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Chapter IV: Relation

The category.

All existents are in relation because events or groups of them are connected within Space-Time. Relation amongst existents follows from the continuity of Space-Time. The continuity of Space-Time is something primordial and given in experience. When it is described in conceptual terms as the continuous relation of point-instants it is described in terms derived from finite complexes or things, just in the same way as we apply the conception of causality in physical events to mental events though we are familiar with the causal experience first in mental life. Thus there is no circularity, to anticipate the old misapprehension, in explaining relation by continuity of Space-Time. It is a certain determination of Space-Time, afterwards known as its continuity, in virtue of which existents are related to one another. Not all relations of existents are in their immediate character or quality spatio-temporal; but if our hypothesis is sound they are always spatio—temporal in their simplest expression. Relation is, as James has so constantly and rightly insisted, as elementary a feature of the universe as ‘substantive’ things. This is true not only of our mental states, where it is apprehended in enjoyment, but of the external world, where it is apprehended in contemplation. In the end it depends upon and expresses the continuity of Space-Time. Space and Time we have seen are not relations but they are through and through relational. Neither are they mere existence, but they contain all existence. They are the stuff in which existences are related; and the terms and the relations between them are equally spatio-temporal.

Hence it is that relation is as vague a word in philosophy as being. It stands for any connection between things. Specific or empirical relations can be described, mostly by naming their terms. But relation itself, relation as such, is rarely defined or identified. The reason is apparent now. It is a category and can only be indicated by the finger as a characteristic of Space-Time or described by conceptual terms which are later in the order of reality than itself, just as we may describe red as the colour of blood.

Empirical relations.

What then are empirical relations? We have seen that empirical relations of space and time are themselves spaces and times or are homogeneous with their terms, made of the same stuff. Following a distinction drawn by Mr. C. A. Strong, James classes them as “ambulatory” relations in distinction from “saltatory” ones.1 For example, “difference is saltatory, jumping as it were immediately from one term to another, but distance in time or space is made out of intervening parts of experience through which we ambulate in succession.” James goes on to describe the knowing relation as ambulatory, because in it we ambulate from idea to percept or thing, which is of the same stuff as idea, and we ambulate though a medium of the same stuff. With that we are not here concerned. However, the distinction of the two kinds of relation, happy and useful as it is, is not of more than secondary importance. Whether a relation is of the same stuff as the terms or not, it makes the terms into a connected whole, an integral situation. From this point of view all relations are ambulatory. Moreover, on our hypothesis it is clear that in the end all relation is reducible to spatio-temporal terms. Even apart from this ultimate reduction there can be no jump from term to term, for the relation, if it is to be concrete and not a mere thought about its terms, must be some specific bond between its terms which binds them into one continuous tissue. If it falls short of this, the relation fails to relate. Whether the relation is homogeneous with its terms or not is therefore a secondary matter.

Conceived in this concrete fashion a relation may be described as the whole situation into which its terms enter, in virtue of that relation. The qualification, ‘in virtue of that relation,’ is added because terms may have other characters which do not concern the relation in question. Thus a king may, like Saul, be taller than his subjects. But the relation of height does not concern the kingly situation but a different one; or a mother may be more beautiful than her daughters, but this does not concern the maternal relation, but a relation of degree. The situation may be one of successive events as in the causal relation of the blow which fells an ox; or of simultaneous things like the rivalry of two suitors. By the ‘situation’ is meant the concrete system of circumstances which brings the terms into connection with one another. It used to be said that a relation was based on a fundamentum relationis, and the distinction of the relation and its foundation is, as I suppose, merely that the relation itself is the concrete connection between the terms set up by the acts and events or circumstances which constitute the fundamentum. Mill has admirably described this fundamentum in his Logic,2 though the reader must always discount Mill's metaphysical prepossessions. Take the relation of interval between two points or two moments. The interval is the connecting situation of the two terms, in the one case a line, in the other a duration; that interval is the transaction into which two points or instants enter in virtue of their real nature as point-instants. The points or moments themselves do not belong to the connecting situation except as they are the beginnings of that transaction. (It is a subtlety to be mentioned hereafter that the interval, as the stretch of points between two positions, is not the same relation as the interval which is the distance, between them.3) The relation of maternity consists in like manner in the history of bearing the child and the whole set of actions and feelings in which the mother is engaged towards her child and correspondingly (‘correlatively’) the child is engaged towards its mother; always with the proviso in so far as these actions and feelings on one side or the other establish a connection between the two partners, or initiate a transaction between them. For the actions and feelings are prima facie states of the mother or of the child, some of them actions, some passions; services on one part, acceptance on the other of those services. The relation is the situation or connection or transaction set up between the two partners in virtue of these services and acceptances. Similarly the relation of knowing, the cognitive relation, is not the act of knowing or the existence of the object but the situation of connection between the two. To take a further example, the relation of king to subjects is the system of acts and capacities of them or passions and capacities of them in which the king as king is concerned with his subjects, in so far as these set up a certain situation or transaction between the two sides.

