THE MULTIPLICITY OF CONSCIOUS STATES[1]
THE IDEA OF DURATION
[Sidenote: What is number?]
Number maybe defined in general as a collection of units, or, speaking
more exactly, as the synthesis of the one and the many. Every number
is one, since it is brought before the mind by a simple intuition and
is given a name; but the unity which attaches to it is that of a sum,
it covers a multiplicity of parts which can be considered separately.
Without attempting for the present any thorough examination of these
conceptions of unity and multiplicity, let us inquire whether the idea
of number does not imply the representation of something else as well.
[Sidenote: The units which make up a number must be identical.]
It is not enough to say that number is a collection of units; we must
add that these units are identical with one another, or at least that
they are assumed to be identical when they are counted. No doubt we
can count the sheep in a flock and say that there are fifty, although
they are all different from one another and are easily recognized by
the shepherd: but the reason is that we agree in that case to neglect
their individual differences and to take into account only what they
have in common. On the other hand, as soon as we fix our attention on
the particular features of objects or individuals, we can of course
make an enumeration of them, but not a total. We place ourselves at
these two very different points of view when we count the soldiers in
a battalion and when we call the roll. Hence we may conclude that the
idea of number implies the simple intuition of a multiplicity of parts
or units, which are absolutely alike.
[Sidenote: But they must also be distinct.]
And yet they must be somehow distinct from one another, since otherwise
they would merge into a single unit. Let us assume that all the sheep
in the flock are identical; they differ at least by the position which
they occupy in space, otherwise they would not form a flock. But now
let us even set aside the fifty sheep themselves and retain only the
idea of them. Either we include them all in the same image, and it
follows as a necessary consequence that we place them side by side in
an ideal space, or else we repeat fifty times in succession the image
of a single one, and in that case it does seem, indeed, that the series
lies in duration rather than in space. But we shall soon find out that
it cannot be so. For if we picture to ourselves each of the sheep in
the flock in succession and separately, we shall never have to do
with more than a single sheep. In order that the number should go on
increasing in proportion as we advance, we must retain the successive
images and set them alongside each of the new units which we picture to
ourselves: now, it is in space that such a juxtaposition takes place
and not in pure duration. In fact, it will be easily granted that
counting material objects means thinking all these objects together,
thereby leaving them in space. But does this intuition of space
accompany every idea of number, even of an abstract number?
[Sidenote: We can not form an image or idea of number without the
accompanying intuition of space.]
Any one can answer this question by reviewing the various forms which
the idea of number has assumed for him since his childhood. It will be
seen that we began by imagining e.g. a row of balls, that these balls
afterwards became points, and, finally, this image itself disappeared,
leaving behind it, as we say, nothing but _abstract_ number. But at
this very moment we ceased to have an image or even an idea of it; we
kept only the symbol which is necessary for reckoning and which is
the conventional way of _expressing_ number. For we can confidently
assert that 12 is half of 24 without thinking either the number 12 or
the number 24: indeed, as far as quick calculation is concerned, we
have everything to gain by not doing so. But as soon as we wish to
picture _number_ to ourselves, and not merely figures or words, we
are compelled to have recourse to an extended image. What leads to
misunderstanding on this point seems to be the habit we have fallen
into of counting in time rather than in space. In order to imagine the
number 50, for example, we repeat all the numbers starting from unity,
and when we have arrived at the fiftieth, we believe we have built up
the number in duration and in duration only. And there is no doubt that
in this way we have counted moments of duration rather than points in
space; but the question is whether we have not counted the moments
of duration by means of points in space. It is certainly possible to
perceive in time, and in time only, a succession which is nothing but
a succession, but not an addition, i.e. a succession which culminates
in a sum. For though we reach a sum by taking into account a succession
of different terms, yet it is necessary that each of these terms should
remain when we pass to the following, and should wait, so to speak, to
be added to the others: how could it wait, if it were nothing but an
instant of duration? And where could it wait if we did not localize it
in space? We involuntarily fix at a point in space each of the moments
which we count, and it is only on this condition that the abstract
units come to form a sum. No doubt it is possible, as we shall show
later, to conceive the successive moments of time independently of
space; but when we add to the present moment those which have preceded
it, as is the case when we are adding up units, we are not dealing
with these moments themselves, since they have vanished for ever, but
with the lasting traces which they seem to have left in space on their
passage through it. It is true that we generally dispense with this
mental image, and that, after having used it for the first two or three
numbers, it is enough to know that it would serve just as well for the
mental picturing of the others, if we needed it. But every clear idea
of number implies a visual image in space; and the direct study of the
units which go to form a discrete multiplicity will lead us to the same
conclusion on this point as the examination of number itself.
[Sidenote: All unity is the unity of a simple act of the mind. Unity
divisible only because regarded as extended in space.]
Every number is a collection of units, as we have said, and on the
other hand every number is itself a unit, in so far as it is a
synthesis of the units which compose it. But is the word unit taken in
the same sense in both cases? When we assert that number is a unit,
we understand by this that we master the whole of it by a simple
and indivisible intuition of the mind; this unity thus includes a
multiplicity, since it is the unity of a whole. But when we speak of
the units which go to form number, we no longer think of these units
as sums, but as pure, simple, irreducible units, intended to yield
the natural series of numbers by an indefinitely continued process of
accumulation. It seems, then, that there are two kinds of units, the
one ultimate, out of which a number is formed by a process of addition,
and the other provisional, the number so formed, which is multiple
in itself, and owes its unity to the simplicity of the act by which
the mind perceives it. And there is no doubt that, when we picture
the units which make up number, we believe that we are thinking of
indivisible components: this belief has a great deal to do with the
idea that it is possible to conceive number independently of space.
Nevertheless, by looking more closely into the matter, we shall see
that all unity is the unity of a simple act of the mind, and that, as
this is an act of unification, there must be some multiplicity for it
to unify. No doubt, at the moment at which I think each of these units
separately, I look upon it as indivisible, since I am determined to
think of its unity alone. But as soon as I put it aside in order to
pass to the next, I objectify it, and by that very deed I make it a
thing, that is to say, a multiplicity. To convince oneself of this, it
is enough to notice that the units by means of which arithmetic forms
numbers are _provisional_ units, which can be subdivided without limit,
and that each of them is the sum of fractional quantities as small and
as numerous as we like to imagine. How could we divide the unit, if
it were here that ultimate unity which characterizes a simple act of
the mind? How could we split it up into fractions whilst affirming its
unity, if we did not regard it implicitly as an extended object, one
in intuition but multiple in space? You will never get out of an idea
which you have formed anything which you have not put into it; and if
the unity by means of which you make up your number is the unity of
an act and not of an object, no effort of analysis will bring out of
it anything but unity pure and simple. No doubt, when you equate the
number 3 to the sum of 1 + 1 + 1, nothing prevents you from regarding
the units which compose it as indivisible: but the reason is that you
do not choose to make use of the multiplicity which is enclosed within
each of these units. Indeed, it is probable that the number 3 first
assumes to our mind this simpler shape, because we think rather of the
way in which we have obtained it than of the use which we might make
of it. But we soon perceive that, while all multiplication implies the
possibility of treating any number whatever as a provisional unit which
can be added to itself, inversely the units in their turn are true
numbers which are as big as we like, but are regarded as provisionally
indivisible for the purpose of compounding them with one another. Now,
the very admission that it is possible to divide the unit into as many
parts as we like, shows that we regard it as extended.
[Sidenote: Number in process of formation is discontinuous, but, when
formed, is invested with the continuity of space.]
For we must understand what is meant by the of number. It cannot
be denied that the formation or construction of a number implies
discontinuity. In other words, as we remarked above, each of the units
with which we form the number 3 seems to be indivisible _while_ we are
dealing with it, and we pass abruptly from one to the other. Again,
if we form the same number with halves, with quarters, with any units
whatever, these units, in so far as they serve to form the said number,
will still constitute elements which are provisionally indivisible, and
it is always by jerks, by sudden jumps, so to speak, that we advance
from one to the other. And the reason is that, in order to get a
number, we are compelled to fix our attention successively on each of
the units of which it is compounded. The indivisibility of the act by
which we conceive any one of them is then represented under the form
of a mathematical point which is separated from the following point
by an interval of space. But, while a series of mathematical points
arranged in empty space expresses fairly well the process by which we
form the idea of number, these mathematical points have a tendency to
develop into lines in proportion as our attention is diverted from
them, as if they were trying to reunite with one another. And when we
look at number in its finished state, this union is an accomplished
fact: the points have become lines, the divisions have been blotted
out, the whole displays all the characteristics of continuity. This is
why number, although we have formed it according to a definite law, can
be split up on any system we please. In a word, we must distinguish
between the unity which we think of and the unity which we set up as an
object after having thought of it, as also between number in process of
formation and number once formed. The unit is irreducible while we are
thinking it and number is discontinuous while we are building it up:
but, as soon as we consider number in its finished state, we objectify
it, and it then appears to be divisible to an unlimited extent. In
fact, we apply the term _subjective_ to what seems to be completely and
adequately known, and the term _objective_ to what is known in such a
way that a constantly increasing number of new impressions could be
substituted for the idea which we actually have of it. Thus, a complex
feeling will contain a fairly large number of simple elements; but,
as long as these elements do not stand out with perfect clearness,
we cannot say that they were completely realized, and, as soon as
consciousness has a distinct perception of them, the psychic state
which results from their synthesis will have changed for this very
reason. But there is no change in the general appearance of a body,
however it is analysed by thought, because these different analyses,
and an infinity of others, are already visible in the mental image
which we form of the body, though they are not realized: this actual
and not merely virtual perception of subdivisions in what is undivided
is just what we call objectivity. It then becomes easy to determine the
exact part played by the subjective and the objective in the idea of
number. What properly belongs to the mind is the indivisible process by
which it concentrates attention successively on the different parts of
a given space; but the parts which have thus been isolated remain in
order to join with the others, and, once the addition is made, they may
be broken up in any way whatever. They are therefore parts of space,
and space is, accordingly, the material with which the mind builds up
number, the medium in which the mind places it.
