Existence is identity of place and time, or numerical identity, and distinct from other such identities. Universality is identity of kind. It is the existence or subsistence of a universal or concept which unites its particulars, which they imitate or in which they participate, or however else we may provisionally and traditionally describe the relation between the universal and its particulars—the transaction in which they are engaged. An individual is a particular as determined by its universal. Strictly speaking, there is no such thing as a particular or a universal. All things are individuals. But every individual possesses particularity which separates it from others of the same kind, or under the same universal; and it possesses universality which converts its bare particularity into individuality. Universality is thus a categorial character of all things. Such a thing need not be a thing with continued existence in time. It may be a sensory object, a flash of colour, or of sweetness, which is momentary and yet as being of a certain kind, red or sweet, is individual. A bare event or point-instant is particular as distinct from other events, but as qualified by the universal character of existence, its particularity is determined in total Space-Time and it is individual though from the nature of the case momentary and punctual. Can we discover in Space-Time any fundamental feature in virtue of which the empirical complexes within it possess universality and hence are individualised so that throughout the world we have existents embodying laws of construction?
Let us begin with an individual of a low type or organisation, for example a marble ball whose particularity may be supposed secured by its markings of colour. Let us suppose for simplicity that these do not change in colour, and let us disregard the intramolecular movements of the ball, confining our attention to its spherical form. The ball changes its place in space and time as the earth moves, and may also be displaced on the relatively resting earth. Its universality is that in all these changes it is unaffected in form; that wherever it is, it undergoes no distortion, and this arises from the uniformity of Space-Time or, as it may be expressed equivalently, from the constant ‘curvature’1 of Space. The same account applies obviously to balls which are turned out from one machine, so that they differ from one another, let us say, only in their place and time. They are identical in kind because owing to the constant curvature of Space their form is unaffected, and so far as form goes one can take the place of the other. A round ball does not become in another place elliptic or crooked.
We may next take a more highly organised individual, say a person whose life may be regarded as arranged on a certain plan. This is the best instance of the singular universal. Lotze compares it to the structure of a melody. It is such a plan of a man's personality which an artistic portrait endeavours to express, whereas a photograph gives only a picture of the man at a passing moment, unless by artistry of technique the hardness of the momentary outlines may be softened and the photograph approximate to a portrait.2 This individual person contains indeed besides universality the category of substantiality, or substantial identity, a category yet to be investigated. He is highly complex, and the parts are in those conditions of motion to which, as I here assume, qualities are correlated. Yet in all his changes of space and time a certain plan of construction is preserved. It is preserved in his internal changes of body or mind, so that for instance he does not alter the colour of his skin from hour to hour like certain crustaceans; and so that a certain balance of actions is maintained. But it is also preserved not only in these subtle changes of space and time within his bodily outlines, but also in the grosser external transferences from position to position in space or time. I shall call a grouping or complex of point-instants or pure events a configuration of space-time or of motion. Now the universality of this highly complex person (as distinct from his substantiality) means as in the simpler case of the ball, that though at each particular moment of his life his configuration varies and is particular, the configuration follows a certain plan and remains within the limits of that plan. In other words, his configuration remains relatively unaltered while he changes in his place or time or both. However much he be transferred or otherwise more subtly changed internally in space-time, he preserves a certain proportion of his parts and is undistorted. When he is so distorted as to forsake the plan he becomes (as happens for instance in double personality) a different individual. Once more, in this more difficult case, he being himself a highly intricate complex of space-time owes his universality to the uniformity of his medium, that is to the constant curvature of Space.
Now the identification of universality with this uniformity was easy enough with our single ball, or our identical balls, for here the configuration was repeated exactly. But with the person the actual configuration changes from moment to moment and only the plan of it persists. This difficulty which was slurred over above is still more pressing, when we come to the ordinary generic universal, like tree or dog or justice. Dogs vary in size and shape and disposition. How then can we speak of the universality of dog as a plan or form of configuration of space-time, since the spatio-temporal patterns of no two dogs can be superposed and fit into each other?