These examples illustrate the truth that, not merely in bare Space or Time but in the empirical relations that subsist between things with qualities, the relation is just as concrete and just as much a reality (being ultimately spatio-temporal) as the terms and belongs to the same tissue with them. This is what James in the Psychology affirmed of spatial and temporal relations. The relation may in fact be on occasion the centre of importance and the terms, as it were, adjectival of it, instead of its being adjectival of them. The fringe may be central and the centre a fringe. Illustrations were given in a previous passage, and fresh ones may be added here. The two ends of a line may be merely its ends, the line itself, the relation between them, being central, or they may be thought of as the limits which bound the line, and, as it were, press it in—in which case the points are central. This difference of emphasis has been used by Th. Lipps to explain various illusions to which we are subject in the estimation of the interval between two points.4 Again, in a Homeric battle, it is the personality of the champions which is central, the engagement is a fringe. But in a battle of the great war, what we thought of first was the swaying backwards and forwards, the advance and retreat of the combatants, while the combatants themselves were dim and confused masses.

Sense of relations.

Every relation is a situation or more properly a transaction between its terms. If the terms, are transposed they enter into a new relation which is of the same kind as before but differs from it in ‘sense’ or direction. Thus if A is the mother of B, B is a child born of A. Two such relations differing only in sense are said to be the one the converse of the other. This result might seem at first sight to be incompatible with the account we have given of relation. Since the situation of mother and child involves both parties, it would seem that the maternal and the filial relation are not different but the same. And so they are if the terms are merely interchanged and the terms themselves remain the same. There is no difference in the situation or relation if the terms are singular. The propositions, A is the mother of B, and (the same) B is a child born of A, describe precisely the same fact, but they describe it in the light of the general relations of maternity or filial relation. Now these two general relations differ in sense, and the situations though the same in kind are different situations. There is a real difference between the propositions A is the mother of B and A is the child born of B. Actions in the first case are replaced by passions in the second and vice versa. The difference lies in the direction of the connecting movements. Similarly as between A precedes B and A succeeds B. The quality of the situation is the same but its direction is reversed. The journey from Edinburgh to London is not the same journey as that from London to Edinburgh, though it covers the same interval of space. If A is the mother of B and the child of C there are two sets of transactions which are of the same sort but in a different sense, and the situations are also different. It is only if the situation is treated as a resting one and not a transaction that the real empirical difference in the situation is overlooked. When the same situation is expressed in two different senses by interchanging the terms (Edinburgh is north of London, London is south of Edinburgh), the difference is not indeed a merely verbal one, though perilously near to it, but a difference of aspect or description, what Aristotle expressed by saying that the two things are the same but not in their being.5 The same actual situation is interpreted differently according to the plan of the general converse relation by interchanging the terms.

The above is what is meant by saying that a difference of sense depends on the order of the terms.6 It affords also another testimony to the truth that we do not have terms and relations but terms in relation. When terms are transposed the general relation alters with them in direction. Two conclusions follow. First, the difference of sense is not something of which no account can be given. If it cannot be defined, it can be described by indicating what it stands for, the real difference of spatio-temporal direction, that is of direction of motion, to which it corresponds; just in the same way as relation itself is indicated by pointing to its crude primordial basis in Space-Time. Transactions are temporal as well as spatial and are motions with direction. Secondly, we are confirmed in the belief, hinted in a previous chapter, that order arises out of the spatio-temporal character of things, is founded upon Space-Time itself, and is not prior to Space and Time, except when legitimately so considered for artificial purposes.

Relation and other categories.

Primarily relations hold between individual things. But universals have a quasi-individual existence and we may with propriety speak of relations in which universals are concerned. The relation is, however, only indirect and through the particulars. Universality communicates with relation in the strict sense, in that the universal establishes a relation of identity between the particulars. It is doubtful whether we should admit relation between a universal and its particulars; we can only do so, I think, by a substantiation of the universal. The relation between a universal and its particulars is more strictly one between the particulars themselves in respect of the universal. In the same way a thing or substance may be said to be related to a universal which is an adjective of it, though once again this is really a relation of the universal, e.g. sweet, as particularised in sugar, to the other particularised qualities and to the substantial permanence of sugar—all which matters are to be investigated presently.7 Thus we may continue on this understanding to speak of the relation of subject to predicate. What is important is that we shall not confuse the relation of subject to predicate in the ordinary categorical proposition which expresses the relation of substance to attribute with relations of space or time or quantity or quality, or the like, which are specifically relational, or express relation as such. No contortions of language, however ingeniously successful, will overcome the difference between an attribute which inheres in its substance and a relation like that of quantity which does not inhere and cannot therefore be regarded as an adjective in the proper sense.