Properly speaking, it is arithmetic which teaches us to split up
without limit the units of which number consists. Common sense is very
much inclined to build up number with indivisibles.
[Sidenote: It follows that number is actually _thought of_ as a
juxtaposition in space.]
And this is easily understood, since the provisional simplicity of
the component units is just what they owe to the mind, and the latter
pays more attention to its own acts than to the material on which
it works. Science confines itself, here, to drawing our attention
to this material: if we did not already localize number in space,
science would certainly not succeed in making us transfer it thither.
From the beginning, therefore, we must have thought of number as of
a juxtaposition in space. This is the conclusion which we reached
at first, basing ourselves on the fact that all addition implies a
multiplicity of parts simultaneously perceived.
[Sidenote: Two kinds of multiplicity: (1) material objects, counted
in space; (2) conscious states, not countable unless symbolically
represented in space.]
Now, if this conception of number is granted, it will be seen that
everything is not counted in the same way, and that there are two very
different kinds of multiplicity. When we speak of material objects,
we refer to the possibility of seeing and touching them; we localize
them in space. In that case, no effort of the inventive faculty or
of symbolical representation is necessary in order to count them; we
have only to think them, at first separately, and then simultaneously,
within the very medium in which they come under our observation. The
case is no longer the same when we consider purely affective psychic
states, or even mental images other than those built up by means
of sight and touch. Here, the terms being no longer given in space,
it seems, _a priori,_ that we can hardly count them except by some
process of symbolical representation. In fact, we are well aware of a
representation of this kind when we are dealing with sensations the
cause of which is obviously situated in space. Thus, when we hear a
noise of steps in the street, we have a confused vision of somebody
walking along: each of the successive sounds is then localized at a
point in space where the passer-by might tread: we count our sensations
in the very space in which their tangible causes are ranged. Perhaps
some people count the successive strokes of a distant bell in a similar
way, their imagination pictures the bell coming and going; this spatial
sort of image is sufficient for the first two units, and the others
follow naturally. But most people's minds do not proceed in this way.
They range the successive sounds in an ideal space and then fancy
that they are counting them in pure duration. Yet we must be clear on
this point. The sounds of the bell certainly reach me one after the
other; but one of two alternatives must be true. Either I retain each
of these successive sensations in order to combine it with the others
and form a group which reminds me of an air or rhythm which I know: in
that case I do not _count_ the sounds, I limit myself to gathering,
so to speak, the qualitative impression produced by the whole series.
Or else I intend explicitly to count them, and then I shall have
to separate them, and this separation must take place within some
homogeneous medium in which the sounds, stripped of their qualities,
and in a manner emptied, leave traces of their presence which are
absolutely alike. The question now is, whether this medium is time or
space. But a moment of time, we repeat, cannot persist in order to be
added to others. If the sounds are separated, they must leave empty
intervals bet ween them. If we count them, the intervals must remain
though the sounds disappear: how could these intervals remain, if they
were pure duration and not space? It is in space, therefore, that the
operation takes place. It becomes, indeed, more and more difficult
as we penetrate further into the depths of consciousness. Here we
find ourselves confronted by a confused multiplicity of sensations
and feelings which analysis alone can distinguish. Their number is
identical with the number of the moments which we take up when we count
them; but these moments, as they can be added to one another, are
again points in space. Our final conclusion, therefore, is that there
are two kinds of multiplicity: that of material objects, to which the
conception of number is immediately applicable; and the multiplicity of
states of consciousness, which cannot be regarded as numerical without
the help of some symbolical representation, in which a necessary
element is _space._
[Sidenote: The impenetrability of matter is not a physical but a
logical necessity.]
As a matter of fact, each of us makes a distinction between these two
kinds of multiplicity whenever he speaks of the impenetrability of
matter. We sometimes set up impenetrability as a fundamental property
of bodies, known in the same way and put on the same level as e.g.
weight or resistance. But a purely negative property of this kind
cannot be revealed by our senses; indeed, certain experiments in
mixing and combining things might lead us to call it in question if
our minds were not already made up on the point. Try to picture one
body penetrating another: you will at once assume that there are empty
spaces in the one which will be occupied by the particles of the other;
these particles in their turn cannot penetrate one another unless one
of them divides in order to fill up the interstices of the other; and
our thought will prolong this operation indefinitely in preference to
picturing two bodies in the same place. Now, if impenetrability were
really a quality of matter which was known by the senses, it is not at
all clear why we should experience more difficulty in conceiving two
bodies merging into one another than a surface devoid of resistance
or a weightless fluid. In reality, it is not a physical but a logical
necessity which attaches to the proposition: "Two bodies cannot occupy
the same place at the same time" The contrary assertion involves an
absurdity which no conceivable experience could succeed in dispelling.
In a word, it implies a contradiction. But does not this amount to
recognizing that the very idea of the number 2, or, more generally,
of any number whatever, involves the idea of juxtaposition in space?
If impenetrability is generally regarded as a quality of matter, the
reason is that the idea of number is thought to be independent of the
idea of space. We thus believe that we are adding something to the
idea of two or more objects by saying that they cannot occupy the
same place: as if the idea of the number 2, even the abstract number,
were not already, as we have shown, that of two different positions
in space! Hence to assert the impenetrability of matter is simply to
recognize the interconnexion between the notions of number and space,
it is to state a property of number rather than of matter.--Yet, it
will be said, do we not count feelings, sensations, ideas, all of
which permeate one another, and each of which, for its part, takes
up the whole of the soul?--Yes, undoubtedly; but, just because they
permeate one another, we cannot count them unless we represent them
by homogeneous units which occupy separate positions in space and
consequently no longer permeate one another. Impenetrability thus makes
its appearance at the same time as number; and when we attribute this
quality to matter in order to distinguish it from everything which
is not matter, we simply state under another form the distinction
established above between extended objects, to which the conception of
number is immediately applicable, and states of consciousness, which
have first of all to be represented symbolically in space.
[Sidenote: Homogeneous time as the medium in which conscious states
form discrete series. This time is nothing but space, and pure duration
is something different.]
It is advisable to dwell on the last point. If, in order to count
states of consciousness, we have to represent them symbolically in
space, is it not likely that this symbolical representation will alter
the normal conditions of inner perception? Let us recall what we
said a short time ago about the intensity of certain psychic states.
Representative sensation, looked at in itself, is pure quality; but,
seen through the medium of extensity, this quality becomes in a
certain sense quantity, and is called intensity. In the same way, our
projection of our psychic states into space in order to form a discrete
multiplicity is likely to influence these states themselves and to
give them in reflective consciousness a new form, which immediate
perception did not attribute to them. Now, let us notice that when we
speak of _time,_ we generally think of a homogeneous medium in which
our conscious states are ranged alongside one another as in space, so
as to form a discrete multiplicity. Would not time, thus understood, be
to the multiplicity of our psychic states what intensity is to certain
of them,--a sign, a symbol, absolutely distinct from true duration?
Let us ask consciousness to isolate itself from the external world,
and, by a vigorous effort of abstraction, to become itself again.
We shall then put this question to it: does the multiplicity of our
conscious states bear the slightest resemblance to the multiplicity of
the units of a number? Has true duration anything to do with space?
Certainly, our analysis of the idea of number could not but make us
doubt this analogy, to say no more. For if time, as the reflective
consciousness represents it, is a medium in which our conscious states
form a discrete series so as to admit of being counted, and if on the
other hand our conception of number ends in spreading out in space
everything which can be directly counted, it is to be presumed that
time, understood in the sense of a medium in which we make distinctions
and count, is nothing but space. That which goes to confirm this
opinion is that we are compelled to borrow from space the images by
which we describe what the reflective consciousness feels about time
and even about succession; it follows that pure duration must be
something different. Such are the questions which we have been led to
ask by the very analysis of the notion of discrete multiplicity. But we
cannot throw any light upon them except by a direct study of the ideas
of space and time in their mutual relations.
[Sidenote: Does space exist independently of its contents, as Kant
held?]
We shall not lay too much stress on the question of the absolute
reality of space: perhaps we might as well ask whether space is or
is not in space. In short, our senses perceive the qualities of
bodies and space along with them: the great difficulty seems to have
been to discover whether extensity is an aspect of these physical
qualities--a quality of quality--or whether these qualities are
essentially unextended, space coming in as a later addition, but being
self-sufficient and existing without them. On the first hypothesis,
space would be reduced to an abstraction, or, speaking more correctly,
an extract; it would express the common element possessed by certain
sensations called representative. In the second case, space would be a
reality as solid as the sensations themselves, although of a different
order. We owe the exact formulation of this latter conception to Kant:
the theory which he works out in the Transcendental Aesthetic consists
in endowing space with an existence independent of its content, in
laying down as _de jure_ separable what each of us separates _de
facto,_ and in refusing to regard extensity as an abstraction like the
others. In this respect the Kantian conception of space differs less
than is usually imagined from the popular belief. Far from shaking our
faith in the reality of space, Kant has shown what it actually means
and has even justified it.
