CHAPTER IV. Space and Time

SPACE AND TIME

§ 1. Are time and space ultimately real or only phenomenal? § 2. The space and time of perception are limited, sensibly continuous, and consist of a quantitative element together with a qualitative character dependent on relation to the here and now of immediate individual feeling. § 3. Conceptual space and time are created from the perceptual data by a combined process of synthesis, analysis, and abstraction. § 4. They are unlimited, infinitely divisible, and there is valid positive ground for regarding them as mathematically continuous. Thus they form infinite continuous series of positions. They involve abstraction from all reference to the here and now of immediate feeling, and are thus homogeneous, i.e. the positions in them are indistinguishable. They are also commonly taken to be unities. § 5. Perceptual space and time cannot be ultimately real, because they involve reference to the here and now of a finite experience; conceptual space and time cannot be ultimately real, because they contain no principle of internal distinction, and are thus not individual. § 6. The attempt to take space and time as real leads to the difficulty about qualities and relations, and so to the indefinite regress. § 7. Space and time contain no principle of unity; there may be many space and time orders in the Absolute which have no spatial or temporal connection with each other. § 8. The antinomies of the infinite divisibility and extent of space and time arise from the indefinite regress involved in the scheme of qualities and relations, and are insoluble so long as the space and time construction is taken for Reality. § 9. The space and time order is an imperfect phenomenal manifestation of the logical relation between the inner purposive lives of finite individuals. Time is an inevitable aspect of finite experience. How space and time are transcended in the Absolute experience we cannot say.

§ 1. The problems which arise for the metaphysician from the fact that the physical order, as it is presented to our senses, consists of elements having position in space and time, are among the oldest and most perplexing of all the riddles suggested by the course of our experience. Adequate discussion of them would demand not only far more space than we are at liberty to bestow on the topic, but such a familiarity with the mathematical theory of order and series as is scarcely possible to any one but an original mathematician. All that we can do in the present chapter is to deal very superficially with one or two of the leading problems, more with a view to indicating the nature of the questions which Metaphysics has to face, than of providing definite answers to them.

The fundamental problem for Metaphysics is, of course, whether space and time are ultimate Realities or only appearances; that is, would the whole system of Reality, as directly apprehended by an absolute all-containing experience, wear the forms of extension and succession in time, or is it merely a consequence of the limitations of our own finite experience that things come to us in this guise? It may indeed be urged that the contents of the universe must form an order of some sort for the absolute experience, in virtue of their systematic unity, but even so it is not clear that order as such is necessarily spatial or temporal. Indeed, most of the forms of order with which we are acquainted, both in everyday life and in our mathematical studies, appear to be, properly speaking, both non-spatial and non-temporal. Thus, e.g., it is seemingly by a mere metaphor that we speak of the “successive” integers of the natural number-series, the “successive” powers of an algebraical symbol, the “successive” approximations to the value of a continued fraction, in language borrowed from the temporal flow of events, the true relation involved being in the first two cases the non-temporal one of logical derivation, and in the third the equally non-temporal one of resemblance to an ideal standard. The full solution of the metaphysical problem of space and time would thus involve (1) the discrimination of spatial and temporal order from other allied forms of order, and (2) a decision as to the claim of this special form of order to be ultimately coherent and intelligible.

The problem thus presented for solution is often, and usually with special reference to the Kantian treatment of space and time in the Transcendental Æsthetic, put in the form of the question whether space and time are subjective or objective. This is, however, at best a misleading and unfortunate mode of expression which we shall do well to avoid. The whole distinction between a subjective and an objective factor in experience loses most of its significance with the abolition, now effected by Psychology, of the vicious Kantian distinction between the “given” in perception and the “work of the mind.” When once we have recognised that the “given” itself is constituted by the movement of selective attention, it becomes impossible any longer to distinguish it as an objective factor in knowledge from the subjective structure subsequently raised upon it. Kant’s adherence to this false psychological antithesis so completely distorts his whole treatment of the “forms of intuition,” that it will be absolutely necessary in a brief discussion like our own to deal with the subject in entire independence of the doctrines of the Æsthetic, which unfortunately continue to exercise a disproportionate influence on the current metaphysical presentment of the problem. It should scarcely be necessary to point out that the metaphysical questions have still less to do with the psychological problems, so prominent in recent science, of the precise way in which we come by our perception of extension and succession. For Metaphysics the sole question is one not of the origin but of the logical value of these ideas.

It is of fundamental importance for the whole metaphysical treatment of the subject, to begin by distinguishing clearly between space and time as forms of perception, and space and time as conceptual forms in which we construct our scientific notion of the physical order. One chief source of the confusions which beset the Kantian view is the neglect of Kant and most of his followers to make this distinction with sufficient clearness. We cannot insist too strongly upon the point that the space and the time of which we think in our science as containing the entire physical order, are not space and time as directly known to us in sense-perception, but are concepts elaborated out of the space and time of direct perception by a complicated process of synthesis and analysis, and involving abstraction from some of the most essential features of the space and time of actual experience. The following brief discussion may serve to illustrate the general nature of the relation between the two forms of space and time, and to exhibit the leading differences between them.

§ 2. Perceptual Space and Time. Both space and time, as we are aware of them in immediate perception, are (1) limited. The space we actually behold as we look out before us with a resting eye is always terminated by a horizon which has a more or less well-defined outline; the “specious present,” or portion of duration of which we can be at any time aware at once as an immediately presented content, has been shown by elaborate psychological experimentation to have a fairly well-defined span. Whatever lies outside this “span of attention” belongs either to the no longer presented past or to the not yet presented future, and stands to the sensible present much as the space behind my back to the actually beheld space before my eyes. Of course, in either case the limits of the actually presented space or time are not absolutely defined. To right and left of the line of vision the visible horizon gradually fades off into the indistinctly presented “margin of consciousness”; the “sensible present” shades away gradually at either end into the past and the future. Yet, though thus not absolutely defined, sensible space and time are never boundless.