Other categories, then, like universality or existence or quantity or causality, communicate with relation. Existence, e.g., is diverse from other existence; and the like. Relation in its turn communicates with other categories. Thus it exists as being itself a spatio-temporal occupation, what we have called the situation connecting its terms. Again it is either particular or universal: there may be plans of relation as well as individual relations. The relation of paternity or that of difference is universal, though embodied like other universals in particulars. Thus relations as universals are real and the objects of thought; though, in view of the abuse by which this truth is transformed into the proposition that relations are the special object or even product of thought, it is almost more important to insist with James that relations are perceived as well as thought and belong to the same sensible reality as terms. And, above all, universal relations are concrete, and relate terms, and they are not to be floated off from terms as if they could be abstracted from them, a danger not avoided as it seems by certain conceptions of relation.

Relations not merely mental.

Relations, it hardly needs to say, are external realities when they are relations of external things, and mental ones when they belong to enjoyments or mental things. They are in no sense subjective or the work of the mind. Some relations like likeness and difference, identity, equality, greater or less, or those expressed by the words ‘and’ or ‘but’ or ‘however,’ might seem at first sight to be eminently mental, due to comparison. They have sometimes been referred to the experience of the attention which compares (likeness) or hesitates or is obstructed (‘but’) or rejects (‘not’). Red and green are red and green; but it is we who feel them different. We might even think that one magnitude is greater than another because the act of attending has a felt excess in the one case to the other. But it is clear that the theory is circular and that the acts of attention are themselves compared (in enjoyment) in order to feel their likeness or difference or excess. These relations are, in fact, empirical variations of the category relation just as triangles and parabolas are empirical variations of Space, or the various integers or fractions are of the category number, and are felt in mind as well as contemplated outside it. Even ‘but’ and ‘still,’ though apprehended by mental acts of obstruction, are objective situations of opposition in the objects they connect. Negation is not mental only but exists in things as well, and is such difference as is asserted in contrary or contradictory propositions.

What then are the objective situations which constitute such relations as these? In the case of empirical relations, relations of a certain quality like paternity which connect things of empirical quality, the answer is plain. Since qualities are, we assume, correlated with spatio-temporal processes, the relations, however otherwise represented summarily or compendiously by their qualities, are in the end spatio-temporal, though it may be of great complexity. They are at least reducible without residue to such relations, which are themselves configurations of space-time. As to relations which arise out of categories themselves, we must leave the other categories for subsequent description. We have only hitherto dealt with existence and universality. All existence involves the relation of difference from other existence, and this we have seen is the exclusion of other existents from the occupation of its own space-time. The relation of particulars to one another under or by their universal is a more difficult matter. A convenient method is to adopt, like James,8 a pragmatist criterion. The relation is that one particular may be substituted for the other. Likeness is partially successful and partially unsuccessful capacity of substitution. Such a criterion is not open to us, for it carries the relation back to a device of human thought, whereas the relation is in the things and not to be exhausted by a secondary criterion, which gives rather a symptom than the reality. Our previous inquiry supplies the answer. Things of the same sort are in the first place numerically different and exclude each other in Space-Time. But the transaction of conceptual identity9 between them is their co-inclusion in the one Space-Time which, in virtue of its constancy, works at different places according to a plan which does not suffer distortion merely in virtue of the difference of place and time.


Likeness or unlikeness is a derivative relation, which is combined of the relation of sameness of kind with that of difference in kind. Two things are like each other only if they are different, and unlike each other only if they are identical. Hence both likeness and unlikeness are partial identity in kind. We may take as examples a white and a purple pansy, a red triangle and a red square, a tall or short man, a loud or a soft C. In all but the first case, the different kinds are empirical differences of categorial characters, extension, quantity, intensity, which are more than merely numerical differences. Space—Time provides us with likeness or difference in so far as two empirical universals overlap, or, in Plato's phrase, communicate with each other. Owing to the constancy of Space-Time it is possible for one configuration to be partially the same as one set of particulars and partially the same as another set.

The attempt has been made to explain identity as an extreme degree of likeness and thus to make ‘like’ the prior conception. Given a subject of reference A, we may arrange the similars to it in a scale of varying degrees of increasing likeness or decreasing difference. When the difference reaches its minimum or the likeness its maximum we have identity. This view was expounded by James as a psychological thesis and contested by Mr. Bradley.10 Thus, for instance, we may have sounds of the same pitch but different intensity, where as the distance in the intensity from the standard diminishes the compared sensation becomes identical with the standard.