[Sidenote: The empiricists really agree with Kant for extensity can not
result from synthesis of unextended sensations without an act of the
mind.]
Moreover, the solution given by Kant does not seem to have been
seriously disputed since his time: indeed, it has forced itself,
sometimes without their knowledge, on the majority of those who
have approached the problem anew, whether nativists or empiricists.
Psychologists agree in assigning a Kantian origin to the nativistic
explanation of Johann Müller; but Lotze's hypothesis of local signs,
Bain's theory, and the more comprehensive explanation suggested by
Wundt, may seem at first quite independent of the Transcendental
Aesthetic. The authors of these theories seem indeed to have put aside
the problem of the nature of space, in order to investigate simply
by what process our sensations come to be situated in space and to
be set, so to speak, alongside one another: but this very question
shows that they regard sensations as inextensive and make a radical
distinction, just as Kant did, between the matter of representation
and its form. The conclusion to be drawn from the theories of Lotze
and Bain, and from Wundt's attempt to reconcile them, is that the
sensations by means of which we come to form the notion of space are
themselves unextended and simply qualitative: extensity is supposed
to result from their synthesis, as water from the combination of two
gases. The empirical or genetic explanations have thus taken up the
problem of space at the very point where Kant left it: Kant separated
space from its contents: the empiricists ask how these contents, which
are taken out of space by our thought, manage to get back again. It is
true that they have apparently disregarded the activity of the mind,
and that they are obviously inclined to regard the extensive form under
which we represent things as produced by a kind of alliance of the
sensations with one another: space, without being extracted from the
sensations, is supposed to result from their co-existence. But how can
we explain such an origination without the active intervention of the
mind? The extensive differs by hypothesis from the inextensive: and
even if we assume that extension is nothing but a relation between
inextensive terms, this relation must still be established by a mind
capable of thus associating several terms. It is no use quoting the
example of chemical combinations, in which the whole seems to assume,
of its own accord, a form and qualities which did not belong to any
of the elementary atoms. This form and these qualities owe their
origin just to the fact that we gather up the multiplicity of atoms
in a single perception: get rid of the mind which carries out this
synthesis and you will at once do away with the qualities, that is
to say, the aspect under which the synthesis of elementary parts is
presented to our consciousness. Thus inextensive sensations will remain
what they are, viz., inextensive sensations, if nothing be added to
them. For their co-existence to give rise to space, there must be an
act of the mind which takes them in all at the same time and sets them
in juxtaposition: this unique act is very like what Kant calls an _a
priori_ form of sensibility.
[Sidenote: This act consists in the intuition of an empty homogeneous
medium: perhaps peculiar to man and not shared by animals.]
If we now seek to characterize this act, we see that it consists
essentially in the intuition, or rather the conception, of an empty
homogeneous medium. For it is scarcely possible to give any other
definition of space: space is what enables us to distinguish a number
of identical and simultaneous sensations from one another; it is
thus a principle of differentiation other than that of qualitative
differentiation, and consequently it is a reality with no quality.
Someone may say, with the believers in the theory of local signs, that
simultaneous sensations are never identical, and that, in consequence
of the diversity of the organic elements which they affect, there are
no two points of a homogeneous surface which make the same impression
on the sight or the touch. We are quite ready to grant it, for if these
two points affected us in the same way, there would be no reason for
placing one of them on the right rather than on the left. But, just
because we afterwards interpret this difference of quality in the sense
of a difference of situation, it follows that we must have a clear
idea of a homogeneous medium, i.e. of a simultaneity of terms which,
although identical in quality, are yet distinct from one another. The
more you insist on the difference between the impressions made on
our retina by two points of a homogeneous surface, the more do you
thereby make room for the activity of the mind, which perceives under
the form of extensive homogeneity what is given it as qualitative
heterogeneity. No doubt, though the representation of a homogeneous
space grows out of an effort of the mind, there must be within the
qualities themselves which differentiate two sensations some reason
why they occupy this or that definite position in space. We must thus
distinguish between the perception of extensity and the conception of
space: they are no doubt implied in one another, but, the higher we
rise in the scale of intelligent beings, the more clearly do we meet
with the independent idea of a homogeneous space. It is therefore
doubtful whether animals perceive the external world quite as we do,
and especially whether they represent externality in the same way as
ourselves. Naturalists have pointed out, as a remarkable fact, the
surprising ease with which many vertebrates, and even some insects,
manage to find their way through space. Animals have been seen to
return almost in a straight line to their old home, pursuing a path
which was hitherto unknown to them over a distance which may amount
to several hundreds of miles. Attempts have been made to explain this
feeling of direction by sight or smell, and, more recently, by the
perception of magnetic currents which would enable the animal to take
its bearings like a living compass. This amounts to saying that space
is not so homogeneous for the animal as for us, and that determinations
of space, or directions, do not assume for it a purely geometrical
form. Each of these directions might appear to it with its own shade,
its peculiar quality. We shall understand how a perception of this
kind is possible if we remember that we ourselves distinguish our right
from our left by a natural feeling, and that these two parts of our own
extensity do then appear to us as if they bore a different _quality;_
in fact, this is the very reason why we cannot give a proper definition
of right and left. In truth, qualitative differences exist everywhere
in nature, and I do not see why two concrete directions should not be
as marked in immediate perception as two colours. But the conception of
an empty homogeneous medium is something far more extraordinary, being
a kind of reaction against that heterogeneity which is the very ground
of our experience. Therefore, instead of saying that animals have a
special sense of direction, we may as well say that men have a special
faculty of perceiving or conceiving a space without quality. This
faculty is not the faculty of abstraction: indeed, if we notice that
abstraction assumes clean-cut distinctions and a kind of externality
of the concepts or their symbols with regard to one another, we shall
find that the faculty of abstraction already implies the intuition
of a homogeneous medium. What we must say is that we have to do
with two different kinds of reality, the one heterogeneous, that of
sensible qualities, the other homogeneous, namely space. This latter,
clearly conceived by the human intellect, enables us to use clean-cut
distinctions, to count, to abstract, and perhaps also to speak.
[Sidenote: Time, in so far as it is a homogenious medium, and not
concrete duration, is reducible to space.]
Now, if space is to be defined as the homogeneous, it seems that
inversely every homogeneous and unbounded medium will be space. For,
homogeneity here consisting in the absence of every quality, it is hard
to see how two forms of the homogeneous could be distinguished from
one another. Nevertheless it is generally agreed to regard time as an
unbounded medium, different from space but homogeneous like the latter:
the homogeneous is thus supposed to take two forms, according as its
contents co-exist or follow one another. It is true that, when we make
time a homogeneous medium in which conscious states unfold themselves,
we take it to be given all at once, which amounts to saying that we
abstract it from duration. This simple consideration ought to warn us
that we are thus unwittingly falling back upon space, and really giving
up time. Moreover, we can understand that material objects, being
exterior to one another and to ourselves, derive both exteriorities
from the homogeneity of a medium which inserts intervals between them
and sets off their outlines: but states of consciousness, even when
successive, permeate one another, and in the simplest of them the whole
soul can be reflected. We may therefore surmise that time, conceived
under the form of a homogeneous medium, is some spurious concept,
due to the trespassing of the idea of space upon the field of pure
consciousness. At any rate we cannot finally admit two forms of the
homogeneous, time and space, without first seeking whether one of them
cannot be reduced to the other. Now, externality is the distinguishing
mark of things which occupy space, while states of consciousness are
not essentially external to one another, and become so only by being
spread out in time, regarded as a homogeneous medium. If, then, one of
these two supposed forms of the homogeneous, namely time and space,
is derived from the other, we can surmise _a priori_ that the idea of
space is the fundamental datum. But, misled by the apparent simplicity
of the idea of time, the philosophers who have tried to reduce one of
these ideas to the other have thought that they could make extensity
out of duration. While showing how they have been misled, we shall see
that time, conceived under the form of an unbounded and homogeneous
medium, is nothing but the ghost of space haunting the reflective
consciousness.
[Sidenote: Mistake of the attempt to derive relations of extensity from
those of succession. The conception of pure "duration."]