(2) Perceptual space and time are both internally sensibly continuous or unbroken. Concentrate your attention on any lesser part of the actually seen expanse, and you at once find that it is itself an expanse with all the characteristics of the wider expanse in which it forms a part. Space as actually seen is not an aggregate of minima visibilia or perceptual points in which no lesser parts can be discriminated; so long as space is visually or tactually perceived at all, it is perceived as containing lesser parts which, on attending to them, are found to repeat the characteristics of the larger space. So any part of the “specious present” to which special attention can be directed, turns out itself to be a sensible duration. Perceived space is made of lesser spaces, perceived time of lesser times; the “parts” not being, of course, actually distinguished from each other in the original percept, but being capable of being so distinguished in consequence of varying movements of attention.

(3) On investigating the character of our actual perception of space and time, it appears to contain two aspects, which we may call the quantitative and the qualitative. On the one hand, whenever we perceive space we perceive a certain magnitude of extension, whenever we perceive time we perceive a longer or shorter lapse of duration. Different spaces and different times can be quantitatively compared in respect of the bigness of the extension or the duration comprised in them. On the other hand, the percept of space or time is not one of mere extension or duration. It has a very different qualitative aspect. We perceive along with the magnitude of the extension the form of its outline. This perception of spatial form depends in the last resort upon perception of the direction assumed by the bounding line or lines. Similarly, in dealing with only one dimension of perceived space, we never perceive length (a spatial magnitude) apart from the perception of direction (a spatial quality). The same is true of the perception of time. The lapses of duration we immediately perceive have all their special direction-quality; the “specious present” is essentially a simultaneously presented succession, i.e. a transition from before to after. It must be added that, in perceptual space and time, the directions thus perceived have a unique relation to the perceiving subject, and are thus all qualitatively distinct and irreversible. Direction in space is estimated as right, left, up, down, etc., by reference to axes through the centre of the percipient’s body at right angles to each other, and is thus for any given moment of experience uniquely and unambiguously determined. Direction in time is similarly estimated with reference to the actual content of the “focus of consciousness.” What is actually focal is “now,” what is ceasing to be focal is “past,” what is just coming to be focal is “future” in its direction.

This is perhaps the most fundamental and important peculiarity of the space and time of actual perception. All directions in them are unambiguously determined by reference to the here and now of the immediate experience of an individual subject. As a consequence, every individual subject has his own special perceptual space and time; Geometry and Mechanics depend, to be sure, on the possibility of the establishment of correspondences between these spatial and temporal systems, but it is essential to remember that, properly speaking, the space and time system of each individual’s perception is composed of directions radiating out from his unique here and now, and is therefore individual to himself.

§ 3. The Construction of the Conceptual Space and Time Order of Science. For the purposes of practical life, no less than for the subsequent object of scientific description of the physical order, it is indispensably necessary to establish equations or correspondences between the individual space and time systems of different percipients. Apart from such correspondences, it would be impossible for one subject to translate the spatial and temporal system of any other into terms of his own experience, and thus all practical intercourse for the purpose of communicating directions for action would come to an end. For the communication of such practical directions it is imperative that we should be able mentally to reconstruct the spatial and temporal aspects of our experience in a form independent of reference to the special here and now of this or that individual moment of experience. Thus, like the rest of our scientific constructions, the establishment of a single conceptual space and time system for the whole of the physical order is ultimately a postulate required by our practical needs, and we must therefore be prepared to face the possibility that, like other postulates of the same kind, it involves assumptions which are not logically defensible. The construction is valuable, so far as it does its work of rendering intercommunication between individuals possible; that it should correspond to the ultimate structure of Reality any further than the requirements of practical life demand is superfluous.

The main processes involved in the construction of the conceptual space and time of descriptive science are three,—synthesis, analysis, abstraction. (a) Synthesis. Psychologically speaking, it is ultimately by the active movements of individual percipients that the synthesis of the individual’s various perceptual spaces into one is effected. As attention is successively directed, even while the body as a whole remains stationary, to different parts of the whole expanse before the eye, the visual space which was originally “focal” in presentation becomes “marginal,” and the “marginal” focal by a sensibly gradual transition. When to the movements of head and eyes which accompany such changes in attention there are added movements of locomotion of the whole body, this process is carried further, and we have the gradual disappearance of originally presented spaces from presentation, accompanied by the gradual emergence of spaces previously not presented at all. This leads to the mental construction of a wider space containing all the individual’s different presentation-spaces, the order in which it contains them being determined by the felt direction of the movements required for the transition from one to another.

As we learn, through intercommunication with our fellows, of the existence for their perception of perceptual extension never directly presented to our own senses, the process of synthesis is extended further, so as to comprise in a single spatial system all the presentation-spaces of all the individual percipients in an order once again determined by the direction of the movements of transition from each to the others. Finally, as there is nothing in the principle of such a synthesis to impose limits upon its repetition, we think of the process as capable of indefinite continuance, and thus arrive at the concept of a space stretching out in all directions without definite bounds. This unending repetition of the synthesis of perceived spaces seems to be the foundation of what appears in theory as the Infinity of Space.

Precisely similar is the synthesis by which we mentally construct a single time system for the events of the physical order. Now means for me the content which occupies the centre of attentive interest. As attention is concentrated on the different stages in the realisation of an interest, this centre shifts; what was central becomes first marginal and then evanescent, what was marginal becomes central. Hence arises the conception of the events of my own inner life as forming a succession of moments, with a determinate order, each of which has been a now, or point of departure for directions in perceptual time, in its turn. As with space so with time, the intrasubjective intercourse of man with man makes it possible for me mentally to extend this conceptual synthesis of moments of time so as to include nows belonging to the experience of others which were already past before the first now of their experiences which I can synchronise with a now of my own, and again nows of their experiences relatively to which the last now which synchronises with one of my own is past. The indefinite repetition of such a synthesis leads, as before with space, to the thought of a duration reaching out endlessly into past and future, and thus gives us the familiar concept of the Infinity of Time.