This would seem, however, metaphysically erroneous, for distance can only mean a greater or less degree of unlikeness in respect of something which remains constant or the same. The scale of unlike or like sensations postulates identity and diversity. Being metaphysically erroneous, the view is also psychologically so; for nothing can be true for one science which is false for another. But James's doctrine admits of a different interpretation. It is true that we apprehend distinctly the shock of unlikeness or distance before we apprehend the underlying identity. And it is the series of diminishing distances ending in zero which forces on our minds the explicit identity of kind. Thus James is explaining how we become aware of identity as such and disentangle it from its concomitants. Still it remains the case psychologically (and not merely metaphysically) that the identity must be in our minds, our minds must be working in the same way and have the same sort of object, in order that we should apprehend likeness or unlikeness.11 Thus identity is primordial and likeness derivative.

A more difficult question is whether likeness (or unlikeness) is an empirical relation, as I have implied above, or is itself a category though a derived one. Though a relation of the most extreme generality, it must be declared to be empirical. There is nothing in Space-Time which requires (though Space-Time admits) the overlapping of empirical universals. It might seem that one kind involved in itself relation to other kinds, in the same way as numerical identity is of itself the exclusion of other point-instants and is therefore different from other numerical identity. But the cases are not parallel. For universality is a relation of identity between its own individuals, but is not as such a relation to other universals. Hence there is no reason in Space-Time itself (no non-empirical reason) why two individuals identical in kind should be also different in kind. Plato himself was careful to distinguish the overlapping of empirical universals from the overlapping of categories as such.

Are relations internal or external?

Relations, then, are the spatio-temporal connections of things, these things themselves being also in the end spatio-temporal complexes. Since Space-Time is continuous, the connecting situation which constitutes a relation is but spatio-temporal continuity in another form. The relations and the things they relate are equally elements in the one reality and so far are separate realities. But the business of a relation is to relate, and there is consequently no relation without things it relates, which are then called its terms. On the other hand, there are no things which are unrelated to others, which would imply spatio—temporal discontinuity. They must at least be connected in Space and Time, and it is plain that they must be connected by all the relations which arise out of the categories, seeing that categories are pervasive features of all things. Bearing these considerations in mind we can answer directly certain controversial questions about relations.

Are relations external or internal to their terms? We must answer that everything depends on what is meant by external and internal. If to be external means to have a recognisable existence as much as terms have, relations are external. If it means that relations can exist in separation from their terms or things, they do not so exist; for if they did so they would not relate. The habit of describing relations by abstract terms instead of concrete ones, e.g. the relation of paternity, is partly responsible for this misapprehension. Substitute the phrase ‘the paternal relation,’ and remember that a relation is a spatio-temporal fact which may, as in the examples given, itself turn into a thing; and it is seen at once to be untrue that a relation exists somewhere from whence it descends upon its terms like a bed-cover upon the sleepers in a common lodging-house. For instance, the cognitive relation is distinguishable both from the act of knowing and the object known, but if it existed without them it would have nothing to do.

On the other hand, if to be internal means that a relation is a quality of its terms, or belongs to them as a quality does, then a relation is not internal to its terms. Inherence is itself a relation, as between the quality which inheres and the rest of the qualities. But a relation does not inhere in its terms taken singly. On the contrary, inherence we shall see means to be included spatially in a thing; and relation from the nature of the case, as being the situation which unites things, is outside each of them spatially (or rather spatio-temporally). Thus the act of cognition or the cognitive capacity is inherent in the knower, but the cognitive relation to the object is outside that act, is its compresence with the object. Indeed, it is clear that if relation were inherent like a quality in a term, then since the relation implies the correlative term, the correlative would in some sense be internal to the other term. Thus the child would be internal to the father and the object known internal to the knower, as has in fact been sometimes held. No one would, of course, pretend that a relation can be a quality of both its terms taken together. We must therefore say that no relation is internal to its terms in this sense of inherence. But if internality of relation means only that it cannot exist without its terms, relations are in this sense internal; that is, if the things between which they exist are really terms of the relation. For a thing may be outside the relation in other respects. Thus paternity is external to a man before he is a father; but when he is a father he is a term in the paternal relation, which as it relates him to the child is internal in this sense to both. It is a further question and, as we shall see, the only question of real importance whether things can be considered outside certain relations, and which are such relations, as e.g. this one of paternity.