Let us follow our usual prescription and turn to our own minds which we know more intimately than external things. There, in our minds, we find habits which are dispositions of response to situations of a certain kind. On each occasion the response, let it be an act of will like telling the truth when we are asked a question, or the simpler instinctive response to a perception like holding our hands to catch a ball which is thrown to us—on each occasion the response is particular or rather individual, but it obeys a plan or uniform method. It varies on each occasion by modifications particular to that instance. It may be swift or slow, eager or reluctant, slight or intense; the hands move to one side or another with nicely adapted changes of direction according to the motion of the ball; the words are adjusted not merely to the subject of the question, but to the requirements, which vary in each case, of exactitude and sincerity or of that tactfulness in telling the truth which takes account of the mental condition of the questioner, and regards his intelligence and his feelings and susceptibilities, so that there is a fine art of truth-telling as there is of catching a cricket ball. But however great or fine the variations in conduct, they have their limits within the plan of the response which is uniform. The response proceeds with these allowances for modification, or rather with these necessities of modification, on established and constant mental lines which are also constant plans of direction within the neural space. We may tell the truth facing a person or with our back to him, but within that neural space which we enjoy in mind the configuration of the response follows a certain plan. In all the variations of particular response there is no distortion of the pattern of response.
What mental dispositions in general are, in distinction from their effective realisation in actual conduct, I need not inquire too minutely. I am content to regard them as psychophysical, indicating by that word that being themselves physical they are ready upon occasion to start up into mental life. It may be that, as some think, there is a perpetual process of fainter actual functioning along the neural lines. It is at least certain that the disposition is not a bare physical one, but at least physiological. It is not represented merely by purely anatomical patterns and is something more than a mere physical arrangement, such as is supposed to exist in a permanently magnetised steel bar through the tilting of the molecules in one direction. It is more than this, because the elements which are tilted in our neural lines are living cells. This important question I must leave. But at any rate besides those mental habits which are purely psychophysical, or latent, we can detect conditions of mind which are actually conscious, and though not definite and individual but vaguely defined have a more special claim to be considered mental dispositions or schemes of response. The underlying psychophysical disposition may not be actualised in an individual mental response, but in a mental outline or scheme of one, which is a diagram of response, but yet is mental. It may betray or reveal itself in shoots of consciousness which are not so individual as if I were actually performing the action, but are of a specific sort or on a recognisable plan. I mean by the term specific, to take an illustration, that the vague premonitory shoots of consciousness which anticipate at times the actual winding up of my watch at night are recognisably different (I should say in ‘direction’) from the premonitory shoots of consciousness connected with some other habit, like turning off the electric light in my study before I go to bed. These attitudes, rather than actions, of mind can be verified most easily in the uneasiness which warns us to perform the action or reminds us that we have failed to do so. In each case the uneasiness is of a different sort, and has a vaguely specific direction.
The clearest instances, perhaps the only ones, of these mental schemes in the proper sense, are afforded by the action of conceiving, of which concepts or universals are the compresent objects. Observation conducted first under ordinary conditions and then under the conditions of the laboratory3 has convinced us of the existence of ‘imageless thinking,’ which seemed so inconceivable to some earlier psychologists. Though our thinking does not proceed without attachment to some particular of sense, it may be to a word, it may be to the button which we twist while we think, or the lock of hair which we pull to the distraction of our companions, it may be to some mere external circumstance contained in the conditions of the experiment; yet it may proceed without any individual embodiment or illustration of the thought itself:
By the pricking of my thumbs
Something wicked this way comes.
The witch is a true psychologist. The pricking of her thumbs is the particular sensory experience to which the thought of something wicked (observe the conceptual expression) is attached though it is no image of wickedness.
Habits of Space-Time.