(b) Analysis. Equally important is the part played by mental analysis in the formation of the conceptual space and time system. As we have already seen, successive attention to lesser parts of a presented extension, or a presented lapse, reveals within each lesser part the same structure which belongs to the whole, and thus establishes the sensible continuity of space and time. In actual fact, the process of attending successively to smaller and yet smaller portions of space and time cannot, of course, be carried on indefinitely, but we can conceptually frame to ourselves the thought of the indefinite repetition of the process beyond the limits arbitrarily imposed on it by the span of our own attention. Thus, by an act of mental analysis, we arrive at the concept of space and time as indefinitely divisible, or possessed of no ultimately unanalysable last parts, which is an indispensable pre-requisite of Geometry and Dynamics.

This indefinite divisibility of conceptual space and time is not of itself enough, as is often supposed, to establish their continuity in the strict mathematical sense of the word; their continuity depends upon the further assumption that whatever divides a series of positions in space or events in time unambiguously into two mutually exclusive classes, is itself a position in the space or event in the time series. This assumption does not seem to be absolutely requisite for all scientific treatment of the problems of space and time, but is demanded for the systematic establishment of the correspondence between the spatial and temporal series and the continuous series of the real numbers. Moreover, it seems impossible to assign any positive content to the notion of a something which should bisect the spatial or temporal order without occupying a position in that order. Hence we seem inevitably led by the same analytical process which conducts us to the conception of the spatial and temporal orders as infinite series to think of them also as continuous series in the strict sense of the term. The alternative conception of them as discontinuous, if not absolutely excluded, does not seem to be called for by any positive motive, and is incompatible with the complete execution of the purposes which demand application of the number-series to a spatial or temporal content.

(c) Abstraction. The part played by abstraction in the formation of the conceptual space and time order out of the data of perception is often overlooked by theorists, but is of fundamental importance, as we shall see immediately. We have already learned that the most significant fact about the time and space order of individual experience is that its directions are unique, because they radiate out from the unique here and now of immediate feeling. In the construction of the conceptual space and time order we make entire abstraction from this dependence on the immediate feeling of a subject. Conceptual space contains an infinity of positions, but none of them is a here; conceptual time an infinity of moments, but none of them is a now. As the time and space of the conceptual order are taken in abstraction from the differences between individual points of view, no one point in either can be regarded as having more claim than any other to be the natural “origin of co-ordinates” with reference to which directions are estimated. We shall have repeated opportunity in the remainder of this chapter to observe how important are the consequences of this abstraction.

Abstraction also enters in another way into the construction by which conceptual space and time are created. Actual perceived space and time are indeed never empty, but always filled with a content of “secondary” qualities. In other words, they are always one aspect of a larger whole of fact. Extension is never perceived apart from some further visual or tactual quality of the extended, temporal lapse never perceived without some change in presented content, however slight. But in constructing the conceptual space and time system, we abstract altogether from this qualitative aspect; we think solely of the variety of positions and directions in time and space without taking any account of the further qualitative differences with which they are accompanied in concrete experience. Thus we come by the notion of an empty space and an empty time as mere systems of positions into which various contents may subsequently be put.

Strictly speaking, the notion of an empty space or an empty time is unmeaning, as the simple experiment of thinking of their existence is sufficient to show. We cannot in thought successfully separate the spatial and temporal aspects of experience from the rest of the whole to which they belong and take them as subsisting by themselves, any more than we can take timbre as subsisting apart from musical pitch or colour-tone from saturation. We can, however, confine our attention to the spatial-temporal system of positions without taking into account the special secondary properties of the extended and successive. It is from this logical abstraction that the illusion arises when we imagine an empty set of spatial and temporal positions as having first to exist in order that they may be subsequently “filled” with a variety of contents.

§ 4. Characteristics of the Conceptual Time and Space Order. The following characteristics of the conceptual space and time created by the construction we have just examined, call for special notice. Conceptual space and time are necessarily taken, for reasons already explained, to be unlimited, and indefinitely divisible. Though it does not seem inevitable that they should be continuous, we appear to be unable to attach any positive meaning to the notion of their discontinuity, and, in the practical need for the application to them of the complete number-series, we have a valid positive ground for taking them as continuous. But space and time are thus resolved, in the process of their conceptual construction, into continuous infinite series of which the terms are spatial and temporal positions or points. Unlike the parts of perceptual space and time, these conceptual terms are not themselves spaces or times, as they contain no internal multiplicity of structure. Conceptual space and time are thus not wholes or aggregates of parts, but systems of relations between terms which possess no quantitative character.

Between any two terms of the spatial, or again of the temporal, series there is one unique relation, which is completely determined by the assignment of the terms, their distance. In the temporal series, which has only one dimension, you can only pass from any one given term to any other through a series of intermediate terms which is once and for all determined when the initial and final terms are given, hence nothing is required beyond the terms themselves to fix their distance. The spatial series is multi-dimensional, i.e. you can pass from any one term in it to any second by an indefinite variety of routes through intermediate terms, but it is still true that there is one and only one such route which is completely determined when the terms in question are known, namely, the straight line passing through both. This straight line constitutes the unique distance of the two points from each other. Thus the genuine concept of which those of space and time are species is not that of magnitude or quantity, but of serial order.

