CHAP, ii NUMERICAL MULTIPLICITY AND SPACE 87 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 between 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 sensa tions and feelings which analysis alone can dis tinguish. 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 num ber is immediately applicable; and the multiplicity of states of consciousness, which cannot be re garded as numerical without the help of some symbolical representation, in which a necessary element is space.
88 TIME AND FREE WILL CHAP, n As a matter of fact, each of us makes a distinc tion between these two kinds of multiplicity The impene- whenever he speaks of the impenetra- ratteHs not & bility °f matter. We sometimes set up iScialnbe«es- impenetrability as a fundamental pro perty of bodies, known in the same way and put on the same level as e.g. weight or resist ance. But a purely negative property of this kind cannot be revealed by our senses; indeed, cer tain 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 pene trate 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 con ceivable experience could succeed in dispelling.
CHAP, n NUMERICAL MULTIPLICITY AND SPACE 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 juxtaposi tion 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 inter-connexion 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 whichf occupy separate positions in space and conse^ quently no longer permeate one another. Im penetrability 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 TIME AND FREE WILL CHAP, n conception of number is immediately applicable, and states of consciousness, which have first of all to be represented symbolically in space.
It is advisable to dwell on the last point. If, in order to count states of consciousness, we have Homogeneous to represent them symbolically in space, in 9 is it not likely that this symbolical repre- states sentation will alter the normal con This ditions of inner perception? Let us recall what we said a short time ago pu£eiduration about the intensity of certain psychic is something T-.,...,, different, 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 at tribute to them. Now, let us notice that when we speak of time, we generally think of a homo geneous 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 I 91 / CHAP, n SPACE AND HOMOGENEITY shall then put this question to it: does the multi plicity 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, under stood 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.
We shall not lay too much stress on the question of the absolute reality of space: perhaps we might Does space as well ask whether space is or is not in exist inde- T, pendentiy oi space. In snort, our senses perceive its contents, as,...,,...Kant held p the qualities of bodies and space along 02 TIME AND FREE WILL CHAP, n 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 com mon 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 Transcen dental 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 be lief. Far from shaking our faith in the reality of space, Kant has shown what it actually means and has even justified it.
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 CHAP, n SPACE AND HOMOGENEITY 93 agree in assigning a Kantian origin to the na- The empiri- tivistic explanation of Johann Miiller; Lotze's hypothesis of local signs, Stensity°can- Bain's theory, and the more comprehen- fa°omes?j^the- siye explanation suggested by Wundt, traded wmsa- may seem a* nrs* sight quite independent tions without of ^ne Xranscen dental Aesthetic. The an act of 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 repre- 04 TIME AND FREE WILL CHAP, n sent 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 associ ating 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 conscious ness. 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.
If we now seek to characterize this act, we see that it consists essentially in the intuition, or CHAP, n SPACE AND HOMOGENEITY 95 rather the conception, of an empty homo- TWS act con- geneous medium. For it is scarcely oithe possible to give any other definition of space i space is what enables us to dis- a number of identical and not simultaneous sensations from one ananimais. other; it is thus a principle of differentia tion 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 after wards 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 repre- 96 TIME AND FREE WILL CHAP, n sentation 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 verte brates, 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 geome trical form. Each of these directions might appear to it with its own shade, its peculiar quality. We CHAP, ri SPACE AND HOMOGENEITY 97 shall understand how a perception of this kind is possible if we remember that we ourselves distin guish 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 homo geneous medium is something far more extraordi nary, being a kind of reaction against that hetero geneity 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 con ceiving 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 heterogene ous, that of sensible qualities, the other homo geneous, namely space. This latter, clearly con ceived by the human intellect, enables us to use clean-cut distinctions, to count, to abstract, and perhaps also to speak.
98 TIME AND FREE WILL CHAP, n Now, if space is to be defined as the homogene ous, it seems that inversely every homogeneous rime, in »o an(^ unbounded medium will be space. eneousa For> homogeneity here consisting in the absence of every quality, it is hard to reducible to See n°W ^WO ^orms °f the homOgenCOUS space. 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 homogene ous 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 them selves, we take it to be given all at once, which amounts to saying that we abstract it from dura tion. 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 ex terior 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 conscious ness. At any rate we cannot finally admit two CHAP, n HOMOGENEOUS TIME AND SPACE 99 iorms of the homogeneous, time and space, without first seeking whether one of them cannot be re duced to the other. Now, externality is the dis tinguishing 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 homogene ous 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 un bounded and homogeneous medium, is nothing but the ghost of space haunting the reflective conscious ness.
The English school tries, in fact, to reduce relations of extensity to more or less complex Mistake of relations of succession in time. When, deriJe^rTia-*0 with our eyes shut, we run our hands t«£2ty0from" al°ng a surface, the rubbing of our cess?on°!Ti£c~ fingers against the surface, and especially «0jSeti0dura! *ne variec^ P^aY °f our joints, provide tion-" 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 IOQ TIME AND FREE WILL CHAP, n 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 suc cession of our conscious states assumes when our ego lets itself live, when it refrains from separat ing 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 con trary, 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 along side 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