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Chapter X: The One and the Many

The categories indefinable.

Space-Time is thus the source of the categories, the non-empirical characters of existent things, which those things possess because of certain fundamental features of any piece of Space-Time. These fundamental features cannot be defined. For to define is to explain the nature of something in terms of other and in general simpler things, themselves existents. But there is nothing simpler than Space-Time, and nothing beside it to which it might be compared by way of agreement or contrast. They cannot even be described completely. For description, like definition, is effected by reference to existent entities. Not only all our language but all our conceptions are derived from existents, including in existents those of mathematics, particular figures or numbers. The utmost that we can do is therefore to describe in terms of what is itself the creation of Space-Time with its various features, and however little our description borrows from metaphor, it cannot but be a circuitous way of describing what is prior to the terms we use in our description and can therefore in the end only be indicated and known by acquaintance. Space-Time itself and all its features are revealed to us direct as red or sweet are. We attempt to describe what is only to be accepted as something given, which we may feel or apprehend; to describe, as has been said above, the indescribable. With each category in turn we have indicated the basis of it in Space-Time—the occupation of Space-Time, the continuity of it which lies at the base of relation, its uniformity or the constancy of its ‘curvature’ and the like. But it is plain that these descriptions are merely the best means open to us of inducing the reader to look and accept what he sees. The descriptions do nothing more than take the place of pointing with the finger.

More than once this has been propounded with regard to continuity, or to the statement that Space-Time is a continuum. A series of existents, say real numbers, occurs under certain conditions and then becomes a continuum. But we are in stating these conditions approximating to the original and indescribable feature of Space-Time which makes continuity of things in series possible. This original continuity is known only by acquaintance. The same thing is true of the infinity of Space-Time, and the remarks made upon this topic in a previous chapter1 need not be repeated. Of the categories the same thing is true. Our description of Space-Time itself and of the features which belong to any bit of it is but a means of reaching by thought to what is deeper and more fundamental than the products of thought. It is a method which redounds to the honour of Space-Time in the same sense as it redounded to the honour of Cornelia to be named as the mother of the Gracchi.

Space-Time not subject to the categories.

Kant was thus mistaken in the sharp distinction which he drew between the forms of Space and Time and the categories. If our hypothesis is correct, empirical things are in the end complexes within that pure manifold of intuition of which he sometimes speaks; and the categories belong to them because they are the fundamental features of Space-Time stuff. But there is a well-worn proposition familiar to idealists, and derived from Kant, that the source of the categories is not itself subject to the categories. This proposition is true. The categories applied for Kant to objects of experience, not to the mind which contributes them to experience. They apply in our conception of the matter to the empirical things which are special configurations in Space-Time and because they are such; but they do not apply to Space-Time itself. Space-Time does not exist but is itself the totality of all that exists. Existence belongs to that which occupies a space-time. There is a perennial question which is stilled by no assertion of its futility, how the world came to exist or what made the world? We can see at once the answer to the question, and how far it is futile. The world which is Space-Time never and nowhere came into existence, for the infinite becoming cannot begin to become. It could only do so in a larger Space and Time and at the order of some cause exterior to it. Now all existence arises within Space-Time, and there is no cause which is not itself a part of it. Nor can we say that it has some neutral kind of being, some being for thought. For thought or thinking, on our hypothesis that mind and things may be treated on the same footing with proper regard for their empirical difference, is an existent within Space-Time, and to say that anything has being for thought means only that it can be the object of thinking. The being of the world if it had such neutral being cannot be being for its own creature. Space-Time therefore does not exist but it is existence itself, taken in the whole. The question is thus not so much futile as it needs enlightenment. Space-Time exists only in the loose usage of words in virtue of which we have to say it is in Space and Time rather than out of them—a matter to which we shall recur.

Space-Time is not universal; for there is no plan of it distinct from the execution. Its only plan is to be Space-Time. Were it universal it must be repeated or at least capable of repetition. But how should the whole of Space-Time be repeated? For if it could be, it would not be the whole. It is not, as we have attempted to show at length, a relation, nor even a system of relations, but it is through and through relational in the sense that in virtue of its continuity there are relations between its parts and the relations are themselves spatio-temporal. Perhaps it is not necessary to run through the whole list of categories to be assured that the father of them is not also their child. But two of them seem to lay special claim to be applicable to Space-Time, the category of substance and that of whole and part with its related category of number. Is not Space-Time a whole, and a one which includes many, and a substance? In each case we must answer, no.

Not a whole of parts.