Further, and this is a point of fundamental difference between conceptual space and time, and the spaces and times of immediate perception, any one position in either order, taken by itself, is qualitatively indistinguishable from any other. All points of space, all moments of time, are alike, or, as it is also phrased, conceptual space and time are homogeneous throughout. It is not until you take at least two terms of the spatial or temporal series and consider the relation they determine, that distinction becomes possible. This homogeneity of conceptual space and time is an inevitable consequence of the abstraction from the immediate feelings of the individual subject of experience involved, as we saw, in the process of their construction. In our actual perception of spatial and temporal extension, that part of perceived space and time which stands in direct unity with immediate feeling is qualitatively distinguished as the here and now from all the rest, and thus does not depend upon the specification of a second spatial or temporal position for its recognisability. Here is where I am, now is this felt present. And similarly, every other part of the actually presented space and time gets a unique qualitative character from its special relation to this here and now; it is right or left, behind or in front, before or after. When we abstract altogether from the unique relation with individual experience which thus makes the here and now of perception, as we do in constructing our conceptual space and time order, every position alike becomes the mere possibility of a here or a now, and as such mere possibilities the various positions are indistinguishable. Practically, this homogeneity is important as the indispensable condition for the quantitative comparison of different portions of extension or duration.

An apparently inevitable consequence of the homogeneity of conceptual space and time is the relativity of spatial and temporal position. As we have seen, positions in conceptual space and time are not distinguishable until you take them in pairs. In other words, to fix one position in space or one date you have to give its relation to another position or date, and similarly to fix this you must specify a third, and so on indefinitely. To say where A is means to say how you get to it from B, and B again is only known by the way it is reached from C, and so on without end. Logically, this is a simple consequence of the nature of space and time as conceptually analysed into endless series. To specify any term in the series you must give the unique relation it bears to some other term, its logical distance. And, in a series which has neither first nor last term, this second term cannot be defined except by its logical distance from a third. In actual perception this difficulty is avoided, owing to the fact that immediate feeling gives us the here and now from which all our directions are measured. But in conceptual space or time there is nothing to distinguish any one here which we may take as our “origin of co-ordinates,” or any one now which we take as our present from any other, and hence the endless regress seems inevitable.

It follows, of course, that in conceptual space and time there is no principle by which to distinguish different directions. In perception they can be distinguished as right and left, up and down, and so forth. But since what is right to one percipient is left to another, in conceptual space, where complete abstraction is made from the presence of an individual percipient, there is neither right nor left, up nor down, nor any other qualitative difference between one direction and another, all such differences being relative to the individual percipient. When we wish to introduce into conceptual space distinctions between directions, we always have to begin by arbitrarily assigning some standard direction as our point of departure. Thus we take, e.g., an arbitrarily selected line A—————B as such a standard for a given plane, and proceed to distinguish all other directions by the angle they make with A B and the sense in which they are estimated (whether as from B to A or from A to B). But both the line A B and the difference of sense between A B and B A can only be defined by similar reference to some other standard direction, and so on through the endless regress.

Similarly with conceptual time. Here, as there is only one dimension, the difficulty is less obvious, but it is no less real. In conceptual time there is absolutely no means of distinguishing before from after, past from future. For the past means the direction of our memories, the direction qualified by the feeling of “no longer”; the future is the direction of anticipation and purposive adaptation, the direction of “not yet.” And, apart from the reference given by immediate feeling to the purposive life of an individual subject, these directions cannot be discriminated. In short, conceptual time and space are essentially relative, because they are systems of relations which have no meaning apart from qualitative differences in the terms which they relate; while yet again, for the purpose of the conceptual construction which yields them, the terms have to be taken as having no character but that which they possess in right of the relations.

One other feature of the space and time construction is sufficiently important to call for special mention. Space and time are commonly thought of as unities of some kind. All spatial positions, it is usually assumed, fall within one system of space-relations; all dates have their place in one all-inclusive time. This character of unity completes the current conception of the spatial and temporal order. Each of those orders is a unity, including all possible spatial or temporal positions; each is an endless, infinite, continuous series of positions, which all are purely relative. There are other peculiarities, especially of the current concepts of space, with which it is not necessary to deal here, as they are of an accidental kind, not arising out of the essential nature of the process by which the conception is constructed. Thus it is probably a current assumption that the number of dimensions in space is three and no more, and again that the Euclidean postulate about parallels is verified by its constitution. As far as perceptual space is concerned, those assumptions depend, I presume, upon empirical verification; there seems to be no reason why they should be made for the conceptual space-order, since it is quite certain that a coherent science of spatial relations can be constructed without recourse to them.

§ 5. The question now is, whether the whole of this spatial and temporal construction is more than imperfect, and therefore contradictory, appearance. I will first state in a general form the arguments for regarding it as appearance, and then proceed to reinforce this conclusion by dealing with some special difficulties. Finally, I propose to ask whether we can form some positive conception of the higher order of Reality of which the spatial and temporal series are phenomenal.

That the space and time order is phenomenal and not ultimate, can, I think, be conclusively shown by a general argument which I will first enunciate in principle and then develop somewhat more in detail. An all-comprehensive experience cannot apprehend the detail of existence under the forms of space and time for the following reason. Such an experience could be neither of space and time as we perceive them, nor of space and time as we conceptually reconstruct them. It would not be of perceptual space and time, because the whole character of our perceptual space and time depends upon the very imperfections and limitations which make our experience fragmentary and imperfect. Perceptual space and time are for me what they are, because I see them, so to say, in perspective from the special standpoint of my own particular here and now. If that standpoint were altered, so that what are actually for me there and then became my here and now, my whole outlook on the space and time order would suffer change. But the Absolute cannot look at the space and time order from the standpoint of my here and now. For it is the finitude of my interests and purposes which confine me in my outlook to this here and now. If my interests were not bound up in the special way in which they are with just this special part or aspect of the life of a wider whole, if they were co-extensive with the life of that whole, every place and every time would be my here and now. As it is, here is where my body is, now is this particular stage in the development of European social life, because these are the things in which I am primarily interested. And so with all the other finite experiences in which the detail of the absolute experience finds expression. Hence the absolute experience, being free from the limitations of interest which condition the finite experiences, cannot see the order of existence from the special standpoint of any of them, and therefore cannot apprehend it under the guise of the perceptual space and time system.