Thus neither of the alternatives, relations are external, relations are internal, is true without qualification or in a valuable sense. If we separate the world into terms and their relations we are making an abstraction. The things are conceived as if they did nothing to each other (which is impossible in Space-Time) or were unrelated; and the relations as if they did not relate. The world consists of things in their relations. Since this is the notion which is most obviously denied by the alleged externality of relations (let us call it the crude externality of relations), we may reject crude externality. It implies an original or crude discontinuity in Space-Time; and, as we have seen, without a primordial or crude continuity of Space-Time we could never understand its constitution out of its parts. In truth we form this notion only because we first dissect the things from the original continuum and then build it up again. We hew our stones from the quarry and then restore the quarry from the stones.

Intrinsic and extrinsic relations.

But though the question whether relations are external or internal ceases thus to be of great importance, there are distinctions to be drawn amongst relations themselves; according as they are categorial or empirical, and according as they are intrinsic or extrinsic to their terms; which raise a different question but one connected with the other question. For relations are clearly enough not external to their terms as terms. The idea of their externality only arises because things before they become terms in a relation are not necessarily the same as when they have entered it. Categorial characters and the relations founded on them belong to everything. Anything stands in some relation of space and time to other things; it has quantity and is greater or less than something else and the like. Its size may alter but some size it retains. It has attributes and is causally related with other things, though it may change its colour or affect a different substance. Strictly, categorial relations are not altered by entry into a relation, it is only the empirical determinations of them that may be altered.

Empirical characters of things are those which they have from the grouping of Space-Time elements into complexes, and empirical relations are the non-categorial relations of things which they have in virtue of their being parts of Space-Time. But under the designation empirical I include two sets of characters. One set are variations of Space-Time itself or of the categories. For example, triangularity is an empirical determination of shape, for not every finite is triangular. It is what is commonly known as a primary quality. Again ‘and’ and ‘but’ are empirical variations of the category of relation, as ‘like’ is of the category universal. The other set are in a stricter or more special sense empirical, for they carry with them variation of what is called quality, secondary quality like colour or higher quality like life or consciousness.

Now, amongst these empirical relations some are intrinsic to the things and some are extrinsic. Thus a man as man stands in human relations to other human beings; for instance, he must be the son of somebody or possess sociality. But he need not be a king or a father or a servant. His intrinsic qualities are expressed in his intrinsic relations, which therefore are in a manner internal to him. But his extrinsic relations depend on circumstances, such as juxta-position or the environment, and when he enters into these relations they are in a manner external to him. This distinction corresponds to the logical distinction of what is essential to a thing and what is accidental to it. What is most intrinsic to a thing is its typical character, manhood for instance to man; but the intrinsic qualities and relations expressing them include what is specific to the individual and all the so-called ‘properties’ which follow from them, as well as those truly inseparable accidents which are only properties awaiting the disclosure of their connection with the essential characters. Thus a man's relation to his kind is intrinsic or essential; but to have a son or a wife is an accident, and, thanks to death or the law-courts, it is what the logicians call a separable accident. It is plain that categorial relations are intrinsic also, but they are absolutely intrinsic, for nothing can be which does not carry into all its relations its categorial characters. What varies with the relation is the empirical character of the relation arising out of the category. A thing may now be above and now under another; it may be far off or near another thing, five feet or two inches longer than another. Extrinsic empirical relations may therefore be pure variations of categorial relations, or these variations may themselves be attended by qualities, as for example in the paternal relation.

Thus there are in fact three kinds of relations, the stricdy categorial, the essential, and the extrinsic. The first two classes are both called intrinsic. Empirically intrinsic relations are relatively unalterable. So long as the things retain their individuality their intrinsic relations are not changed by entering into extrinsic ones. A man remains a man though he becomes a king or a father or a slave. But just because its qualities are empirical and not categorial, the extrinsic relation may alter the qualities of the thing. Thus a man may be brutalised by the possession of power, or become egotistic or parochialised by the concentration of his affections on his child to the neglect of society. Misfortune may turn him from a genial to a sour man, he may become a disappointed man. The qualities intrinsic to the individual suffer first, but extrinsic relations may affect even the typical characters. For example, in the stages of intoxication, where a man may be said to enter into an extrinsic situation, first his voice loses its individual character, then he loses the more typical capacity of rational speech, and finally the most typical of characters, the capacity of co-ordinated movement and locomotion. A man may become subhuman by degradation or isolation, or monstrous by insanity, or he may by natural death or violence cease to be a man at all. No wonder that such extrinsic relations which alter the parties to it, seem to be external and indifferent to the real nature of the thing.

The ultimate question raised.