It is not a whole of parts, for a whole of parts is constituted by its parts, and is relative to other wholes of parts. Whereas Space-Time breaks up into parts and wholes of them as it lives and moves. It is true a rock may disintegrate into powder and still remain an aggregate or whole; but the whole is given to begin with. If Space-Time were such a whole it would be given all at once. But being Time (or indeed Space, which is the same thing) it is not, as Mr. Bergson rightly says, given altogether. To suppose so is to ignore the reality of Time, to fail to take Time seriously. At any one moment the universe is the whole of its existent parts, but at any one moment the universe is not the whole universe of parts. For in the redistribution of dates among places, new existents are generated within the one Space-Time. It may indeed be called not a whole of parts, but the whole or system of all existents. But this designation does but help us, by reference to the category of whole and parts, to feel towards the infinitude of Space-Time. In like manner Space-Time is in no case a unity of many things; it is not a one. For that implies that it can descend into the field of number, and be merely an individual, and be compared as one with two or three. The universe is neither one in this sense, nor many. Accordingly it can only be described not as one and still less as a one, but as the one; and only then because the quasi-numerical adjective serves once more to designate not its number but its infinite singularity; or, as is more clearly still expressed by calling it substance, that it is not so much an individual or a singular as the one and only matrix of generation, to which no rival is possible because rivalry itself is fashioned within the same matrix.

Not a substance.

It is not a substance, and only by a metaphor or analogy can it be called the infinite substance. For substance is an existent configuration of space in so faras it is the theatre of Time; it is a space with definite contour occupied by time, that is, is a space enduring in time. But infinite Space has no contours and is thus no substance. We are tempted still to call it substance because a complex substance like man is a grouping within its contour of many different substances, and we imagine Space-Time to be an extension of such a complex substance. In doing so we are forgetting that a substance however complex is related (by causality) to other substances and no such relation is possible for Space-Time as a whole. It may still be urged, substance is the occurrence of a space in time or the extension of time over a space, and infinite Space and Time are in the same relation to one another. But it is really only when you cut a finite2 space out of the whole, or a finite time out of the whole, that it is possible in strictness to speak of a relation between the space and time of a substance. You can think of them apart from one another just because the time of which you speak is that part of a larger Time which is appropriated to the space in question, or because that part of Space is appropriated to the time in question. Infinite Space and infinite Time are one and the same thing, and cannot in reality be considered apart from one another. This statement is wholly independent of the question whether a finite space may not be sustained in its configuration through infinite time; whether there may not be substances which having come into existence endure for ever; which is entirely an empirical question to be settled by evidence.

When we attempt to extend the notion of substance to infinite Space-Time, we are in fact once more merely helping ourselves towards a statement of its infinite character, and the whole value of the attempt lies therein, and not in the use of the conception of substance. We are describing the infinite Space-Time as the substance which includes all substances and is the system of them. But the idea of infinity is prior to that of an infinite system of existents, which is really derived from it. We approximate to infinity by the notion of an infinite system of existents, like numbers or substances, which is our conceptual reconstruction, by means of the blocks, of the quarry from which the stones were hewn. The infinite Space-Time is the totality of all substances, but it is prior to the substances by whose composition it is described. Thus to call it the one or the whole or the infinite substance is no more than to aim at its infinitude, in terms of the finite creatures of it. Only in this sense is it legitimate therefore to speak of the infinite substance.

Space-Time as the stuff of things.

In truth, infinite Space-Time is not the substance of substances, but it is the stuff of substances. No word is more appropriate to it than the ancient one of hyle (υλη). Just as a roll of cloth is the stuff of which coats are made but is not itself a coat, so Space-Time is the stuff of which all things, whether as substances or under any category, are made. If I call it the stuff and not the material, it is to avoid confusion with the very much more specific idea of matter, as matter is commonly understood. Matter is a finite complex of space-time with the material quality, as we shall afterwards see. The substance of the great writers of the seventeenth century is different from this stuff. It is the highest expression of the universe and not like Space-Time the universe in its lowest expression. Substance so understood is not mere persistence of Space in Time but means that which is absolutely self-contained and is the cause of itself. The stuff of the world is indeed self-contained in that there is nothing not included in it. But it is not the supreme individual or person or spirit, but rather that in which supreme individuality or personality is engendered, as we shall have to note in the sequel. Nor can it intelligibly be called the cause of itself. For causation is the more intimate relation between existent substances. To think of the world as causing itself is to imagine the world at one moment generating itself at the next moment, and splits the life of the world into independent moments which can no more account for causal relation than a motion can be explained as the succession of separate point-instants.