Again, it cannot apprehend existence under the forms of space and time as we conceptually reconstruct them. For Reality, for the absolute experience, must be a complete individual whole, with the ground of all its differentiations within itself. But conceptual space and time are constructed by deliberate abstraction from the relation to immediate experience implied in all individuality, and consequently, as we have just seen, they contain no real principle of internal distinction, their constituent terms being all exactly alike and indistinguishable. In short, if the perceptual time and space systems of our concrete experience represent individual but imperfect and finite points of view, the conceptual space and time of our scientific construction represents the mere abstract possibility of a finite point of view; neither gives a point of view both individual and infinite, and neither, therefore, can be the point of view of an absolute experience. An absolute experience must be out of time and out of space, in the sense that its contents are not apprehended in the form of the spatial and temporal series, but in some other way. Space and time, then, must be the phenomenal appearance of a higher reality which is spaceless and timeless.

§ 6. In principle, the foregoing argument appears to me to be complete, but, for the sake of readers who care to have its leading thought more fully developed, it may be re-stated thus. Perceptual space and time cannot be ultimately real as they stand. They are condemned already by the old difficulty which we found in the notion of reality as made up of qualities in relation. Perceptual space and time are aggregates of lesser parts, which are themselves spaces and times; thus they are relations between terms, each of which contains the same relation once more in itself, and so imply the now familiar indefinite regress. Again, when we try in our conceptual space and time construction to remedy this defect by reducing space and time altogether to mere systems of relations, the difficulty turns out to have been merely evaded by such a process of abstraction. For, so long as we keep rigidly to our conceptual construction, the terms of our relations are indistinguishable. In purely conceptual space and time, as we have seen, there is no possibility of distinguishing any one direction from any other, since all are qualitatively identical.

Indeed, it is obvious from first principles that when the sets of terms between which a number of relations of the same type holds are indistinguishable, the relations cannot be discriminated. To distinguish directions at all, we must, in the end, take at least our starting-point and one or more standard directions reckoned from it—according to the number of dimensions with which we are dealing—as independently given, that is, as having recognisable qualitative differences from other possible starting-points and standard directions. (Thus, to distinguish before and after in conceptual time, you must at least assume some moment of time, qualitatively recognisable from others, as the epoch from which you reckon, and must also have some recognisable qualitative distinction between the direction “past” and the direction “future.”) And with this reference to qualitative differences we are at once thrown back, as in the case of perceptual time and space, on the insoluble old problem of Quality and Relation. The assumed starting-point and standard directions must have qualitative individuality, or they could not be independently recognised and made the basis for discrimination between the remaining directions and positions: yet, because of the necessary homogeneity of the space and time of conceptual construction, they cannot have any such qualitative individuality, but must be arbitrarily assumed. They will therefore themselves be capable of determination only by reference to some other equally arbitrary standard, and thus we are once more committed to the indefinite regress. The practical usefulness of these constructions thus depends on the very fact that we are not consistent in our use of them. In all practical applications we use them to map out the spatial and temporal order of events as seen in perspective from a standpoint which is, as regards the conceptual time and space order itself, arbitrary and indistinguishable from others.

§ 7. Instead of further elaborating this general argument, a task which would be superfluous if its principle is grasped, and unconvincing if it is missed, I will proceed to point out one or two special ways in which the essential arbitrariness of the spatial and temporal construction is strikingly exemplified. To begin with, a word may be said about the alleged unity of space and time. It is constantly taken for granted, by philosophers as well as by practical men, that there can be only one spatial and one temporal order, so that all spatial relations, and again all temporal relations, belong to the same system. Thus, if A has a spatial relation to B and C to D, it is assumed that there must be spatial relations between A and C, A and D, and B and C, B and D. Similarly if A is temporally related with B, and C with D. This view is manifestly presupposed in the current conception of Nature, the “physical universe,” the “physical order,” as the aggregate of all processes in space and time. But there seems to be no real logical warrant for it. In principle the alleged unity of all spatial and temporal relations might be dismissed, on the strength of the one consideration that space and time are not individual wholes, and therefore can contain no principle of internal structural unity. This is manifest from the method by which the space and time of our conceptual scheme have been constructed. They arose, as we saw, from the indefinite repetition of a single type of relation between terms in which we were unable to find any ultimately intelligible principle of internal structure. But unity of structure cannot be brought into that which does not already possess it by such mere endless repetition. The result of such a process will be as internally incoherent and devoid of structure as the original data. Hence space and time, being mere repetitions of the scheme of qualities in relation, cannot be true unities.

This becomes clearer if we reflect on the grounds which actually warrant us in assigning position in the same space and the same time to a number of events. For me A and B are ultimately in the same space when there is a way of travelling from A to B; they are in the same time when they belong to different stages in the accomplishment of the same systematic purposes. Thus in both cases it is ultimately from relation to an identical system of purposes and interests that different sets of positions or events belong to one space or one time. The unity of such a space or time is a pale reflection in abstract form of the unity of a life of systematic purpose, which is one because it has unique individual structure. It is in this way, from the individual unity of the purpose and interests of my ordinary waking life, that I derive the right to refer its experiences to a single space and time system. Similarly, it is in virtue of the inclusion of my own and my fellow-men’s purposes in a wider whole of social systematic purpose that I can bring the space and time relations of their experience into one system with my own. And again, the sensible occurrences of the physical order belong to one space and time with the space and time relations of human experience, because of the varying ways in which they condition the development of our own inner purposive life. But there are cases, even within our own conscious life, where this condition appears to be absent, and in these cases we do not seem to be able to make intelligible use of the conception of a single time or a single space.