It is the contrast of the categorial and empirical characters and relations which is of the greater importance for metaphysics. For it sheds light upon the question whether the partial character of existents affects their claim to be considered real or true, whether, that is, we must allow reality to the parts or deny it to anything but the whole. The categorial characters of things remain, whatever extrinsic relations they may enter into, and hence their reality in these regards is unaffected. It is only the empirical modifications of these categorial characters and relations which are affected. Now partiality can only vitiate the reality of anything so far as entering into a whole changes the thing. Therefore the categorial determinations of things are perfectly and absolutely real or true. For, assuming them all to be fundamental determinations of Space-Time, we can recognise no higher standard of their reality. But empirical characters (whether modifications of the categories or qualitative) may be affected by extrinsic relations. Hence it follows that we cannot be sure that we have the intrinsic nature of a thing or a relation unless we have satisfied ourselves that no extrinsic relations will affect them, and universal propositions are therefore only possible under this proviso. This is the first limitation on empirical truth. There is a further question which the time has not yet arrived to discuss, for it belongs to the problem of the ‘one and the many’: whether the liability of all finites to suffer in their non-categorial intrinsic characters destroys their reality or only affects the difficulty of discovering it. But it will already be apparent that subject though they are to change, to conversion into things of different nature, this does not destroy their claim to be real so far as they are what they are. For they are of the same stuff as the Space-Time which connects them and in which those relations arise which may alter or destroy them. They only become in changing, as for example by death, other variations of the same matrix, and they remain relatively real.

Alleged contradictions in relations.

The difficulties which Mr. Bradley has found in the notion of qualities and relations12 are due in the first place to the inversion of the natural order of things. Begin with the primordial fact of the parts of Space-Time in organic connection with one another; qualities and relations are then mutually implied without contradiction, because, as we have seen, the very notion of contradiction is a birth of Space-Time itself, which is the ultimate standard of reference. I return to this below. But put aside this consideration. The difficulties then arise from treating relations in the abstract as if they did not relate; the opposite error to that committed by those who, maintaining relations to be external, treat them as if there were nothing for them to relate.

In the first place, relations are said to depend on qualities, and qualities on their relations, and this is thought to be contradictory. It could only be self-contradictory if the dependence were identical in the two cases. But Mr. Stout has pointed out that while relations depend on the qualities for their very being, qualities depend on their relations only for the fact that they are related, not for the qualities themselves. Thus the distance of Glasgow and Manchester arises from, depends on, is the manifestation of, the positions of those towns. But they do not owe their position to their distance, they only owe to it their distance. The towns must be there to be so many miles distant, but their distance is not something by itself which steps down and connects the town, but is the fact of their connection in space. Or, again, a man is a father because he is a male, whose functions have been realised; he does not owe his being a father to the paternal relation, but that relation implies his being a father.

Mr. Stout has endeavoured13 to simplify the discussion by adding to the notion of quality and relation that of “relatedness.” Relations then depend on qualities for being what they are, but qualities depend on relations only for their relatedness. It is difficult to see, convincing as the argument is, that relatedness adds anything to enlighten the matter. It in fact suggests that relations can be relations without relatedness, that is without relating; otherwise the distinction would not be drawn. This is the very proposition which is contested. We have the conception of qualities independent of relation and relation independent of relatedness. The last is not a fact. Nor is it true that qualities can exist outside some relation or other, though there may be a quality, e.g. maleness, which may exist outside the relation of paternity. But then the male quality is in certain relations of its own, of likeness and difference, to the female.

Qualities, terms, and relations are alleged to be “infected” with the evil of the so-called infinite regress. But this allegation appears once more to depend on the abstraction of relation from its business of relating, so that we have the ironical result that relations whose externality Mr. Bradley strenuously denies are treated in effect as if they were external. The relation it is urged is itself related to the qualities. The paternal relation is related to the father. Thus for a relation to be applied a new relation is required, not of course the same as the original relation or necessarily so; and this intercalation of relations can plainly go on to infinity. But is it not clear that if a relation is itself in relation to its term, it is not doing its work of relating? If it really relates, it relates; by itself and without the interposition of a fresh relation. If A is the father of B, his paternity is continuous with, being the situation which connects, A and B. Similar considerations apply to a subtler form of the same supposition, that a relation can be one without relating. Consider A as he is in the relation, say B, and as he is in himself, say C. There is then a new relation between B and C breaking out within A. But if B stands for a quality outside the relation, like maleness outside paternity, it is irrelevant, for this is not the quality which enters into the relation. If it does not, and the quality in itself is different from the quality in relation, the relation is being regarded as external to the quality, in other words, as not relating it to its correlative.

Space and Time—their alleged inconsistency.

