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.