judgment of proportion between figures as a mere affair of sense, because such relation depends entirely on the ideas compared, without reflecting that the existence of the figures presupposes those relations of space to which, because (as he admits) they do not depend on the comparison of ideas, the only excuse for reckoning any relation sensible does not apply. In the same way he contents himself with the fact that the judgment of cause and effect implies a comparison of present with past experience, and may thus be brought under his definition of ‘philosophical relation,’ without observing that the experiences compared are themselves by no means reducible to comparison. We judge that an object, which we now find to be precedent and contiguous to another, is its cause when, comparing present experience with past, we find that it always has been so. That in effect is Hume’s account of the relation, ‘considered as a philosophical one:’ and it implies that the constitution of the several experiences compared involves two sorts of relation which Hume admits not to be derived from comparison, (a) relation in time and place, (b) relation in the way of identity.

Observation of succession already goes beyond sense.

300. As to relations in time and space, we have already traced out the inconsistencies which attend Hume’s attempt to represent them as compound ideas. The statement at the beginning of Part III., that they are relations not dependent on the nature of compared ideas, is itself a confession that such representation is erroneous. If the difficulty about the synthesis of successive feelings in a consciousness that consists merely of the succession could be overcome, we might admit that the putting together of ideas might constitute such an idea of relation as depends on the nature of the combined ideas. But no combination of ideas can yield a relation which remains the same while the ideas change, and changes while they remain the same. Thus, when Hume tells us that ‘in none of the observations we may make concerning relations of time and place can the mind go beyond what is immediately present to the senses, to discover the relations of objects’ [1] the statement contradicts itself. Either we can make no observation concerning relation in time and place at all, or in making it we already ‘go beyond what is immediately present to the senses,’ since we observe what is neither a feeling nor several feelings put together. If then Hume had succeeded in his reduction of reasoning from cause or effect to observation of this kind, as modified in a certain way by habit, the purpose for which the reduction is attempted would not have been attained. The separation between perception and inference, between ‘intuition’ and ‘discourse,’ would have been got rid of, but inference and discourse would not therefore have been brought nearer to the mere succession of feelings, for the separation between feeling and perception would remain complete; and that being so, the question would inevitably recur—If the ‘observation’ of objects as related in space and time already involves a transition from the felt to the unfelt, what greater difficulty is there about the interpretation of a feeling as a change to be accounted for (which is what is meant by inference to a cause), that we should do violence to the sciences by reducing it to repeated observation lest it should seem that in it we ‘go beyond’ present feeling?

[1] P. 376. [Book I, part III., sec. II.]

As also does the ‘observation concerning identity,’ which the comparison involves.

301. Relation in the way of identity is treated by Hume in the third part of the Treatise [1] pretty much as he treats contiguity and distance. He admits that it does not depend on the nature of any ideas so related—in other words, that it is not constituted by feelings as they would be for a merely feeling consciousness—yet he denies that the mind ‘in any observations we may make concerning it’ can go beyond what is immediately present to the senses. Directly afterwards, however, we find that there is a judgment of identity which involves a ‘conclusion beyond the impressions of our senses’—the judgment, namely, that an object of which the perception is interrupted continues individually the same notwithstanding the interruption. Such a judgment, we are told, is a supposition founded only on the connection of cause and effect. How any ‘observation concerning identity’ can be made without it is not there explained, and, pending such explanation, observations concerning identity are freely taken for granted as elements given by sense in the experience from which the judgment of cause and effect is derived. In the second chapter of Part IV., however, where ‘belief in an external world’ first comes to be explicitly discussed by Hume, we find that ‘propensities to feign’ are as necessary to account for the judgment of identity as for that of necessary connection. If that chapter had preceded, instead of following, the theory of cause and effect as given in Part III., the latter would have seemed much less plain sailing than to most readers it has done. It is probably because nothing corresponding to it appears in that later redaction of his theory by which Hume sought popular acceptance, that the true suggestiveness of his speculation was ignored, and the scepticism, which awakened Kant, reduced to the commonplaces of inductive logic. To examine its purport is the next step to be taken in the process of testing the possibility of a ‘natural history’ of knowledge. Its bearing on the doctrine of cause will appear as we proceed.

[1] P. 376. [Book I, part III., sec. II.]

Identity of objects an unavoidable crux for Hume. His account of it.

302. The problem of identity necessarily arises from the fusion of reality and feeling. We must once again recall the propositions in which Hume represents this fusion—that ‘everything which enters the mind is both in reality and appearance as the perception;’ that ‘so far as the senses are judges, all perceptions are the same in the manner of their existence;’ that ‘perceptions’ are either impressions, or ideas which are ‘fainter impressions;’ and ‘impressions are internal and perishing existences, and appear as such.’ If these propositions are true—and the ‘new way of ideas’ inevitably leads to them—how is it that we believe in ‘a continued existence of objects even when they are not present to the senses,’ and an existence ‘distinct from the mind and perception’? They are the same questions from which Berkeley derived his demonstration of an eternal mind—a demonstration premature because, till the doctrine of ‘ideas,’ and of mind as their subject, had been definitely altered in a way that Berkeley did not attempt, it was explaining a belief difficult to account for by one wholly unaccountable. Before Theism could be exhibited with the necessity which Locke claimed for it, it was requisite to try what could be done with association of ideas and ‘propensities to feign’ in the way of accounting for the world of knowledge, in order that upon their failure another point of departure than Locke’s might be found necessary. The experiment was made by Hume. He has the merit, to begin with, of stating the nature of identity with a precision which we found wanting in Locke. ‘In that proposition, an object is the same with itself, if the idea expressed by the word object were no ways distinguished from that meant by itself, we really should mean nothing.’ ‘On the other hand, a multiplicity of objects can never convey the idea of identity, however resembling they may be supposed. … Since then both number and unity are incompatible with the relation of identity, it must lie in something that is neither of them. But at first sight this seems impossible.’ The explanation is that when ‘we say that an object is the same with itself, we mean that the object existent at one time is the same with itself existent at another. By this means we make a difference betwixt the idea meant by the word object and that meant by itself without going the length of number, and at the same time without restraining ourselves to a strict and absolute unity.’ In other words, identity means the unity of a thing through a multiplicity of times; or, as Hume puts it, ‘the invariableness and uninterruptedness of any object through a supposed variation of time’. [1]