Turn now from mental habits or universals to the non-mental universals which are found in external things. They are ‘habits’ of Space-Time, and empirical universals like dog or tree or justice are possible because Space-Time is uniform and behaves therefore on plans which are undistorted by difference of place and time. There is only one respect in which the transition from mental habits to habits of Space-Time appears to limp. Mental habits occur in assignable neural places, though the limits of these areas are extensible. But the habits of Space-Time are localised indifferently all over Space-Time. Given the appropriate empirical conditions a triangle or a dog may be drawn anywhere according to their universal plan of configuration. We have indicated in a previous chapter the reason for this difference between mind and Space-Time.4 The mind is not like Space-Time an infinite but a finite whole. Moreover its consciousness of things is awaked through the senses with their highly specialised machinery of nerve endings and nerve centres and paths. For specific objects specific means of apprehension are necessary, and vision, taste and the other senses, and still more the complex patterns for apprehending complex objects have their specific lodgings in the brain. What is said here of mind or consciousness applies of course with proper qualifications to all kinds of finites, so far as these have specific methods of response to their surroundings. Such habits are localised in specific portions of the spatio-temporal structure; as will be clearer in the sequel. Further it follows as a consequence of the want of localisation of the habits of Space-Time to definite portions of it, that different habits may have certain parts of Space-Time in common, though not at the same time. Thus the same point may be the beginning of a circle or a parabola; though the point-instant will have different values in the different cases, because it will be the beginning of different lines of advance.
I may add that the comparison of universals with habits is not made for the first time by me, though I do not know that the comparison has been made with the same implications.5
Universality is therefore a category or determination of Space-Time. Every finite possesses universality or identity of kind in so far as it admits without distortion of repetition in Space-Time, that is, can itself undergo change of place or time or both without alteration, or can be replaced by some other finite. Empirical universals are plans of configuration of particulars which are identical in kind. They may be called patterns of configuration or, to use the old Greek word, ‘forms’ of Space-Time. They are essentially in their simplest terms spatio-temporal forms or shapes.
If this is true of empirical universals like dog or plant or triangle it is still more obviously true of the most comprehensive of all universals, the categories themselves, which are a priori plans of configuration. I am anticipating the complete verification that they all of them are fundamental determinations of any space-time. In so far as relation or substance or existence, etc., is an a priori determination of Space-Time, these are forms or plans or patterns of configuration of Space-Time or motion. They are the key plans of all plans of empirical determination. The rest of them excluding universality communicate with universality, and universality itself stands for the fact that everything has its form. We cannot say that universality itself is a universal any more than we can say that the empirical universal dog is a dog. Universality is the category in virtue of which there are universals, whether empirical or a priori ones.
Universality is thus the name of the constancy of any existent in Space-Time, so far as it is constant, that is, its freedom from distortion wherever it is in Space-Time, and this is equivalent to the uniformity of Space (or what is the same thing, Space-Time). Just as existence is the name for occupation of a space-time in relation to other occupation.
Why Space is uniform.
If it be objected that the uniformity of Space and with it Space-Time is after all only an empirical character and that there need not be such constancy, I can only answer that Space-Time though itself categorial or a priori is empirical in the sense of being presented in experience with certain characters. I should be content with this simple fact. It is true that a geometry may be imagined whose ‘Space’ is not uniform. But our Space is not such, whether the Euclidean or some other geometry be the closest approximation to the description of it. For I am not assuming Space to be flat, with zero curvature, but merely to have a constant curvature. In a ‘Space’ which is not uniform I do not see how there should be universals, for each plan would suffer distortion as it was transferred.6 The world would consist of nothing but particulars, not even of individuals, for there would be no meaning in the contrast of individual and particular without the idea of a plan of configuration. But if we seek to understand the deeper meaning of the constancy of Space and Space-Time we may refer to the relations set out in a previous chapter between Space and Time, though with the same feeling of modesty in our assurance as beset us there. Time as we saw was not an addition to Space, but the characters of Space were conformable to those of Time. It is the conformity of Space to the one-dimensional Time, which is uniform—flows uniformly as Newton said—that involves with it the uniformity of Space. Universality is thus, in our drastic metaphor, begotten like the other categories by Time on Space. In all this the constancy or uniformity of Space-Time or Space is carefully to be separated from the notion of the bare homogeneity of Space or Time, in the sense that there is imagined to be no real difference between one part of Space or Time and another. This notion is justly the bugbear of philosophers; though some have thought to retain it by distinguishing between conceptual and perceptual Space or Time. I need not now revert to the errors which underlie this distinction, which would make conceptual Space a falsification of perceptual Space. But in fact we have seen that Space and Time differentiate each other: that every point differs from any other by its instant and every instant by its point. Point-instants are concepts but singular ones, and each point-instant is an individual. As Mr. Russell has observed, points seem all alike to us only because we have no interest in discriminating them. The uniformity of Space or Time or Space-Time does not mean this supposed conceptual indifference of point-instants but merely that a given plan of configuration is repeated in any part of Space-Time where it occurs without distortion.