The English school tries, in fact, to reduce relations of extensity to
more or less complex relations of succession in time. When, with our
eyes shut, we run our hands along a surface, the rubbing of our fingers
against the surface, and especially the varied play of our joints,
provide a series of sensations, which differ only by their _qualities_
and which exhibit a certain order in time. Moreover, experience teaches
us that this series can be reversed, that we can, by an effort of
a different kind (or, as we shall call it later, _in an opposite
direction),_ obtain the same sensations over again in an inverse order:
relations of position in space might then be defined as reversible
relations of succession in time. But such a definition involves a
vicious circle, or at least a very superficial idea of time. There are,
indeed, as we shall show a little later, two possible conceptions of
time, the one free from all alloy, the other surreptitiously bringing
in the idea of space. Pure duration is the form which the succession of
our conscious states assumes when our ego lets itself _live,_ when it
refrains from separating its present state from its former states. For
this purpose it need not be entirely absorbed in the passing sensation
or idea; for then, on the contrary, it would no longer _endure._ Nor
need it forget its former states: it is enough that, in recalling these
states, it does not set them alongside its actual state as one point
alongside another, but forms both the past and the present states
into an organic whole, as happens when we recall the notes of a tune,
melting, so to speak, into one another. Might it not be said that,
even if these notes succeed one another, yet we perceive them in one
another, and that their totality may be compared to a living being
whose parts, although distinct, permeate one another just because they
are so closely connected? The proof is that, if we interrupt the rhythm
by dwelling longer than is right on one note of the tune, it is not
its exaggerated length, as length, which will warn us of our mistake,
but the qualitative change thereby caused in the whole of the musical
phrase. We can thus conceive of succession without distinction, and
think of it as a mutual penetration, an interconnexion and organization
of elements, each one of which represents the whole, and cannot be
distinguished or isolated from it except by abstract thought. Such
is the account of duration which would be given by a being who was
ever the same and ever changing, and who had no idea of space. But,
familiar with the latter idea and indeed beset by it, we introduce it
unwittingly into our feeling of pure succession; we set our states
of consciousness side by side in such a way as to perceive them
simultaneously, no longer in one another, but alongside one another;
in a word, we project time into space, we express duration in terms of
extensity, and succession thus takes the form of a continuous line or a
chain, the parts of which touch without penetrating one another. Note
that the mental image thus shaped implies the perception, no longer
successive, but simultaneous, of a _before_ and _after,_ and that it
would be a contradiction to suppose a succession which was only a
succession, and which nevertheless was contained in one and the same
instant. Now, when we speak of an _order_ of succession in duration,
and of the reversibility of this order, is the succession we are
dealing with pure succession, such as we have just defined it, without
any admixture of extensity, or is it succession developing in space, in
such a way that we can take in at once a number of elements which are
both distinct and set side by side? There is no doubt about the answer:
we could not introduce _order_ among terms without first distinguishing
them and then comparing the places which they occupy; hence we must
perceive them as multiple, simultaneous and distinct; in a word, we set
them side by side, and if we introduce an order in what is successive,
the reason is that succession is converted into simultaneity and
is projected into space. In short, when the movement of my finger
along a surface or a line provides me with a series of sensations of
different qualities, one of two things happens: either I picture these
sensations to myself as in duration only, and in that case they succeed
one another in such a way that I cannot at a given moment perceive a
number of them as simultaneous and yet distinct; or else I make out an
order of succession, but in that case I display the faculty not only of
perceiving a succession of elements, but also of setting them out in
line after having distinguished them: in a word, I already possess the
idea of space. Hence the idea of a reversible series in duration, or
even simply of a certain _order_ of succession in time, itself implies
the representation of space, and cannot be used to define it.
[Sidenote: Succession cannot be symbolized as a line without
introducing the idea of space of three dimensions.]
To give this argument a stricter form, let us imagine a straight line
of unlimited length, and on this line a material point A, which
moves. If this point were conscious of itself, it would feel itself
change, since it moves: it would perceive a succession; but would
this succession assume for it the form of a line? No doubt it would,
if it could rise, so to speak, above the line which it traverses, and
perceive simultaneously several points of it in juxtaposition: but
by doing so it would form the idea of space, and it is in space and
not in pure duration that it would see displayed the changes which it
undergoes. We here put our finger on the mistake of those who regard
pure duration as something similar to space, but of a simpler nature.
They are fond of setting psychic states side by side, of forming a
chain or a line of them, and do not imagine that they are introducing
into this operation the idea of space properly so called, the idea of
space in its totality, because space is a medium of three dimensions.
But how can they fail to notice that, in order to perceive a line as
a line, it is necessary to take up a position outside it, to take
account of the void which surrounds it, and consequently to think
a space of three dimensions? If our conscious point A does not yet
possess the idea of space--and this is the hypothesis which we have
agreed to adopt--the succession of states through which it passes
cannot assume for it the form of a line; but its sensations will add
themselves dynamically to one another and will organize themselves,
like the successive notes of a tune by which we allow ourselves to be
lulled and soothed. In a word, pure duration might well be nothing but
a succession of qualitative changes, which melt into and permeate one
another, without precise outlines, without any tendency to externalize
themselves in relation to one another, without any affiliation with
number: it would be pure heterogeneity. But for the present we shall
not insist upon this point; it is enough for us to have shown that,
from the moment when you attribute the least homogeneity to duration,
you surreptitiously introduce space.
[Sidenote: Pure duration is wholly qualitative. It cannot be measured
unless symbolically represented in space.]
It is true that we count successive moments of duration, and that,
because of its relations with number, time at first seems to us to
be a measurable magnitude, just like space. But there is here an
important distinction to be made. I say, e.g., that a minute has just
elapsed, and I mean by this that a pendulum, beating the seconds, has
completed sixty oscillations. If I picture these sixty oscillations
to myself all at once by a single mental perception, I exclude by
hypothesis the idea of a succession. I do not think of sixty strokes
which succeed one another, but of sixty points on a fixed line, each
one of which symbolizes, so to speak, an oscillation of the pendulum.
If, on the other hand, I wish to picture these sixty oscillations in
succession, but without altering the way they are produced in space,
I shall be compelled to think of each oscillation to the exclusion
of the recollection of the preceding one, for space has preserved no
trace of it; but by doing so I shall condemn myself to remain for ever
in the present; I shall give up the attempt to think a succession or a
duration. Now if, finally, I retain the recollection of the preceding
oscillation together with the image of the present oscillation, one of
two things will happen. Either I shall set the two images side by side,
and we then fall back on our first hypothesis, or I shall perceive one
in the other, each permeating the other and organizing themselves like
the notes of a tune, so as to form what we shall call a continuous or
qualitative multiplicity with no resemblance to number. I shall thus
get the image of pure duration; but I shall have entirely got rid of
the idea of a homogeneous medium or a measurable quantity. By carefully
examining our consciousness we shall recognize that it proceeds in this
way whenever it refrains from representing duration symbolically. When
the regular oscillations of the pendulum make us sleepy, is it the last
sound heard, the last movement perceived, which produces this effect?
No, undoubtedly not, for why then should not the first have done the
same? Is it the recollection of the preceding sounds or movements, set
in juxtaposition to the last one? But this same recollection, if it
is later on set in juxtaposition to a single sound or movement, will
remain without effect. Hence we must admit that the sounds combined
with one another and acted, not by their quantity as quantity, but
by the quality which their quantity exhibited, i.e. by the rhythmic
organization of the whole. Could the effect of a slight but continuous
stimulation be understood in any other way? If the sensation remained
always the same, it would continue to be indefinitely slight and
indefinitely bearable. But the fact is that each increase of
stimulation is taken up into the preceding stimulations, and that the
whole produces on us the effect of a musical phrase which is constantly
on the point of ending and constantly altered in its totality by the
addition of some new note. If we assert that it is always the _same_
sensation, the reason is that we are thinking, not of the sensation
itself, but of its objective cause situated in space. We then set it
out in space in its turn, and in place of an organism which develops,
in place of changes which permeate one another, we perceive one and
the same sensation stretching itself out lengthwise, so to speak,
and setting itself in juxtaposition to itself without limit. Pure
duration, that which consciousness perceives, must thus be reckoned
among the so-called intensive magnitudes, if intensities can be called
magnitudes: strictly speaking, however, it is not a quantity, and as
soon as we try to measure it, we unwittingly replace it by space.
[Sidenote: Time, as dealt with by the astronomer and the physicist,
does indeed _seem_ to be measurable and therefore homogeneous.]
But we find it extraordinarily difficult to think of duration in its
original purity; this is due, no doubt, to the fact that we do not
_endure_ alone, external objects, it seems, _endure_ as we do, and
time, regarded from this point of view, has every appearance of a
homogeneous medium. Not only do the moments of this duration seem to
be external to one another, like bodies in space, but the movement
perceived by our senses is the, so to speak, palpable sign of a
homogeneous and measurable duration. Nay more, time enters into the
formulae of mechanics, into the calculations of the astronomer, and
even of the physicist, under the form of a quantity. We measure the
velocity of a movement, implying that time itself is a magnitude.
Indeed, the analysis which we have just attempted requires to be
completed, for if duration properly so-called cannot be measured,
what is it that is measured by the oscillations of the pendulum?
Granted that inner duration, perceived by consciousness, is nothing
else but the melting of states of consciousness into one another, and
the gradual growth of the ego, it will be said, notwithstanding, that
the time which the astronomer introduces into his formulae, the time
which our clocks divide into equal portions, this time, at least, is
something different: it must be a measurable and therefore homogeneous
magnitude.--It is nothing of the sort, however, and a close examination
will dispel this last illusion.
[Sidenote: But what we call measuring time is nothing but counting
simultaneities. The clock taken as an illustration.]
When I follow with my eyes on the dial of a clock the movement of
the hand which corresponds to the oscillations of the pendulum, I
do not measure duration, as seems to be thought; I merely count
simultaneities, which is very different. Outside of me, in space, there
is never more than a single position of the hand and the pendulum,
for nothing is left of the past positions. Within myself a process
of organization or interpenetration of conscious states is going on,
which constitutes true duration. It is because I _endure_ in this way
that I picture to myself what I call the past oscillations of the
pendulum at the same time as I perceive the present oscillation. Now,
let us withdraw for a moment the ego which thinks these so-called
successive oscillations: there will never be more than a single
oscillation, and indeed only a single position, of the pendulum, and
hence no duration. Withdraw, on the other hand, the pendulum and its
oscillations; there will no longer be anything but the heterogeneous
duration of the ego, without moments external to one another, without
relation to number. Thus, within our ego, there is succession without
mutual externality; outside the ego, in pure space, mutual externality
without succession: mutual externality, since the present oscillation
is radically distinct from the previous oscillation, which no longer
exists; but no succession, since succession exists solely for a
conscious spectator who keeps the past in mind and sets the two
oscillations or their symbols side by side in an auxiliary space.