Thus Space-Time, the universe in its primordial form, is the stuff out of which all existents are made. It is Space-Time with the characters which we have found it to reveal to experience. But it has no ‘quality’ save that of being spatio-temporal or motion. All the wealth of qualities which makes things precious to us belongs to existents which grow within it, and which are in the first instance characterised by the categories. It is greater than all existent finites or infinites because it is their parent. But it has not as Space-Time their wealth of qualities, and being elementary is so far less than they are. Hence it repels two possible kinds of misdescription. It is first something positive. Not being subject to the categories it might be supposed to be entirely negative, not relation nor substance nor quantity nor number, not in time nor in space. It is in fact something very positive to which these determinations and all the qualities which depend on them owe their being. The other misconception is far more serious. Because it is not describable by categories the universe might be supposed to have characters or qualities superior to them. Thus Space-Time is not in space or time as though there were some enveloping Space or Time. It is itself the whole of spaces and times, as it is all existence, and all substance. But it must not therefore be supposed to be spaceless or timeless, out of Space or Time and to possess spacelessness or timelessness (eternity) as some superior qualities which confer upon it a unique character. All its characters are reflected in its children. Call it by what name you will, universe or God or the One, it is not above Space or Time. It is truer to use the careless expression, the universe is in Space and Time, than to describe it as timeless. Space and Time are, in the words of Spinoza, though not with the significance which he attaches to the phrase, attributes of the universe or Space-Time. In what sense there is divinity in the universe, we shall not attempt to understand till much later in our inquiry. Nor are we free to call it timeless or spaceless in order to separate it from the Time which is measured by the clock or the Space which is measured by the footrule. There is only one Space and one Time, and though the mathematicians may deal with it by methods different from those of philosophy and common sense, it is still the same Space and Time which they all investigate each in his different way. It is such a misconception which has given rise to the notion of eternity as something different from Time and superior to it. But the only eternity which can be construed in terms of experience is infinite Time. If it is different from this it is out of all relation to Time, and if attributed to the world requires justification on its merits, and not because it may be thought to derive its nature from contrast with the alleged defects of ordinary empirical and mathematical Time. Space-Time therefore is neither in Time nor in Space; but it is Time and it is Space.

Categorial and empirical.

Two topics now claim discussion which arise out of the relation of the whole Space-Time to its existents, and the questions so raised are answered from the same consideration, that the existents are of the same stuff as the whole. One is the ancient subject of the relation of the One and the Many. The other, which I will take first, is the distinction of the categorial and the empirical, the use of which must have already been the source of some difficulty in the course of the exposition. The nature of the distinction has been explained, but it must have seemed at times a shifting or evanescent one. I do not so much propose to ask again what is the distinction as to recapitulate the cases in. which categorial and empirical seem to grade into each other. The categorial is the pervasive, and the empirical is the variable or contingent. But since categories are the fundamental features of, and space-time and empirical existents are variable complexes within, Space-Time, the boundaries of the categorial and the empirical are from the nature of the case hard to draw, and may seem indistinct and fluid. The a priori and the empirical are distinguished within experience itself. Both are experiential or in a general sense empirical. The strictly empirical is only the non-pervasive parts of experience, all experience being ultimately expressible in terms of Space-Time.

Strictly speaking, the empirical coincides with that which has quality. But we are compelled to recognise mere spatio-temporality as, in a sense, a quality, though it is in itself categorial. It is the meeting-point of the categorial and the empirical. Motion is categorial and is allied with the other categories which it sums up. But it is allied, on the other hand, in virtue of its unitary character with the series of obviously empirical qualities, red, sweet, life, consciousness. Hence it is that the various special determinations of the categories, of number, quantity, motion, are described in common philosophical language as primary qualities. To call spatio-temporality quality is little more than a name, but it illustrates the essential identity of stuff between the categorial and the empirical.

Once more the various geometrical figures are described as empirical, and the various numbers of arithmetic, including not only the ordinary integers but infinite numbers and surds. Number itself is categorial and so is Space. But the numbers and different figures in space are not pervasive but empirical. And yet we might be seeming to deal with categorial matter in treating these subjects. The distinction here is not so difficult to draw. It becomes much more difficult when we call point-instants themselves empirical,3 though they are the very constituents of Space-Time, which is a priori, and the source of all that is a priori.

Another symptom of the intimacy of categorial and empirical was the difficulty experienced in respect of certain notions in determining whether they were categorial or not. Change being a relation of empirical terms could be assigned to the empirical, without much hesitation. But likeness and such thoughts as ‘and’ and ‘but’ and ‘if’ might easily be taken for categories of a derived order. ‘Like’ we decided to be empirical because it implied the overlapping of different universals in the same thing, and such overlapping is empirical and does not follow from the nature of Space-Time itself, but only from the fact that it breaks up into complexes, and these complexes may exhibit the overlapping of empirical universals.4 ‘And’ means combination and ‘but’ disjunction or obstruction between empirical data, but they are empirical relations and arise from the empirical character of their terms, when they are not purely extrinsic. Such notions as these, however categorial they may appear, lack the note of pervasiveness, and the reason of this is that they are not fundamental to any space-time as such.