Objections and elucidations.
We have first to enter a caveat against the old possibility of misunderstanding which has been noted from the beginning. Plans, it may be thought, of space-time are nothing but the universals of different patches of Space-Time, the circular plan, for example, the universal of all circular patches. They are but particular applications of a conceptual universal which is prior to Space and Time and is supplied from understanding or thought, it matters not how. Universality belongs to Space-Time but comes down upon it, either it may be imagined from mind or from some eternal region as the Forms are supposed to enter into Space by Timaeus. Our answer is the old one. It is not because there are universals that any space-time has a plan, but because Space-Time is uniform, or constant in curvature, and admits a plan that existents which are patches of space-time possess universality. Or the misunderstanding may take another form. A constant curvature means that the curvature is the same, and there is a prior notion of generic sameness. I answer that the constancy of curvature is an experienced or empirical fact or character of Space-Time, and that it is this which makes particulars of a sort the same in different positions. Sameness (generic identity) follows from the constant curvature; the logical denomination of things follows from or expresses the real nature of Space-Time.
These are misunderstandings. There is however a different objection to meet which has much better pretensions to be heard. The very name of plan or pattern or form or law implies, it will be said, the idea of universality; and the problem is concealed by a word. For a plan is something of which many copies are possible. If only a definite configuration of space-time were concerned, like a right angle or a definite loudness of the note C, we might be content with a reference to the constancy of Space-Time. But when you allege that an acute angle at A and an obtuse angle at B are instances of one and the same plan or habit, the angular habit, you are really under the protection of a name introducing the universal ‘angle.’ For there is no one configuration of space-time which can be called an angle. Thus to account for the generic identity of angles you are introducing between the constancy of Space to which you appeal and the particular angles a universal under the name of a plan, which is the condition under which that constancy can be applied to individual angles of such great variation. The universal you say belongs to Space-Time as such, but a new universal is needed on your own showing to mediate between the particulars and Space-Time. This objection is highly relevant, and it is analogous to one of the kinds of objection taken in ancient Greece to the Forms under the name of the argument of the ‘third man.’7 Besides the individual men and the form Man there is a third man. But it is in truth groundless as directed against the present conception of universals. It arises only from the latitude of the universal in question. Angle means a configuration formed by two straight lines of divergent directions in a plane. The habit of Space-Time to which it is equivalent is the possibility of the existence of such a configuration at any point. The magnitude of the angle does not enter into the plan. If the universal were the limited one of an angle of 60°, there would be no variation of magnitude in the copies. The plan triangle allows for variation in the magnitude of angles and sides within the limits fixed by triangularity. The four-sided figure with equal sides is similarly a plan or pattern which is satisfied by the rhombus or the square.
What is true of the empirical universals of geometry, which have been chosen in these examples, is true in like manner of ordinary ‘qualified’ universals, like dog or tree or justice. The relation between the universal and the particulars is the same in these cases as the relation between the universal triangle or circle and the particular triangles or circles, which Plato called mathematical objects. For a particular dog is in the end a spatio-temporal configuration, where the groupings of motion are such as to have sensible qualities correlative with them. So regarded a particular dog differs from a particular triangle only in its much greater complexity. It too is spatially considered a geometrical figure, but of an order which is too complicated to be treated by the geometry of simpler figures. Particular triangles are perfectly rectilinear because the triangle is a figure ideally constructed within Space, or selected from it. But irregular as the contours of a dog may be, he is none the less a geometrical figure. Mathematical particulars are therefore not as Plato thought intermediate between sensible figures and universals. Sensible figures are only less simple mathematical ones. This is the whole of the difference. In any case whether it is with a mathematical or a qualified universal that we are concerned, there is no question of any plan mediating between the particular and the uniformity of Space-Time; the plan is an embodiment of that uniformity. The universality of the plan is the capacity of Space-Time to respond on each occasion according to that plan.