Take the case of our dreams. The events of my dreams stand in spatial and temporal relations within the dream itself, but there would be no sense in asking what are the spatial relations between the places seen in my dreams and the places marked on the map of England; or what are again the temporal relations between the events of last night’s dream and those of this morning, or those of the dreams of last week. Precisely because there is usually no systematic identity of purpose connecting the dream with the waking life or with other dreams, the time and space of the dream have no position with respect to the time and space system of waking life, nor those of one dream with relation to those of another. Of course, it may be said that the dream-space and dream-time are “imaginary,” but the problem cannot be got rid of by the use of an epithet. To call them imaginary is merely to say that they are not systematically connected with the time and space of waking life, not to disprove their genuineness as actual space and time constructions.

Similarly, if there are intelligent purposes of which our human purposive life is debarred from taking account as such, as we urged that there must be behind the phenomenal physical order, the time and space within which those purposes are conceived and executed would have no place in our spatial and temporal system. The phenomenal events of the physical order would fall within our system, but not the life of inner purpose of which that order is the manifestation to our senses. Ultimately, in fact, all spaces and all times could only form one spatial and temporal system on condition that the infinite absolute experience views all its contents in spatial and temporal form; then the various space and time systems corresponding to the purposes of the various groups of finite individuals would finally, for the infinite individual, form one great system of time and space relations. But we have already seen that the infinite experience cannot comprehend its contents in spatial or temporal forms.

We infer, then, that there may be—indeed, if our interpretation of the physical order is valid, there must be—a plurality of spaces and times within the Real. Within any one such space or time all its members are spatially and temporally interrelated, but the various spaces are not themselves related in space, nor the various times before or after one another in time. Their relation is the purely logical one of being varying modes of the expression in a finite detail of the underlying nature of the ultimate Reality. For the absolute experience they must be all at once and together, not in the sense of being in “one space and time,” but in the sense of forming together the systematic embodiment of one coherent ground or principle.

§ 8. Similar consequences, as to the phenomenal character of space and time, follow from the consideration of the familiar Kantian antinomies founded upon the concept of spatial and temporal infinity. Space and time must be externally boundless and internally indefinitely divisible, and yet again cannot be either. Freed from unessential accessories, the argument for either side of the antinomy may be stated thus. Space and time must be boundless because all spatial and temporal existence means spatial and temporal relation to a second term, itself similarly related to a third term. For precisely the same reason both must be indefinitely divisible. Yet again, they can be neither, since only the individual exists, and within such an interminable network of relations between terms which are nothing but the supporters of these relations there is no principle of individual structure. Thus the Kantian antinomies are a simple consequence of the old difficulty about quality and relation. Space and time must be mere relations, and the terms of those relations therefore qualitatively indistinguishable; again, since they are relations they cannot be relations between nothings or, what is the same thing, between terms with no individual character. As in all cases where the problem of relation and quality arises, it then conducts us to the indefinite regress.

So long as we continue to look upon space and time as real, we have therefore to choose between two equally illogical alternatives. We must either arbitrarily refuse to continue the indefinite regress beyond the point at which its difficulties become apparent, as is done by the assertion that space and time have finite bounds or indivisible parts, or we must hold that the absolute experience actually achieves the summation of an unending series. With the recognition that space and time are phenomenal, the result of a process of construction forced on us by our practical needs, but not adequately corresponding to the real nature of individual existence, the difficulty disappears. Both sides of the antinomy become relatively true, in the sense that for our practical purposes we must be content to adopt now the one and again the other; both become ultimately untrue in the sense that space and time, being constructions of our own, are really neither finite nor infinite series, but are the one or the other according to the purposes for which we use our construction.

§ 9. If spatial and temporal position and direction must thus in the end be appearance, phenomenal of some more individual reality, we have finally to ask, Of what are they the appearance? It is not enough to say “of ultimate Reality,” or “of the Absolute.” Ultimately this is, no doubt, true of space and time, as it is of everything else, but we desire further to know if they are not proximately the appearance of some special features of the inner physical life of the lesser individuals which compose the Absolute. We naturally look for some third term, in the nature of finite individuality, to mediate between the structureless abstract generality of space and time relation, and the perfect individual structure of the spaceless and timeless Absolute Individual. We want, in fact, to connect the spatial and temporal form which our experience wears, with some fundamental aspect of our nature, as beings at once individual and finite.

Nor is it particularly difficult to make the connection. When we remember that space and time, as they actually condition our perception and movement, are the space and time which radiate out from an unique here and now of immediate feeling, it is fairly evident that the spatial and temporal aspect of our experience is, as already suggested, a consequence of that limitation of our attentive interests which constitutes our finitude. It is the narrowness of my interests, or at least of those which are sufficiently explicit to rise into the “focus” of consciousness, that is reflected in the distinction of my here from all the theres which are around me. Here is where my body is, because of the specially intimate connection of the realisation of my interests and purposes with those events in the phenomenal physical order which I call the state of my body. Were my interests widened so as to embrace the whole scheme of the universe, I should no longer perceive the contents of that universe as dispersed through space, because I should no longer have as my special standpoint a here to which other existence would be there.

My special standpoint in space may thus be said to be phenomenal of my special and peculiar interests in life, the special logical standpoint from which my experience reflects the ultimate structure of the Absolute. And so, generally, though the conclusion can for various reasons not be pressed in respect of every detail of spatial appearance, the spatial grouping of intelligent purposive beings is phenomenal of their inner logical affinity of interest and purpose. Groups of such beings, closely associated together in space, are commonly also associated in their peculiar interests, their special purposes, their characteristic attitude towards the universe. The local contiguity of the members of the group is but an “outward and visible sign” of an “inward and spiritual” community of social aspiration. This is, of course, only approximately the case; the less the extent to which any section of mankind have succeeded in actively controlling the physical order for the realisation of their own purposes, the more nearly is it the truth that spatial remoteness and inner dissimilarity of social purposes coincide. In proportion as man’s conquest over his non-human environment becomes complete, he devises for himself means to retain the inner unity of social aims and interests in spite of spatial separation. But this only shows once more how completely the spatial order is a mere imperfect appearance which only confusedly adumbrates the nature of the higher Reality behind it. Thus we may say that the “abolition of distance” effected by science and civilisation is, as it were, a practical vindication of our metaphysical doctrine of the comparative unreality of space.

