Elements of metaphysics

by A. E. Taylor

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.[^[144]]

(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,[^[145]] 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.[^[146]]

§ 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.[^[147]] 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.[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.