[1] Pp. 489, 490. [Book I, part IV., sec. II.]

Properly with him it is a fiction, in the sense that we have no such idea. Yet he implies that we have such idea, in saying that we mistake something else for it.

303. Now that ‘an object exists’ can with Hume mean no more than that an ‘impression’ is felt, and without succession of feelings according to him there is no time. [1] It follows that unity in the existence of the object, being incompatible with succession of feelings, is incompatible also with existence in time. Either then the unity of the object or its existence at manifold times—both being involved in the conception of identity—must be a fiction; and since ‘all impressions are perishing existences,’ perishing with a turn of the head or the eyes, it cannot be doubted which it is that is the fiction. That the existence of an object, which we call the same with itself, is broken by as many intervals of time as there are successive and different, however resembling, ‘perceptions,’ must be the fact; that it should yet be one throughout the intervals is a fiction to be accounted for, Hume accounts for it by supposing that when the separate ‘perceptions’ have a strong ‘natural relation’ to each other in the way of resemblance, the transition from one to the other is so ‘smooth and easy’ that we are apt to take it for the ‘same disposition of mind with which we consider one constant and uninterrupted perception;’ and that, as a consequence of this mistake, we make the further one of taking the successive resembling perceptions for an identical, i.e. uninterrupted as well as invariable object. [2] But we cannot mistake one object for another unless we have an idea of that other object. If then we ‘mistake the succession of our interrupted perceptions for an identical object,’ it follows that we have an idea of such an object—of a thing one with itself throughout the succession of impressions—an idea which can be a copy neither of any one of the impressions nor, even if successive impressions could put themselves together, of all so put together. Such an idea being according to Hume’s principles impossible, the appearance of our having it was the fiction he had to account for; and he accounts for it, as we find, by a ‘habit of mind’ which already presupposes it. His procedure here is just the same as in dealing with the idea of vacuum. In that case, as we saw, having to account for the appearance of there being the impossible idea of pure space, he does so by showing, that having ‘an idea of distance not filled with any coloured or tangible object,’ we mistake this for an idea of extension, and hence suppose that the latter may be invisible and intangible. He thus admits an idea, virtually the same with the one excluded, as the source of the ‘tendency to suppose’ which is to replace the excluded idea. So in his account of identity. Either the habit, in virtue of which we convert resembling perceptions into an identical object, is what Hume admits to be a contradiction, ‘a habit acquired by what was never present to the mind’; [3] or the idea of identity must be present to the mind in order to render the habit possible.

[1] ‘Wherever we have no successive perceptions, we have no notion of time.’ (p. 342) [Book I, part II., sec. III.].

[2] P. 492. [Book I, part IV., sec. II.]

[3] P. 487. [Book I, part IV., sec. II.]

Succession of like feelings mistaken for an identical object: but the feelings, as described, are already such objects.

304. The device by which this petitio principii is covered is one already familiar to us in Hume. In this case it is so palpable that it is difficult to believe he was unconscious of it. As he has ‘to account for the belief of the vulgar with regard to the existence of body,’ he will ‘entirely conform himself to their manner of thinking and expressing themselves;’ in other words, he will assume the fiction in question as the beginning of a process by which its formation is to be accounted for. The vulgar make no distinction between thing and appearance. ‘Those very sensations which enter by the eye or ear are with them the true objects, nor can they readily conceive that this pen or this paper, which is immediately perceived, represents another which is different from, but resembling it. In order therefore to accommodate myself to their notions, I shall at first suppose that there is only a single existence, which I shall call indifferently object and perception, according as it shall seem best to suit my purpose, understanding by both of them what any common man may mean by a hat, or shoe, or stone, or any other impression conveyed to him by his senses’. [1] Now it is of course true that the vulgar are innocent of the doctrine of representative ideas. They do not suppose that this pen or this paper, which is immediately perceived, represents another which is different from, but resembling, it; but neither do they suppose that this pen or this paper is a sensation. It is the intellectual transition from this, that, and the other successive sensations to this pen or this paper, as the identical object to which the sensations are referred as qualities, that is unaccountable if, according to Hume’s doctrine, the succession of feelings constitutes our consciousness. In the passage quoted he quietly ignores it, covering his own reduction of felt thing to feeling under the popular identification of the real thing with the perceived. With ‘the vulgar’ that which is ‘immediately perceived’ is the real thing, just because it is not the mere feeling which with Hume it is. But under pretence of provisionally adopting the vulgar view, he entitles himself to treat the mere feeling, because according to him it is that which is immediately perceived, as if it were the permanent identical thing, which according to the vulgar is what is immediately perceived.