These reflections are, as it seems to me, sufficient to show that relations between terms and qualities though they present difficulties do not present inherent contradiction. But I am very ready to admit that in the form in which I have presented them, in the insistence that a relation must relate, there is an undercurrent which bears us back continually to the real and given fact of continuity contained in Space-Time, without which such a postulate that a relation must relate loses concreteness. Now for Mr. Bradley himself Space and Time are but special cases of the difficulties of relation; and he would repel the assumption of an original continuity, because continuity in its conceptual description is so patently a relation between terms. For us the criterion of contradiction is a derivative of Space-Time. For Mr. Bradley, Space and Time are to be judged in respect of reality or appearance by the human or reflective criterion of contradiction, which draws its authority from our thought. We are bound therefore to examine the alleged contradiction of Space and Time independently, and our answer must be that they seem contradictory because neither the Space nor the Time which is examined is real Space or real Time, I mean that it is not even the real appearance which it is alleged to be. For each of them is supposed really, and not merely as in mathematics provisionally, to be distinct from the other. When this error of fact is corrected, the arguments against their ultimate reality are seen to be fragile.

Suppose then (what is not the case) that relations and terms are only apparent characters of things, not ultimately real; and consider Space by itself. We may plausibly maintain two propositions which seem to contradict each other: first, Space consists of extended substances (shall we say?); and second, it is a mere relation. It cannot be substances, or spaces, alone, for these themselves contain parts and involve relation among them; and every term we choose for the relations breaks up into relations without end. “Space is essentially a relation of what vanishes into relations, which seek in vain for their terms. It is lengths of lengths of—nothing that we can find. On the other hand it cannot be a mere relation. For every such relation is a relation between terms which are themselves Spaces.”14 Space is thus neither a relation nor anything else, and the contradiction, even verbally, seems hopeless. But the spaces are supposed to be resting and the relations to be distinct from what they relate. Now there is no such thing as resting Space. It is essentially temporal. Spaces, if we could conceive them at all as existing by themselves, might be stationary, and the relation between two spaces might be a kind of mechanical bond, a relation which does not relate. It might be supposed even to be the connecting or intermediate space, but there would be no cohesion, and hence the contradiction. But Space is spatio-temporal. Now Time is of its essence fluid, is succession. The Time which is in Space drives on any space into connection with some other space, and secures to it continuity. Thus spatial relation is of the very being of any two spaces, for it is their connecting situation into which they are compelled by their time. The terms and the relations are distinguishable elements in one and the same empirical fact which is spatio-temporal. For the same reason any space breaks up into parts without end because the time which is in it distinguishes it into parts within the original piece of space; and the infinity of this process being vital to space is not the bad infinity which is the counterpart of our human helplessness, but the good infinity which is implied in the real nature of the thing15 and is self-representativeness.

Let us now turn to Time. If Time be taken apart from Space it is, as we have so often seen, a mere ‘now’ and can admit no before or after. The argument starts by affirming, what is true, that the now of Time implies before and after; but it takes a somewhat different form from the argument about Space. For there the parts of Space are presented together. But when they are taken apart from Space we cannot have present and past or future presented together. “Presented time is time present.” But if the now involves before and after, there is a relation between before and after, and the puzzles of relation and its terms reappear. Either the now is a duration and breaks up into parts or nows without end; or if it is not a duration it becomes a relation between terms which are in themselves timeless, for these terms not containing a before or after are not time. Duration is either substantive and breaks up into parts, or a relation, or rather a number of relations, connecting timeless elements and therefore not having the unity necessary to time.

Now all this maze of difficulties (which I hope I have rendered the spirit of) comes from neglecting the intrinsic spatiality of Time. You may indeed admit that Time is represented by a line. The mere pictorial representation of Time by Space does not however help, for you are then faced with the difficulties alleged against Space. But if Space is of the very being of Time, Space sustains Time as it fades into the past or dawns into the future. It is then not true as an empirical fact that “presented time is the present time.” The now and the then are presented as now and then, and are presented together but not in the present of the enjoying consciousness but, as befits them, the one in the present, the other in the past.16 The then is never a part or aspect of the now. The now is continuous with the then which was and the then which is to be. Space gives to Time its continuity as Time gives to Space its continuity. Space enables Time to be Time, that is a duration of succession. Any relation between moments of time is then a piece of Time itself, and duration is not a relation of the timeless but of the timeful; and while duration is made of the instants it connects, these instants are connected by duration. For the relation and the terms are of the same stuff. This possibility is overlooked by the antagonist view, just because Time is treated as unspatial, and consequently before and after have no attachment but are degraded into aspects of the so-called present. Just as Time drives the pieces of Space into connection, Space compels the moments of Time to remain attached, and not vanish into nothingness.

What Mr. Bradley has done then is to take a fictitious or abstract Space and Time and demonstrate that they are abstractions. The effort to show up abstractions can never be praised too much. But it is misdirected when it seeks to prove that realities, misdescribed so as to be abstractions, are abstract. And now mark the revenge which the universe takes upon those who do not accept it upon its own conditions. Thought which sets up its canon of satisfactoriness to itself loses its contact with the world of Space and Time which it declares to be appearance. The “what” of things is severed from their “that”; and thought moves in a world of its own. Thought which repudiates the Space-Time of which it is an element cannot be truly concrete.