Such difficulties in the working out of the distinction of categorial and empirical serve only to accentuate the intrinsic solidarity of the two. The whole empirical world may be described as, in its simplest terms, a multiform determination under various circumstances of categorial characters. If the variable and the pervasive are alike Space-Time, this conclusion is natural. Any empirical thing is a configuration of space-time, when the thing is expressed in its simplest terms. And all categories are configurations of space-time. The only difference is in pervasiveness of the categorial as distinct from the empirical determinations. I am a fairly definite configuration of space-time; but I possess universality in so far as, being a man, my pattern is repeated elsewhere. In that respect I possess a character which everything shares with me. My empirical universal, the pattern of man, is shared with me only by other men. But all my empirical characters are specifications under my empirical conditions of categorial ones.

The One and the Many.

We come finally to the relation of the One to the Many? We are not asking yet what the One is, nor asserting anything other than that it is Space-Time; nor whether the elementary point-instants are monads like those of Leibniz or whether the complexes of them are governed by a dominating monad. These topics are not yet in place. Our question is whether the existents within Space-Time, being only crystals within that matrix, are lost in the reality of Space-Time or conserve their own. This question too has been already answered in part by anticipation under the head of relation. For it is clear that Space-Time takes for us the place of what is called the Absolute in idealistic systems. It is an experiential absolute. All finites being complexes of space-time are incomplete. They are not the sum of reality. But their absorption into the One does not destroy their relative reality.5 That could happen only if the real in which they are absorbed were of a different stuff from themselves. But to be a complex of space-time is to be of the stuff of which the universe consists. Now a configuration of motion is not destroyed by its relation to the circumambient medium but is, on the contrary, sustained thereby. It is the surrounding space from which the triangle is cut off which secures it its existence as a triangle. The society or State which is composed of individual men as citizens does not destroy the reality of its members as citizens but sustains it. Thus things being reducible in the end to these complex groupings of motions have such reality as falls to their share. They may be brief as the lightning in the collied night. They may be annihilated in the shock of motions within the domain of Space-Time, they may enter into new complexes and take on fresh empirical qualities, there may be ceaseless variation from the interplay of things; or a thing may persist through appreciable durations, undergoing redistribution of motions and changing its qualities in correlation therewith, waxing and waning in bulk, even varying in shape and texture and yet preserving its substantial individuality, as when a man is mutilated by war or disease; or it may persist eternally except for violence as the germ-plasm is said to do. My body (for 1 say nothing at present of my mind) dies and is resolved, like the rock, into its elements. There is here but a replacement of one kind of empirical reality by another. All these empirical variations take place within Space-Time and are changing configurations of it, and each of them being of Space-Time shares in the reality which belongs to its matrix. The difficulty is therefore not to be sure that a thing or a state of a thing or an event which happens to it really is but to know what it truly is. To discover this is the object of science. And owing to the imperfection of our, minds which makes exact qualitative observation unattainable and the difficulties to be studied hereafter which stand in the way of exact apprehension of spatio-temporal figures of things, this object may be one to which we can only approach, but not attain.

Consider Space-Time, or indeed the universe however conceived, as lifted above its parts (or appearances as they then are called), as something from which they represent a fall and degeneration; and the parts are unreal ultimately because of their finitude. Let it be the stuff or medium in which things are cultivated, and things of all kinds suffer from their finitude only in their incompleteness. They are not the whole reality but they are real in themselves, and it is only our imperfection as finites which conceals from us partially their true nature; how that is they are delimited against each other in Space-Time. Within this matrix there may then be progressive types not so much of reality as of merit or perfection, as a rose may be a more perfect thing than a stone. There is room for an ascending scale of such perfection. But everything that truly is is really. The One is the system of the Many in which they are conserved not the vortex in which they are engulfed.

  • 1.

    Bk. I. ch. i. p. 40.

  • 2.

    Or any space less than the whole.

  • 3.

    See above, ch. ix. pp. 324 ff.

  • 4.

    See above, ch. iv. pp. 247 ff.

  • 5.

    In the general conception of the relation of the parts to the whole of experience (which here appears as part of a systematic doctrine) I have been chiefly stimulated by Mr. Stout's metaphysical writings (in the Proceedings of the Aristotelian Society).