Thus the universal is related to its particulars as the equation of a curve is related to the instances of it which may be obtained by varying the so-called constants in the equation. For example the equation to the parabola (y2 = 4ax) is universal as the formula which applies to all curves described by the formula, where the element a varies.8 A more satisfactory statement still is that the equation of the second degree Ax2 + By2 + Cxy + Dx + Ey + F = O is the universal of all conic sections which can be obtained by appropriate values in the capital letters. This brings out most clearly how the universal or plan is the key to the utmost range of variation not merely in magnitude but in configuration within the limits of the pattern configuration. For it includes under its formula such different configurations as the ellipse and the parabola and the hyperbola which yet are subject to the one more comprehensive pattern or habit of Space-Time. The formula of the circle whose centre is the origin x2 + y2 = r2 has a much smaller limit of variation in the magnitude of its one constant, while the equation x2 + y2 = 36 is limited to the one definite kind of configuration.
It will be observed that I do not call the equation to the circle or the parabola the universal of the points of which the circle or parabola consists, the significance of which reservation will appear in another context.9
Subsistence and existence.
It has not seemed to me necessary to insist that the universals of physical things are non-mental; for this is the only statement which is consistent with the whole spirit of our hypothesis, even if the mentality of Forms had not been summarily disposed of by Plato himself.10 But what kind of reality, it may be asked, do universals possess? Half the difficulty, or perhaps all of it, disappears when once it is admitted that particulars are complexes of space-time and belong therefore to the same order or are of the same stuff as the universals which are plans of space-time. The objections taken to the conception that the particulars participate in the universals or imitate them, a conception which plays so great a part in the history of the theory of universals, vanish upon this doctrine. The argument of the ‘third man’ arose from the apparent separation of the form from its particulars because the particulars were sensible. But if sensibles are made of space-time stuff they follow their spatio-temporal pattern, and whether we call the relation one of imitation or participation, either designation is valid and true. Of the two, participation is to be preferred because imitation suggests a separate independent reality of the universal, and participation means that the plan is not copied but modified to suit the special circumstances of time and place.
To say with Aristotle in his mood of antagonism to his master that the universal is predicable of the particulars converts the universal into a simple predicate and risks confusion with the notion of the inherence of a quality in its substance, a very different relation, the discussion of which belongs to the head of substance. For the proposition ‘this is yellow or sweet’ has an entirely different meaning from the proposition ‘this is a dog’ or ‘this is a yellow or a sweet.’ Taken in extension this last proposition means that this is one of a class, but that class is itself defined and designated (denoted) by its constitutive universal. Taken in intension the predicate here is not a quality at all but a plan of construction. The universal is never therefore something which we assert of its particulars or which merely obtains of its particulars, and the universal does not depend on the predication but the predication on the universal.
On the other hand to call the universal an independent reality appears to give it a unique position from which as it were it should descend upon its particulars and inform them with its spirit. It seems to transfer universals into a neutral world, whereas their stuff is the same as the stuff of their particulars. The same objection applies to the notion that the universal is the limit towards which the particulars are a progression. For the limit of a series is never itself a member of that series but outside it.11 Thus the series, 1, 1 + ½, 1 + ½ + ¼, etc. approaches to 2 as its limit, but 2 is not a member of the series. It is true that the limit of a series is of the same order as the series, the limit of a series of numbers is itself a number, and this is what makes the conception of universals as limits enlightening. But the limit is constitutive of the series only to the afterthought which recognises that the series has the limit. What corresponds in the series to the universal is the law of its formation and this is not outside but ‘within’ the series, though it is not of course a particular member of the series.
The universal exists therefore only so far as it is realised in its particulars and it has such reality as, to use a phrase of Mr. Bosanquet, is possible to it. It may be said to have that reality of existence which is called subsistence. For it is free from limitation to one particular space and time. But subsistence must not be understood to imply a neutral being which is distinct from the world of spatio-temporal existence. The universal subsists in so far as its particulars exist and is spatio-temporal though not particular. The universal is nowhere and nowhen in particular but anywhere and anywhen, and in Hume's language is in readiness to start into being (which is existence) when the occasion calls. It is not timeless or eternal as being out of time, but as being free from limitation to a particular time.