Once more we return to the truth that the difficulties of continuity and infinity, of which these embarrassments as to Space and Time are examples, arise from neglecting the initial or crude continuity and infinity, positive characteristics, of Space-Time itself. The conceptual notions of continuity and infinity build up again the original which they have begun by dissecting. But it remains true that Space-Time itself in its empirical character is the basis of continuity and infinity, of order and series, and of all the categorial characters of things which a thinking resting on human standards, not spatio-temporal ones, seeks to degrade into realities which in comparison with the ultimate are only appearances.17

  • 1.

    W. James, The Meaning of Truth, New York, 1909. ‘A word more about Truth,’ p. 138. For the whole subject of relation see his Appendix A on ‘The thing and its relations’ in A Pluralistic Universe, New York, 1909.

  • 2.

    Logic, Bk. III. ch. ii. sec. 7, and particularly ch. iii. sec. 10. I mean by Mill's prepossessions his leaning (1) to subjective idealism in metaphysics, and along with that (2) to atomism in psychology.

  • 3.

    The distance between two points as distinguished from the stretch of points between them is their unlikeness in respect of position. [Cf. the distinction drawn by A. Meinong between ‘difference or interval’ (Unterschied) and ‘unlikeness’ (Verschiedenheit), used below in respect of intensity, in ch. vii. (Über die Bedeutung des Weberschen Gesetzes. Hamburg, Leipzig, 1896).] The points are identical as points but different in position. Now such unlikeness in position is the situation constituted by the interval, but that interval taken not as divisible into points but as the occupation of a space to a certain extent taken as a whole. It is a matter of subsequent experience that degrees of spatial unlikeness are themselves expressible by extensive measurement, so that one distance may be two feet and another three feet. Consequently, though distance of two points is as a matter of fact the spatial interval of the two points and can be resolved into parts and measured, it does not follow that any distance, as between the intensities of a quality, e.g. the sound C, or between qualitative units themselves like pitches of sound, is necessarily extensive, that is, is an extensive quantity. See later, ch. vii. on intensive quantity, pp. 307 ff.

  • 4.

    Th. Lipps: Raumästhetik und geometrisch-optische Täuschungen. (Schriften d. Ges. f. psych. Forschung (II. Leipzig, 1893–7, Section 3). Thus the empty horizontal distance between two points looks shorter than a horizontal line of the same length, because the points in the first case are more independent and seem to shut in their space interval.

  • 5.

    Εστι μεν το αυτο, το δε ειναι ου το αυτο. Aristotle's example is the road from Peiraeus to Athens.

  • 6.
    In so-called logical conversion there is no difference of ‘sense’ involved. There the relation or “pseudo-relation” as Mr. Russell calls it is unaltered. Conversion alters or may alter the quantity of the terras. Here, too, the converse is not a mere verbal change.

    I have not referred to the accidental matter that in some relations, symmetrical ones, the converse is the same as the original relation; for example, equality. On the whole subject of the sense of relations see Mr. Russell's Princ. of Math. ch. ix. pp. 95, 96. My differences from him will be plain from the text.

  • 7.

    Ch. vi. A, ‘Substance.’

  • 8.

    Some Problems of Philosophy (London, 1911), p. 103.

  • 9.

    W. James, Psychology, vol. i. p. 528 ff. For the controversy by the two writers see Mind, N. S. vol. ii. pp. 83, 208, 366, 509.

  • 10.

    Compare on this point F. H. Bradley, Logic (London, 1883), p. 422.

  • 11.

    Appearance and Reality, ch. iii.

  • 12.

    Cf. for the phrase Mr. G. E. Moore's paper on Identity, Proc. Arist. Soc. N. S. vol. i., 1900–1, pp. 103 ff.

  • 13.

    Proc. Arist. Soc. N. S. vol. ii., 1901–2, ‘Alleged self-contradictions,’ etc., pp. 1 ff.

  • 14.

    Appearance and Reality, ch. iv. pp. 36–7 (ed. 1).

  • 15.

    For the distinction of the two sorts of infinite regress, see B. Russell, Principles of Mathematics, ch. iv. pp. 50–1, § 55.

  • 16.

    In a later chapter (A. and R. ch. xviii.), Mr. Bradley completes his assault on Space and Time by suggesting that there may be more than one Space or Time, and that in different Times the order may be reversed. This raises questions which belong to a later stage, when we are considering ideas in their relation to reality. I much regret that my criticism of Mr. Bradley should be thus divided, but I cannot discuss everything at once. (See Bk. III. ch. viii. Suppl. Note.)

  • 17.

    Above, Bk. I. ch. iii.