Similarly with time, though the temporal series may, in a sense, be said to be less of an unreality than the spatial. For it does not seem possible to show that spatial appearance is an inevitable form of finite experience. We can at least conceive of a finite experience composed entirely of successive arrangements of secondary qualities, such as sounds or smells, and the accompanying feeling-tones, though we have no positive ground for affirming the existence of such a type of experience. But the temporal form seems inseparable from finite intelligence. For the limitation of my existence to a certain portion of time is clearly simply the abstract and external aspect of the fact that my interests and purposes, so far as I can apprehend the meaning of my own life, occupy just this special place in the logical development of the larger whole of social life and purpose of which my own life is a member. So the position of a particular purposive act in the temporal series of acts which I call the history of my own life, is the outward indication of the logical place filled by this particular act in the connected scheme of interests which form my life on its inner side. But it is an inevitable consequence of the want of complete internal harmony we call finitude, that the aims and interests of the finite subject cannot be in the same degree present to its apprehension all at once and together. In being aware of its own internal purpose or meaning, it must, because it is finite and therefore not ultimately a completely harmonious systematic whole, be aware of that purpose as only partially fulfilled. And in this sense of one’s own purposes as only partially fulfilled, we have the foundation of the time-experience, with its contrast between the “now” of fulfilment and the “no longer” and “not yet” of dissatisfied aspiration.

For this reason, dissatisfaction, unfulfilled craving, and the time-experience seem to be bound up together, and time to be merely the abstract expression of the yearning of the finite individual for a systematic realisation of its own purpose which lies for ever beyond its reach as finite. If this is so, only the absolute and infinite individual whose experience is throughout that of perfectly harmonious systematic realisation of meaning, can be outside the time-process; to it, “vanished and present are the same,” because its whole nature is once for all perfectly expressed in the detail of existence. But the finite, just because its very nature as finite is to aspire to a perfection which is out of reach, must have its experience marked with the distinction of now from by and by, of desire from performance. In this temporal character of all finite experience we may perhaps afterwards discern the ultimate ground of morality, as we can already discern in the unresting struggle of the finite to overcome its finitude, practical evidence that time is not a form which adequately expresses the nature of Reality, and must therefore be imperfect appearance.

Thus we seem finally to have reached the conclusion that time and space are the imperfect phenomenal manifestation of the logical relations between the purposes of finite individuals standing in social relations to each other; the inner purposive life of each of these individuals being itself in its turn, as we have previously seen, the imperfect expression, from a special logical “point of view,” of the structure and life of the ultimate infinite individual. For the infinite individual itself the whole of the purposes and interests of the finite individuals must form a single harmonious system. This system cannot itself be in the spatial and temporal form; space and time must thus in some way cease to exist, as space and time, for the absolute experience. They must, in that experience, be taken up, rearranged, and transcended, so as to lose their character of an endless chain of relations between other relations.

Precisely how this is effected, we, from our finite standpoint, cannot presume to say. It is natural to draw illustrations from the “specious present” of perception, in which we appear to have a succession that is also simultaneous; or again, from the timeless and purely logical character science seeks to ascribe to its “laws of nature.” But in the “specious present” we seem obliged to attend to one aspect, succession or simultaneity, to the exclusion of the other; probably we never succeed in equally fixing both aspects at once. It thus presents us rather with the problem than with its solution. And again, after our discussion of the meaning of law, we cannot affirm that Nature is, for the absolute experience, a system of general laws. Hence it seems well not to take these illustrations for more than they are actually worth as indications of the merely phenomenal character of time. Metaphysics, like the old scholastic theology, needs sometimes to be reminded that God’s thoughts are not as ours, and His ways, in a very real sense when Philosophy has done its best, still past finding out.

Consult further:—F. H. Bradley, Appearance and Reality, chaps. 4 (Space and Time), 18 (Temporal and Spatial Appearance); L. Couturat, L’Infini Mathématique, pt. 2, bk. iv. chap. 4 (against the Kantian antinomies); H. Poincaré, La Science et L’Hypothèse, pp. 68-109; H. Lotze, Metaphysic, bk. ii. chaps. 1-3; W. Ostwald, Vorlesungen über Naturphilosophie, lects. 5, 8; J. Royce, The World and the Individual, Second Series, lect. 3; B. Russell, Foundations of Geometry: Is Position in Space and Time Absolute or Relative (Mind, July 1901), Principles of Mathematics, pt. 6, vol. i.; H. Spencer, First Principles, pt. 2, chap. 3.

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Footnote 141:

The student who desires to think out the problems for himself would probably do well to take the discussions of Locke (Essay, bk. ii. chaps. 13-15) and Hume (Treatise of Human Nature, bk. i. pt. 2) rather than that of Kant as his starting-point, as they are less vitiated by psychological superstitions. In recent metaphysical work the chapters on the subject in Mr. Bradley’s Appearance and Reality will probably be found most useful. Much may be learned from Mr. Russell’s work, Foundations of Geometry, with which should, however, be compared the largely discrepant results of his later article, “Is Position in Space and Time Relative or Absolute?” (Mind, July 1901).

Footnote 142:

We are not called upon to enter into such specially psychological questions as, e.g., whether both directions, past and future, can be detected within the “specious present” of direct perception, or whether the specious present only contains the elements “now” and “no longer,” the “not yet” being a subsequent intellectual construction, as is held, e.g., by Mr. Bradley and Mr. Shadworth Hodgson.