Moreover not only does the universal exist in this qualified sense which is called subsistence, but we must add, extreme as the statement may sound, the universals are spatio-temporal, physical, biological, mental, according to the level of existence to which their individuals belong. Universals are not necessarily like triangle or square merely spatio-temporal. When we reach rocks or plants or minds, we have plans or habits of Space-Time which include plans to which various qualities are correlated and which are a plan of the combination of such plans. In this sense we must say, though the full meaning cannot be developed, at present, that universals of physical things are physical, and that the universal man though it is not a man is man or human. A physical universal is a physical subsistent and a mental one a mental subsistent. This does not interfere with their being ultimately all alike spatio-temporal, for all things no matter what their qualities are bits of Space-Time.
In order to realise more clearly the meaning of the subsistence of universals we may first revert to mental dispositions. Such a disposition is either experienced consciously in imageless thought (by what may be called a diagrammatic process of mind) or else we can conceive it as a neural (psychophysical) disposition, or physical tilt of cells. Now our habits as we saw are localised. But there is nothing lower than Space-Time in which to locate a disposition of it. What then is this disposition? It is certainly not something which we who think can say, aprés coup, about Space and Time, merely because upon occasion we have particulars of a certain kind which we put into classes. On the contrary, only because of the universal and at its guidance can we arrange in a class. It is itself something spatio-temporal. Nor is it a bare potentiality. When a part of Space-Time is not occupied by a real dog, it is occupied by something else, if not by something material, then by Space-Time. For Space-Time is always full; there are no vacua in that matrix of things. It differs only at one moment and another (and the difference may be enormous) by the different configuration of its motions. Thus there may be no dog or chalk triangle at this moment here in the space before me—those are not the lines of advance within that space—yet when the occasion comes the dog may be there, because the actual grouping of movements has been replaced by that grouping of movements, with their correlative qualities, which is a dog. Provided of course the empirical circumstances do not impede; for no dog can replace a stone wall which is not removed. To take a more obvious instance, which is suggested to me by an interruption to my writing, a volume of space-time filled by wind may be displaced by that highly complex grouping of qualities, my body, as I walk. We may make the matter easier for imagination by saying that any space contains actually all geometrical patterns as soon as the time comes to draw them.
Such instances do nothing more than illustrate the feature of Space-Time that within any part of it the distribution of point-instants may take any plan permitted or required by the empirical conditions. It is only in this sense that the plan of a universal is potential; its potentiality is a reality consisting in the readiness of Space-Time to adopt it, because Space-Time is built up of point-instants whose place and time are perpetually changing their distribution. This is the general potentiality of Space-Time. Its specific potentiality, as when an acorn is said to be potentially an oak, is describable in more specific real terms. But all potentiality is real though it is not an existence in particular. And in fact can anything be more real, a more concrete (though elementary and not specific) determination than the constancy to which all universality has been traced? From the point of view of this question, perhaps our labour to give a more definite meaning to subsistence is labour lost.
Universals then though they have not existence in particular have subsistence in so far as Space-Time suffers or allows existence according to the plan of the universal. They are the formulae according to which Time brings forth particulars in a Space which can receive this plan. Time is not therefore the moving image of eternity as Plato or Timaeus said, holding the forms to be eternal. The forms are not imposed on Space. But the Time which is the life of Space brings to birth particulars in their image.
Universals are not more real than their particulars but have greater significance, as the general equation to a circle is of greater significance than the same equation with a numerical magnitude assigned to its radius. They are concrete in the sense that they are not abstract general ideas such as Berkeley directed his invective upon. They are the constitutive plans of things. They are spatio-temporal and have all the concrete reality of Space-Time. For the matrix and its determinations are as concrete as the crystals deposited from it.
Universals not lifeless.
