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.