Now, between this succession without externality and this externality
without succession, a kind of exchange takes place, very similar to
what physicists call the phenomenon of endosmosis. As the successive
phases of our conscious life, although interpenetrating, correspond
individually to an oscillation of the pendulum which occurs at the same
time, and as, moreover, these oscillations are sharply distinguished
from one another, we get into the habit of setting up the same
distinction between the successive moments of our conscious life: the
oscillations of the pendulum break it up, so to speak, into parts
external to one another: hence the mistaken idea of a homogeneous inner
duration, similar to space, the moments of which are identical and
follow, without penetrating, one another. But, on the other hand, the
oscillations of the pendulum, which are distinct only because one has
disappeared when the other appears on the scene, profit, as it were,
from the influence which they have thus exercised over our conscious
life. Owing to the fact that our consciousness has organized them as a
whole in memory, they are first preserved and afterwards disposed in
a series: in a word, we create for them a fourth dimension of space,
which we call homogeneous time, and which enables the movement of the
pendulum, although taking place at one spot, to be continually set in
juxtaposition to itself. Now, if we try to determine the exact part
played by the real and the imaginary in this very complex process,
this is what we find. There is a real space, without duration, in
which phenomena appear and disappear simultaneously with our states of
consciousness. There is a real duration, the heterogeneous moments of
which permeate one another; each moment, however, can be brought into
relation with a state of the external world which is contemporaneous
with it, and can be separated from the other moments in consequence
of this very process. The comparison of these two realities gives
rise to a symbolical representation of duration, derived from space.
Duration thus assumes the illusory form of a homogeneous medium, and
the connecting link between these two terms, space and duration, is
simultaneity, which might be defined as the intersection of time and
space.
[Sidenote: Two elements in motion: (1) the space traversed, which is
homogeneous and divisible; (2) the act of traversing, indivisible and
real only for consciousness.]
If we analyse in the same way the concept of motion, the living symbol
of this seemingly homogeneous duration, we shall be led to make a
distinction of the same kind. We generally say that a movement takes
place _in_ space, and when we assert that motion is homogeneous and
divisible, it is of the space traversed that we are thinking, as if
it were interchangeable with the motion itself. Now, if we reflect
further, we shall see that the successive positions of the moving
body really do occupy space, but that the process by which it passes
from one position to the other, a process which occupies duration and
which has no reality except for a conscious spectator, eludes space.
We have to do here not with an _object_ but with a _progress_: motion,
in so far as it is a passage from one point to another, is a mental
synthesis, a psychic and therefore unextended process. Space contains
only parts of space, and at whatever point of space we consider the
moving body, we shall get only a position. If consciousness is aware
of anything more than positions, the reason is that it keeps the
successive positions in mind and synthesizes them. But how does it
carry out a synthesis of this kind? It cannot be by a fresh setting out
of these same positions in a homogeneous medium, for a fresh synthesis
would be necessary to connect the positions with one another, and so
on indefinitely. We are thus compelled to admit that we have here to
do with a synthesis which is, so to speak, qualitative, a gradual
organization of our successive sensations, a unity resembling that
of a phrase in a melody. This is just the idea of motion which we
form when we think of it by itself, when, so to speak, from motion we
extract mobility. Think of what you experience on suddenly perceiving
a shooting star: in this extremely rapid motion there is a natural and
instinctive separation between the space traversed, which appears to
you under the form of a line of fire, and the absolutely indivisible
sensation of motion or mobility. A rapid gesture, made with one's eyes
shut, will assume for consciousness the form of a purely qualitative
sensation as long as there is no thought of the space traversed. In
a word, there are two elements to be distinguished in motion, the
space traversed and the act by which we traverse it, the successive
positions and the synthesis of these positions. The first of these
elements is a homogeneous quantity: the second has no reality except in
a consciousness: it is a quality or an intensity, whichever you prefer.
But here again we meet with a case of endosmosis, an intermingling
of the purely intensive sensation of mobility with the extensive
representation of the space traversed. On the one hand we attribute to
the motion the divisibility of the space which it traverses, forgetting
that it is quite possible to divide an _object,_ but not an _act_: and
on the other hand we accustom ourselves to projecting this act itself
into space, to applying it to the whole of the line which the moving
body traverses, in a word, to solidifying it: as if this localizing of
a _progress_ in space did not amount to asserting that, even outside
consciousness, the past co-exists along with the present!
[Sidenote: The common confusion between motion and the space traversed
gives rise to the paradoxes of the Eleatics.]
It is to this confusion between motion and the space traversed that the
paradoxes of the Eleatics are due; for the interval which separates two
points is infinitely divisible, and if motion consisted of parts like
those of the interval itself, the interval would never be crossed.
But the truth is that each of Achilles' steps is a simple indivisible
act, and that, after a given number of these acts, Achilles will have
passed the tortoise. The mistake of the Eleatics arises from their
identification of this series of acts, each of which is _of a definite
kind_ and _indivisible,_ with the homogeneous space which underlies
them. As this space can be divided and put together again according
to any law whatever, they think they are justified in reconstructing
Achilles' whole movement, not with Achilles' kind of step, but with
the tortoise's kind: in place of Achilles pursuing the tortoise they
really put two tortoises, regulated by each other, two tortoises which
agree to make the same kind of steps or simultaneous acts, so as
never to catch one another. Why does Achilles outstrip the tortoise?
Because each of Achilles' steps and each of the tortoise's steps are
indivisible acts in so far as they are movements, and are different
magnitudes in so far as they are space: so that addition will soon give
a greater length for the space traversed by Achilles than is obtained
by adding together the space traversed by the tortoise and the handicap
with which it started. This is what Zeno leaves out of account when he
reconstructs the movement of Achilles according to the same law as the
movement of the tortoise, forgetting that space alone can be divided
and put together again in any way we like, and thus confusing space
with motion. Hence we do not think it necessary to admit, even after
the acute and profound analysis of a contemporary thinker,[2] that
the meeting of the two moving bodies implies a discrepancy between
real and imaginary motion, between _space in itself_ and indefinitely
divisible space, between concrete time and abstract time. Why resort
to a metaphysical hypothesis, however ingenious, about the nature of
space, time, and motion, when immediate intuition shows us motion
within duration, and duration outside space? There is no need to assume
a limit to the divisibility of concrete space; we can admit that it
is infinitely divisible, provided that we make a distinction between
the simultaneous positions of the two moving bodies, which are in
fact in space, and their movements, which cannot occupy space, being
duration rather than extent, quality and not quantity. To measure the
velocity of a movement, as we shall see, is simply to ascertain a
simultaneity; to introduce this velocity into calculations is simply to
use a convenient means of anticipating a simultaneity. Thus mathematics
confines itself to its own province as long as it is occupied with
determining the simultaneous positions of Achilles and the tortoise
at a given moment, or when it admits _à priori_ that the two moving
bodies meet at a point _X_--a meeting which is itself a simultaneity.
But it goes beyond its province when it claims to reconstruct what
takes place in the interval between two simultaneities; or rather it
is inevitably led, even then, to consider simultaneities once more,
fresh simultaneities, the indefinitely increasing number of which ought
to be a warning that we cannot make movement out of immobilities, nor
time out of space. In short, just as nothing will be found homogeneous
in duration except a symbolical medium with no duration at all, namely
space, in which simultaneities are set out in line, in the same way no
homogeneous element will be found in motion except that which least
belongs to it, the traversed space, which is motionless.
[Sidenote: Science has to eliminate duration from time and mobility
from motion before it can deal with them.]
Now, just for this reason, science cannot deal with time and motion
except on condition of first eliminating the essential and qualitative
element--of time, duration, and of motion, mobility. We may easily
convince ourselves of this by examining the part played in astronomy
and mechanics by considerations of time, motion, and velocity.
Treatises on mechanics are careful to announce that they do not intend
to define duration itself but only the equality of two durations. "Two
intervals of time are equal when two identical bodies, in identical
conditions at the beginning of each of these intervals and subject to
the same actions and influences of every kind, have traversed the same
space at the end of these intervals." In other words, we are to note
the exact moment at which the motion begins, i.e. the coincidence of
an external change with one of our psychic states; we are to note the
moment at which the motion ends, that is to say, another simultaneity;
finally we are to measure the space traversed, the only thing, in
fact, which is really measurable. Hence there is no question here
of duration, but only of space and simultaneities. To announce that
something will take place at the end of a time _t_ is to declare
that consciousness will note between now and then a number _t_ of
simultaneities of a certain kind. And we must not be led astray by the
words "between now and then," for the interval of duration exists only
for us and on account of the interpenetration of our conscious states.
Outside ourselves we should find only space, and consequently nothing
but simultaneities, of which we could not even say that they are
objectively successive, since succession can only be thought through
_comparing_ the present with the past.--That the interval of duration
itself cannot be taken into account by science is proved by the fact
that, if all the motions of the universe took place twice or thrice as
quickly, there would be nothing to alter either in our formulae or in
the figures which are to be found in them. Consciousness would have
an indefinable and as it were qualitative impression of the change,
but the change would not make itself felt outside consciousness, since
the same number of simultaneities would go on taking place in space.
