A Treatise of Human Nature · David Hume
GENERAL INTRODUCTION TO VOL. I.
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]
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]
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.
Text from Project Gutenberg, public domain in the United States.