Footnote 143:

We may indeed go still further, and say that every unique moment or experience has its own unique spatial and temporal system. The method by which I weave the perceived space-time systems of different experiences within my own mental life into a single conceptual system, is in principle the same by which the spaces and times of myself and other men are made into one system for the purpose of practical intercourse.

Footnote 144:

For an account of the psychological processes involved in all this, see, e.g., Stout, Manual of Psychology,^3 bk. iii. pt. 2, chaps. 3-5; bk. iv. chap. 6.

Footnote 145:

Thus Dedekind (Was sind und was sollen die Zahlen? p. xii.) maintains that none of the constructions of Euclid involve the continuity of space.

Footnote 146:

Of course, a physical vacuum is not the same thing as empty space. For the purposes of any special science a vacuum means a space not occupied by contents of the special kind in which that special science is interested. Thus, in the ordinary parlance of Physics, a vacuum means simply a space in which there is no mass. Whether it is desirable, for the purposes of physical science, to assume the existence of vacuum, is altogether a question for Physics itself, and to decide it in the affirmative is not to maintain the existence of that unmeaning abstraction, absolutely empty space. In any case, it may be observed that the widespread notion that motion is only possible in a physical vacuum is a mistake, motion being perfectly possible in a fluid plenum.

Footnote 147:

It must be carefully noted that distance as thus defined is not properly a quantitative relation, and involves no notion of magnitude, but only of relative place in a series. It should also be observed that in assuming the existence of such a unique relation between every pair of points, it is tacitly taken for granted that the number of dimensions of the spatial order is finite. In a space of an infinite number of dimensions, such unique relation would be impossible. (See Russell, Foundations of Geometry, p. 161 ff.) Our justification for making this assumption, as also for taking time to be of one dimension only, seems to be that it is indispensable for all those practical purposes which depend on our ability to create a science of Geometry, and that we have no positive ground for assuming the opposite. Thus ultimately the assumption appears to be of the nature of a postulate.

Footnote 148:

The ablest detailed account of the relativity of spatial position readily accessible to the English reader, will be found in Mr. Russell’s Foundations of Geometry, chaps. iiiA, iv. Mr. Russell has since, in Mind for July 1901, attempted to prove the opposite view, that positions in space and time are inherently distinct, but without discussing his own previous arguments for relativity. Into the purely mathematical part of Mr. Russell’s later contentions I am not competent to enter. I may, however, suggest that the question of Metaphysics cannot be decided merely by urging, as Mr. Russell does, that fewer assumptions are required to construct a geometry on the hypothesis of absolute than on that of relative position. The superior convenience of an assumption for certain special purposes is no proof of its ultimate intelligibility. And when Mr. Russell goes on to admit that points in space are indistinguishable for us, he seems to me to give up his case. For is not this to admit that, after all, the space with which we deal in our geometrical science is relative from beginning to end? How differences of quality of which we, by hypothesis, can know nothing, can help or hinder our scientific constructions, it is indeed hard to see.

Footnote 149:

This may be brought home even to those who, like myself, are not mathematicians, by the perusal of such a work as Lobatchevsky’s Untersuchungen zur Theorie der Parallel-Linien, where a consistent geometry of triangles is constructed in entire independence of the postulate of parallelism. Of course, in the end it must be a mere question of nomenclature whether a form of serial order independent of these quasi-empirical restrictions is to be called “space” or not.

Footnote 150:

It must be carefully remembered that the essential defect of the indefinite regress is not its interminableness, but its monotony. We ourselves held that Reality is an individual composed of lesser individuals which repeat the structure of the whole, and that the number of these individuals need not be finite. But, in our view, the higher the order of individuality the more self-explanatory was its structure, whereas in the indefinite regress an incomprehensible construction is endlessly repeated in the same form.

Footnote 151:

Normally, that is; for brevity’s sake I omit to note the possible case of a coherent dream-life continued from night to night. In principle there would be a difference between the case of the space and time of such a dream-life and those of our waking hours.

Footnote 152:

So the events of my dreams, though not occupying any place in the temporal series of the events of waking life, are so far logically connected with that series as both sets of events stand in relation to certain identical elements of psychical temperament and disposition. Another interesting case is that of so-called “dual personality.” The experience of both the two alternating personalities can be arranged in a single temporal series only because of the way in which both sets are inwoven with the systematic interests of other men, whose personality does not alternate, or alternates with a different rhythm. If all mankind were subject to simultaneous alternations of personality, the construction of a single time-series for all our experiences would be impossible. In this discussion I have throughout followed the full and thorough treatment of the problem by Mr. Bradley, Appearance and Reality, chap. 18.

Footnote 153:

Otherwise, conceptual space and time are, as we have seen, derivatives of the number-series, and we have already learned that the number-series leads to the problem of summing an endless series, and is therefore not an adequate way of representing ultimate Reality. (Bk. II. chap. 4, § 10). Another form of the same difficulty would be that conceptual space and time are applications of the numerical series,—but application to what? To a material which is already spatial and temporal. All these puzzles are only different ways of expressing the essential relativity of space and time. But see the anti-Kantian view in, e.g., Couturat, L’Infini Mathématique, pt. 2.

Footnote 154:

Compare Prof. Royce’s remarks, The World and the Individual, Second Series, lect. 3, “The Temporal and the Eternal,” p. 134. I should certainly have had to acknowledge considerable obligation to Prof. Royce’s discussion had not the present chapter been written before I had an opportunity of studying it.

Footnote 155:

Against the plausible attempt to solve the problem by simply thinking of the whole physical order as forming a “specious present” to the Absolute Experience, we may urge that the “specious present” itself regularly consists for us of a multiplicity of detail, which we apprehend as simultaneous without insight into its inner unity as the embodiment of coherent system. Hence the direct insight of the Absolute Experience into its own internal meaning or structure cannot be adequately thought of as mere simultaneous awareness of the detail of existence. So long as a succession is merely apprehended as simultaneous, its meaning is not yet grasped.

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