We shall see, later on, that when the astronomer predicts, e.g., an
eclipse, he does something of this kind: he shortens infinitely the
intervals of duration, as these do not count for science, and thus
perceives in a very short time--a few seconds at the most--a succession
of simultaneities which may take up several centuries for the concrete
consciousness, compelled to live through the intervals instead of
merely counting their extremities.
[Sidenote: This is seen in the definition of _velocity._]
A direct analysis of the notion of velocity will bring us to the same
conclusion. Mechanics gets this notion through a series of ideas, the
connexion of which it is easy enough to trace. It first builds up the
idea of uniform motion by picturing, on the one hand, the path AB of a
certain moving body, and, on the other, a physical phenomenon which is
repeated indefinitely under the same conditions, e.g., a stone always
falling from the same height on to the same spot. If we mark on the
path AB the points M, Ν, P ... reached by the moving body at each of
the moments when the stone touches the ground, and if the intervals
AM, MN and NP are found to be equal to one another, the motion will
be said to be uniform: and any one of these intervals will be called
the velocity of the moving body, provided that it is agreed to adopt
as unit of duration the physical phenomenon which has been chosen as
the term of comparison. Thus, the velocity of a uniform motion is
defined by mechanics without appealing to any other notions than those
of space and simultaneity. Now let us turn to the case of a variable
motion, that is, to the case when the elements AM, MN, NP ... are found
to be unequal. In order to define the velocity of the moving body A
at the point M, we shall only have to imagine an unlimited number of
moving bodies A*1, A*2, A*3 ... all moving uniformly with velocities
_v_*1, _v_*2, _v_*3 ... which are arranged, e.g., in an ascending scale
and which correspond to all possible magnitudes. Let us then consider
on the path of the moving body _A_ two points M' and M", situated on
either side of the point M but very near it. At the same time as this
moving body reaches the points M', M, M", the other moving bodies
reach points M'*1 M*1 M"*1, M'*2 M*2 M"*2 ... on their respective
paths; and there must be two moving bodies Ah and Ap such that we
have on the one hand M' M= M'*h M*h and on the other hand M M"= M*p
M"*p. We shall then agree to say that the velocity of the moving body
A at the point M lies between _v_*h and _v_*p. But nothing prevents
our assuming that the points M' and M" are still nearer the point M,
and it will then be necessary to replace _v_*h and _v_*p by two fresh
velocities _v_*i and _v_*n, the one greater than _v_*h and the other
less than _v_*p. And in proportion as we reduce the two intervals M'M
and MM", we shall lessen the difference between the velocities of the
uniform corresponding movements. Now, the two intervals being capable
of decreasing right down to zero, there evidently exists between _v_*i
and _v_*n a certain velocity _v_*m, such that the difference between
this velocity and _v_*h, _v_*i ... on the one hand, and _v_*p, _v_*n ...
on the other, can become smaller than any given quantity. It is this
common limit _v_*m which we shall call the velocity of the moving body
A at the point M.--Now, in this analysis of variable motion, as in
that of uniform motion, it is a question only of spaces once traversed
and of simultaneous positions once reached. We were thus justified in
saying that, while all that mechanics retains of time is simultaneity,
all that it retains of motion itself--restricted, as it is, to a
_measurement_ of motion--is immobility.
[Characters preceded by '*' are in "subscript" in original.]
[Sidenote: Mechanics deals with equations, which express something
finished, and not processes, such as duration and motion.]
This result might have been foreseen by noticing that mechanics
necessarily deals with equations, and that an algebraic equation always
expresses something already done. Now, it is of the very essence
of duration and motion, as they appear to our consciousness, to be
something that is unceasingly being done; thus algebra can represent
the results gained at a certain moment of duration and the positions
occupied by a certain moving body in space, but not duration and
motion themselves. Mathematics may, indeed, increase the number of
simultaneities and positions which it takes into consideration by
making the intervals very small: it may even, by using the differential
instead of the difference, show that it is possible to increase without
limit the number of these intervals of duration. Nevertheless, however
small the interval is supposed to be, it is the extremity of the
interval at which mathematics always places itself. As for the interval
itself, as for the duration and the motion, they are necessarily left
out of the equation. The reason is that duration and motion are mental
syntheses, and not objects; that, although the moving body occupies,
one after the other, points on a line, motion itself has nothing to
do with a line; and finally that, although the positions occupied by
the moving body vary with the different moments of duration, though it
even creates distinct moments by the mere fact of occupying different
positions, duration properly so called has no moments which are
identical or external to one another, being essentially heterogeneous,
continuous, and with no analogy to number.
[Sidenote: Conclusion: space alone is homogeneous: duration and
succession belong not to the external world, but to the conscious mind.]
It follows from this analysis that space alone is homogeneous, that
objects in space form a discrete multiplicity, and that every discrete
multiplicity is got by a process of unfolding in space. It also follows
that there is neither duration nor even succession in space, if we
give to these words the meaning in which consciousness takes them:
each of the so-called successive states of the external world exists
alone; their multiplicity is real only for a consciousness that can
first retain them and then set them side by side by externalizing
them in relation to one another. If it retains them, it is because
these distinct states of the external world give rise to states of
consciousness which permeate one another, imperceptibly organize
themselves into a whole, and bind the past to the present by this
very process of connexion. If it externalizes them in relation to one
another, the reason is that, thinking of their radical distinctness
(the one having ceased to be when the other appears on the scene), it
perceives them under the form of a discrete multiplicity, which amounts
to setting them out in line, in the space in which each of them existed
separately. The space employed for this purpose is just that which is
called homogeneous time.
[Sidenote: Two kinds of multiplicity: two senses of the word
"distinguish," the one qualitative and the other quantitative.]
But another conclusion results from this analysis, namely, that
the multiplicity of conscious states, regarded in its original
purity, is not at all like the discrete multiplicity which goes to
form a number. In such a case there is, as we said, a qualitative
multiplicity. In short, we must admit two kinds of multiplicity, two
possible senses of the word "distinguish," two conceptions, the one
qualitative and the other quantitative, of the difference between
_same_ and _other._ Sometimes this multiplicity, this distinctness,
this heterogeneity contains number only potentially, as Aristotle would
have said. Consciousness, then, makes a qualitative discrimination
without any further thought of counting the qualities or even of
distinguishing them as _several._ In such a case we have multiplicity
without quantity. Sometimes, on the other hand, it is a question of
a multiplicity of terms which are counted or which are conceived as
capable of being counted; but we think then of the possibility of
externalizing them in relation to one another, we set them out in
space. Unfortunately, we are so accustomed to illustrate one of these
two meanings of the same word by the other, and even to perceive
the one in the other, that we find it extraordinarily difficult to
distinguish between them or at least to express this distinction in
words. Thus I said that several conscious states are organized into a
whole, permeate one another, gradually gain a richer content, and might
thus give any one ignorant of space the feeling of pure duration; but
the very use of the word "several" shows that I had already isolated
these states, externalized them in relation to one another, and, in a
word, set them side by side; thus, by the very language which I was
compelled to use, I betrayed the deeply ingrained habit of setting out
time in space. From this spatial setting out, already accomplished, we
are compelled to borrow the terms which we use to describe the state
of a mind which has not yet accomplished it: these terms are thus
misleading from the very beginning, and the idea of a multiplicity
without relation to number or space, although clear for pure reflective
thought, cannot be translated into the language of common sense. And
yet we cannot even form the idea of discrete multiplicity without
considering at the same time a qualitative multiplicity. When we
explicitly count units by stringing them along a spatial line, is it
not the case that, alongside this addition of identical terms standing
out from a homogeneous background, an organization of these units is
going on in the depths of the soul, a wholly dynamic process, not
unlike the purely qualitative way in which an anvil, if it could feel,
would realize a series of blows from a hammer? In this sense we might
almost say that the numbers in daily use have each their emotional
equivalent. Tradesmen are well aware of it, and instead of indicating
the price of an object by a round number of shillings, they will mark
the next smaller number, leaving themselves to insert afterwards a
sufficient number of pence and farthings. In a word, the process by
which we count units and make them into a discrete multiplicity has
two sides; on the one hand we assume that they are identical, which is
conceivable only on condition that these units are ranged alongside
each other in a homogeneous medium; but on the other hand the third
unit, for example, when added to the other two, alters the nature,
the appearance and, as it were, the rhythm of the whole; without this
interpenetration and this, so to speak, qualitative progress, no
addition would be possible. Hence it is through the quality of quantity
that we form the idea of quantity without quality.
[Sidenote: Our successive sensations are regarded as mutually external,
like their objective causes, and this reacts on our deeper psychic
life.]
It is therefore obvious that, if it did not betake itself to a
symbolical substitute, our consciousness our successive would never
regard time as a homogeneous medium, in which the terms of a succession
remain outside one another. But we naturally reach this symbolical
representation by the mere fact that, in a series of identical terms,
each term assumes a double aspect for our consciousness: one aspect
which is the same for all of them, since we are thinking then of
the sameness of the external object, and another aspect which is
characteristic of each of them, because the supervening of each term
brings about a new organization of the whole. Hence the possibility of
setting out in space, under the form of numerical multiplicity, what
we have called a qualitative multiplicity, and of regarding the one
as the equivalent of the other. Now, this twofold process is nowhere
accomplished so easily as in the perception of the external phenomenon
which takes for us the form of motion. Here we certainly have a series
of identical terms, since it is always the same moving body; but, on
the other hand, the synthesis carried out by our consciousness between
the actual position and what our memory calls the former positions,
causes these images to permeate, complete, and, so to speak, continue
one another. Hence, it is principally by the help of motion that
duration assumes the form of a homogeneous medium, and that time is
projected into space. But, even if we leave out motion, any repetition
of a well-marked external phenomenon would suggest to consciousness
the same mode of representation. Thus, when we hear a series of
blows of a hammer, the sounds form an indivisible melody in so far
as they are pure sensations, and, here again, give rise to a dynamic
progress; but, knowing that the same objective cause is at work, we
cut up this progress into phases which we then regard as identical;
and this multiplicity of elements no longer being conceivable except
by being set out in space, since they have now become identical, we
are necessarily led to the idea of a homogeneous time, the symbolical
image of real duration. In a word, our ego comes in contact with the
external world at its surface; our successive sensations, although
dissolving into one another, retain something of the mutual externality
which belongs to their objective causes; and thus our superficial
psychic life comes to be pictured without any great effort as set
out in a homogeneous medium. But the symbolical character of such a
picture becomes more striking as we advance further into the depths of
consciousness: the deep-seated self which ponders and decides, which
heats and blazes up, is a self whose states and changes permeate one
another and undergo a deep alteration as soon as we separate them from
one another in order to set them out in space. But as this deeper
self forms one and the same person with the superficial ego, the two
seem to _endure_ in the same way. And as the repeated picture of one
identical objective phenomenon, ever recurring, cuts up our superficial
psychic life into parts external to one another, the moments which
are thus determined determine in their turn distinct segments in
the dynamic and undivided progress of our more personal conscious
states. Thus the mutual externality which material objects gain from
their juxtaposition in homogeneous space reverberates and spreads
into the depths of consciousness: little by little our sensations are
distinguished from one another like the external causes which gave
rise to them, and our feelings or ideas come to be separated like the
sensations with which they are contemporaneous.
[Sidenote: Eliminate the superficial psychic states, and we no longer
perceive a homogeneous time or measure duration, but feel it as a
quality.]
That our ordinary conception of duration depends on a gradual incursion
of space into the domain of pure consciousness is proved by the fact
that, in order to deprive the ego of the faculty of perceiving a
homogeneous time, it is enough to take away from it this outer circle
of psychic states which it uses as a balance-wheel. These conditions
are realized when we dream; for sleep, by relaxing the play of the
organic functions, alters the communicating surface between the ego
and external objects. Here we no longer measure duration, but we
feel it; from quantity it returns to the state of quality; we no
longer estimate past time mathematically: the mathematical estimate
gives place to a confused instinct, capable, like all instincts, of
committing gross errors, but also of acting at times with extraordinary
skill. Even in the waking state, daily experience ought to teach us
to distinguish between duration as quality, that which consciousness
reaches immediately and which is probably what animals perceive, and
time so to speak materialized, time that has become quantity by being
set out in space. Whilst I am writing these lines, the hour strikes
on a neighbouring clock, but my inattentive ear does not perceive it
until several strokes have made themselves heard. Hence I have not
counted them; and yet I only have to turn my attention backwards to
count up the four strokes which have already sounded and add them to
those which I hear. If, then, I question myself carefully on what has
just taken place, I perceive that the first four sounds had struck
my ear and even affected my consciousness, but that the sensations
produced by each one of them, instead of being set side by side, had
melted into one another in such a way as to give the whole a peculiar
quality, to make a kind of musical phrase out of it. In order, then,
to estimate retrospectively the number of strokes sounded, I tried to
reconstruct this phrase in thought: my imagination made one stroke,
then two, then three, and as long as it did not reach the exact number
four, my feeling, when consulted, answered that the total effect was
qualitatively different. It had thus ascertained in its own way the
succession of four strokes, but quite otherwise than by a process
of addition, and without bringing in the image of a juxtaposition of
distinct terms. In a word, the number of strokes was perceived as a
quality and not as a quantity: it is thus that duration is presented to
immediate consciousness, and it retains this form so long as it does
not give place to a symbolical representation derived from extensity.
[Sidenote: There are therefore two forms of multiplicity, of duration
and conscious life.]
We should therefore distinguish two forms of multiplicity, two very
different ways of regarding duration, two aspects of conscious life.
Below homogeneous duration, which is the extensive symbol of true
duration, a close psychological analysis distinguishes a duration
whose heterogeneous moments permeate one another; below the numerical
multiplicity of conscious states, a qualitative multiplicity; below
the self with well-defined states, a self in which _succeeding each
other_ means _melting into one another_ and forming an organic whole.
But we are generally content with the first, i.e. with the shadow of
the self projected into homogeneous space. Consciousness, goaded by an
insatiable desire to separate, substitutes the symbol for the reality,
or perceives the reality only through the symbol. As the self thus
refracted, and thereby broken to pieces, is much better adapted to the
requirements of social life in general and language in particular,
consciousness prefers it, and gradually loses sight of the fundamental
self.
[Sidenote: The two aspects of our conscious states.]
In order to recover this fundamental self, as the unsophisticated
consciousness would perceive it, a vigorous effort of analysis is
necessary, which will isolate the fluid inner states from their image,
first refracted, then solidified in homogeneous space. In other words,
our perceptions, sensations, emotions and ideas occur under two
aspects: the one clear and precise, but impersonal; the other confused,
ever changing, and inexpressible, because language cannot get hold
of it without arresting its mobility or fit it into its common-place
forms without making it into public property. If we have been led to
distinguish two forms of multiplicity, two forms of duration, we must
expect each conscious state, taken by itself, to assume a different
aspect according as we consider it within a discrete multiplicity or a
confused multiplicity, in the time as quality, in which it is produced,
or in the time as quantity, into which it is projected.
[Sidenote: One of which is due to the solidifying influence of external
objects and language on our constantly changing feelings.]
When e.g. I take my first walk in a town in which I am going to live,
my environment produces on me two impressions at the same time, one
of which is destined to last while the other will constantly change.
Every day I perceive the same houses, and as I know that they are the
same objects, I always call them by the same name and I also fancy
that they always look the same to me. But if I recur, at the end of a
sufficiently long period, to the impression which I experienced during
the first few years, I am surprised at the remarkable, inexplicable,
and indeed inexpressible change which has taken place. It seems that
these objects, continually perceived by me and constantly impressing
themselves on my mind, have ended by borrowing from me something of my
own conscious existence; like myself they have lived, and like myself
they have grown old. This is not a mere illusion; for if to-day's
impression were absolutely identical with that of yesterday, what
difference would there be between perceiving and recognizing, between
learning and remembering? Yet this difference escapes the attention of
most of us; we shall hardly perceive it, unless we are warned of it and
then carefully look into ourselves. The reason is that our outer and,
so to speak, social life is more practically important to us than our
inner and individual existence. We instinctively tend to solidify our
impressions in order to express them in language. Hence we confuse the
feeling itself, which is in a perpetual state of becoming, with its
permanent external object, and especially with the word which expresses
this object. In the same way as the fleeting duration of our ego is
fixed by its projection in homogeneous space, our constantly changing
impressions, wrapping themselves round the external object which is
their cause, take on its definite outlines and its immobility.
[Sidenote: How language gives a fixed form to fleeting sensations.]
Our simple sensations, taken in their natural state, are still more
fleeting. Such and such a flavour, such and such a scent, pleased me
when I was a child though I dislike them to-day. Yet I still give the
same name to the sensation experienced, and I speak as if only my
taste had changed, whilst the scent and the flavour have remained the
same. Thus I again solidify the sensation; and when its changeableness
becomes so obvious that I cannot help recognizing it, I abstract
this changeableness to give it a name of its own and solidify it in
the shape of a _taste._ But in reality there are neither identical
sensations nor multiple tastes: for sensations and tastes seem to me
to be _objects_ as soon as I isolate and name them, and in the human
soul there are only _processes._ What I ought to say is that every
sensation is altered by repetition, and that if it does not seem to
me to change from day to day, it is because I perceive it through the
object which is its cause, through the word which translates it. This
influence of language on sensation is deeper than is usually thought.
Not only does language make us believe in the unchangeableness of our
sensations, but it will sometimes deceive us as to the nature of the
sensation felt. Thus, when I partake of a dish that is supposed to be
exquisite, the name which it bears, suggestive of the approval given to
it, comes between my sensation and my consciousness; I may believe that
the flavour pleases me when a slight effort of attention would prove
the contrary, In short, the word with well-defined outlines, the rough
and ready word, which stores up the stable, common, and consequently
impersonal element in the impressions of mankind, overwhelms or
at least covers over the delicate and fugitive impressions of our
individual consciousness. To maintain the struggle on equal terms,
the latter ought to express themselves in precise words; but these
words, as soon as they were formed, would turn against the sensation
which gave birth to them, and, invented to show that the sensation is
unstable, they would impose on it their own stability.
[Sidenote: How analysis and description distort the feelings.]
This overwhelming of the immediate consciousness is nowhere so striking
as in the case of our feelings. A violent love or a deep melancholy
takes possession of our SOUL: here we feel a thousand different
elements which dissolve into and permeate one another without any
precise outlines, without the least tendency to externalize themselves
in relation to one another; hence their originality. We distort them
as soon as we distinguish a numerical multiplicity in their confused
mass: what will it be, then, when we set them out, isolated from one
another, in this homogeneous medium which may be called either time or
space, whichever you prefer? A moment ago each of them was borrowing an
indefinable colour from its surroundings: now we have it colourless,
and ready to accept a name. The feeling itself is a being which
lives and develops and is therefore constantly changing; otherwise
how could it gradually lead us to form a resolution? Our resolution
would be immediately taken. But it lives because the duration in
which it develops is a duration whose moments permeate one another.
By separating these moments from each other, by spreading out time in
space, we have caused this feeling to lose its life and its colour.
Hence, we are now standing before our own shadow: we believe that
we have analysed our feeling, while we have really replaced it by a
juxtaposition of lifeless states which can be translated into words,
and each of which constitutes the common element, the impersonal
residue, of the impressions felt in a given case by the whole of
society. And this is why we reason about these states and apply our
simple logic to them: having set them up as genera by the mere fact
of having isolated them from one another, we have prepared them for
use in some future deduction. Now, if some bold novelist, tearing
aside the cleverly woven curtain of our conventional ego, shows us
under this appearance of logic a fundamental absurdity, under this
juxtaposition of simple states an infinite permeation of a thousand
different impressions which have already ceased to exist the instant
they are named, we commend him for having known us better than we
knew ourselves. This is not the case, however, and the very fact that
he spreads out our feeling in a homogeneous time, and expresses its
elements by words, shows that he in his turn is only offering us its
shadow: but he has arranged this shadow in such a way as to make us
suspect the extraordinary and illogical nature of the object which
projects it; he has made us reflect by giving outward expression to
something of that contradiction, that interpenetration, which is the
very essence of the elements expressed. Encouraged by him, we have
put aside for an instant the veil which we interposed between our
consciousness and ourselves. He has brought us back into our own
presence.
[Sidenote: On the surface our conscious states obey the laws of
association. Deeper down they interpenetrate and form a part of
ourselves.]
We should experience the same sort of surprise if we strove to seize
our ideas themselves in their natural state, as our consciousness would
perceive them if it were no longer beset by space. This breaking up
of the constituent elements of an idea, which issues in abstraction,
is too convenient for us to do without it in ordinary life and even
in philosophical discussion. But when we fancy that the parts thus
artificially separated are the genuine threads with which the concrete
idea was woven, when, substituting for the interpenetration of the real
terms the juxtaposition of their symbols, we claim to make duration
out of space, we unavoidably fall into the mistakes of associationism.
We shall not insist on the latter point, which will be the subject of
a thorough examination in the next chapter. Let it be enough to say
that the impulsive zeal with which we take sides on certain questions
shows how our intellect has its instincts--and what can an instinct
of this kind be if not an impetus common to all our ideas, i.e. their
very interpenetration? The beliefs to which we most strongly adhere are
those of which we should find it most difficult to give an account, and
the reasons by which we justify them are seldom those which have led
us to adopt them. In a certain sense we have adopted them without any
reason, for what makes them valuable in our eyes is that they match the
colour of all our other ideas, and that from the very first we have
seen in them something of ourselves. Hence they do not take in our
minds that common looking form which they will assume as soon as we try
to give expression to them in words; and, although they bear the same
name in other minds, they are by no means the same thing. The fact is
that each of them has the same kind of life as a cell in an organism:
everything which affects the general state of the self affects it also.
But while the cell occupies a definite point in the organism, an idea
which is truly ours fills the whole of our self. Not all our ideas,
however, are thus incorporated in the fluid mass of our conscious
states. Many float on the surface, like dead leaves on the water of a
pond: the mind, when it thinks them over and over again, finds them
ever the same, as if they were external to it. Among these are the
ideas which we receive ready made, and which remain in us without ever
being properly assimilated, or again the ideas which we have omitted
to cherish and which have withered in neglect. If, in proportion as we
get away from the deeper strata of the self, our conscious states tend
more and more to assume the form of a numerical multiplicity, and to
spread out in a homogeneous space, it is just because these conscious
states tend to become more and more lifeless, more and more impersonal.
Hence we need not be surprised if only those ideas which least belong
to us can be adequately expressed in words: only to these, as we shall
see, does the associationist theory apply. External to one another,
they keep up relations among themselves in which the inmost nature
of each of them counts for nothing, relations which can therefore be
classified. It may thus be said that they are associated by contiguity
or for some logical reason. But if, digging below the surface of
contact between the self and external objects, we penetrate into the
depths of the organized and living intelligence, we shall witness the
joining together or rather the blending of many ideas which, when once
dissociated, seem to exclude one another as logically contradictory
terms. The strangest dreams, in which two images overlie one another
and show us at the same time two different persons, who yet make only
one, will hardly give us an idea of the interweaving of concepts which
goes on when we are awake. The imagination of the dreamer, cut off from
the external world, imitates with mere images, and parodies in its own
way, the process which constantly goes on with regard to ideas in the
deeper regions of the intellectual life.
[Sidenote: By separating our conscious states we promote social life,
but raise problems soluble only by recourse to the concrete and living
self.]
Thus may be verified, thus, too, will be illustrated by a further
study of deep-seated psychic phenomena the principle from which we
started: conscious life displays two aspects according as we perceive
it directly or by refraction through space. Considered in themselves,
the deep-seated conscious states have no relation to quantity, they
are pure quality; they intermingle in such a way that we cannot tell
whether they are one or several, nor even examine them from this
point of view without at once altering their nature. The duration
which they thus create is a duration whose moments do not constitute
a numerical multiplicity: to characterize these moments by saying
that they encroach on one another would still be to distinguish them.
If each of us lived a purely individual life, if there were neither
society nor language, would our consciousness grasp the series of inner
states in this unbroken form? Undoubtedly it would not quite succeed,
because we should still retain the idea of a homogeneous space in
which objects are sharply distinguished from one another, and because
it is too convenient to set out in such a medium the somewhat cloudy
states which first attract the attention of consciousness, in order
to resolve them into simpler terms. But mark that the intuition of
a homogeneous space is already a step towards social life. Probably
animals do not picture to themselves, beside their sensations, as we
do, an external world quite distinct from themselves, which is the
common property of all conscious beings. Our tendency to form a clear
picture of this externality of things and the homogeneity of their
medium is the same as the impulse which leads us to live in common
and to speak. But, in proportion as the conditions of social life are
more completely realized, the current which carries our conscious
states from within outwards is strengthened; little by little these
states are made into objects or things; they break off not only from
one another, but from ourselves. Henceforth we no longer perceive them
except in the homogeneous medium in which we have set their image,
and through the word which lends them its common-place colour. Thus a
second self is formed which obscures the first, a self whose existence
is made up of distinct moments, whose states are separated from one
another and easily expressed in words. I do not mean, here, to split
up the personality, nor to bring back in another form the numerical
multiplicity which I shut out at the beginning. It is the same self
which perceives distinct states at first, and which, by afterwards
concentrating its attention, will see these states melt into one
another like the crystals of a snow-flake when touched for some time
with the finger. And, in truth, for the sake of language, the self has
everything to gain by not bringing back confusion where order reigns,
and in not upsetting this ingenious arrangement of almost impersonal
states by which it has ceased to form "a kingdom within a kingdom."
An inner life with well distinguished moments and with clearly
characterized states will answer better the requirements of social
life. Indeed, a superficial psychology may be content with describing
it without thereby falling into error, on condition, however, that
it restricts itself to the study of what has taken place and leaves
out what is going on. But if, passing from statics to dynamics, this
psychology claims to reason about things in the making as it reasoned
about things made, if it offers us the concrete and living self as an
association of terms which are distinct from one another and are set
side by side in a homogeneous medium, it will see difficulty after
difficulty rising in its path. And these difficulties will multiply
the greater the efforts it makes to overcome them, for all its efforts
will only bring into clearer light the absurdity of the fundamental
hypothesis by which it spreads out time in space and puts succession at
the very centre of simultaneity. We shall see that the contradictions
implied in the problems of causality, freedom, personality, spring from
no other source, and that, if we wish to get rid of them, we have only
to go back to the real and concrete self and give up its symbolical
substitute.
[1] I had already completed the present work when I read in the
_Critique philosophique_(for 1883 and 1884) F. Pillon's very remarkable
refutation of an interesting article by G. Noël on the interconnexion
of the notions of number and space. But I have not found it necessary
to make any alterations in the following pages, seeing that Pillon does
not distinguish between time as quality and time as quantity, between
the multiplicity of juxtaposition and that of interpenetration. Without
this vital distinction, which it is the chief aim of the present
chapter to establish, it would be possible to maintain, with Pillon,
that number may be built up from the relation of co-existence. But what
is here meant by co-existence? If the co-existing terms form an organic
whole, they will never lead us to the notion of number; if they remain
distinct, they are in juxtaposition and we are dealing with space. It
is no use to quote the example of simultaneous impressions received
by several senses. We either leave these sensations their specific
differences, which amounts to saying that we do not count them; or else
we eliminate their differences, and then how are we to distinguish
them if not by their position or that of their symbols? We shall see
that the verb "to distinguish" has two meanings, the one qualitative,
the other quantitative: these two meanings have been confused, in my
opinion, by the philosophers who have dealt with the relations between
number and space.
[2] Évellin, _Infini et quantité._ Paris, 1881.