It has been thought that extramental universals, owing nothing to thought save that they are compresent with thinking and owe to thinking that they are known or thought of, must be lifeless—‘petrified’ is the word used.12 Nothing can be farther from the truth. Universals do not move or act; it is their particulars which do this. But they are the plans of motion and action, to which all action conforms. Like the cockles and mussels of the fishergirl's song they are “alive, alive, O!” But they do not owe their life to mind. On the contrary, the life which universals possess in mind is but an example of the spatio-temporal vitality of all universals. Mental universals are mental habits, and it is in virtue of the dispositional character which they realise that particular mental acts work their effects. The best known instance of this is found in ordinary association of ideas. One particular idea having been united with a second in an interesting experience, another idea which is like the first calls up an idea like the second. For an idea is never repeated identically. What is repeated is its disposition. The new idea which sets this disposition going, set in action the connected disposition which is actualised in a particular. The original experience was a1b1. The new experience is a2b2. The two a's are particulars of the mental habit A, the two b's of the habit B. The variation of b produced by experiencing a2 rather than a1, leads to the reinstatement of B in the form b2 rather than b1, by the operation of what Mr. Stout calls relative suggestion, which is in fact an instance of the organic character of mind. All this has now become the common possession of psychologists. Nothing in it except what is biological is peculiar to mind, and what is biological is shared by mind with life. The plants also exhibit the working of relative suggestion in adapting themselves within settled lines to changing circumstances. In the end the character of all action physical or mental depends on universals, and in the end all universals, mental as well as physical, are spatio-temporal habits, though they are patterns of other qualities as well.
It is in fact the cardinal defect of universals as conceived by Plato or the Pythagoreans that they were changeless and immoveable and eternal. For not even the mind of Plato could be free from the habits of his age, one of whose tendencies was to seek the highest ideals of perfection in gravity of action and statuesque repose rather than in restless motion.13 Hence to account for motion he had to look for another source which he found in soul. It is claiming no great credit that for us universals should have from the beginning the form of motion,14 should be not merely spatial but spatio-temporal. They are not particular motions but the plans of motion and they are actualised in particular motions. As the empirical universals vary from bare geometrical patterns to the universals of material and living and thinking things they become plans of motions which are correlated with qualities. They are plans of configuration of qualities or configurations of matter or mental action. But they are never dead or petrified, because in the end they are spatio-temporal plans and instinct with Time. And above all they are never bare potentialities, the creatures of abstract thinking, but possess such actuality as they can possess, which is not particular actuality or existence. The laws of the construction of things and those of the relations of things to one another are not therefore inventions of the mind imputed to nature, but part and parcel of the constitution of nature, and far more important parts than the particular facts from which they are supposed to be merely derived by our human thought, as if thought could make anything real which it does not find.15
Universals and repetition.
Whatever difficulty there may be in conceiving the nature of a universal and its relation to its particulars, one thing can at least be affirmed, that without repetition or the possibility of it there would be no universality. The idea of a plan contains two features which must be distinguished. A plan is a complex of parts, and accordingly all universals imply such complexity, except in the limiting case of bare existence or point-instants where there is simplicity; though even here an instant is intrinsically (not merely empirically or as a matter of fact) repeated in space and a point in time; point-instants being the bare conceptual elements of Space-Time. A plan or universal involves, outside this case, relations of parts, or when it is a ‘law of nature’ it involves relations of things to one another. The relation within such plan or law is preserved under all instances, though with indefinite scope for variation so long as the relation is preserved. What these limits are is a purely empirical matter. There is no categorial reason why there should not be human beings two miles high. The reason is found in the empirical conditions, the difficulty of obtaining food enough, the extreme difference in the temperature of the atmosphere at the head and the feet, and the like. The experiment has been tried on a modest scale with mammoths and dinosaurs and has failed.
But the internal complexity or systematic character of a plan is not its universality; and because of the ambiguity of the word plan, law, which means universality, is preferable. To a universal, whether the law of construction of a thing or of relation to other things, repetition or the possibility of it is vital. A generic universal may as a matter of fact never be repeated empirically. There may be only one instance of the generic universal ‘a Napoleon.’ But as a universal and not merely a plan it implies repetition. The singular universal, e.g. Napoleon, is repeated in its moments of actual existence. Apart from possible repetition a plan would be only the plan of a particular, and would be in fact not a plan or law but an actual particular, not even an individual. This is in fact only to say again that a universal is a habit.
The problem of multiplicity.
Why certain universals should occur only once and others repeated in varying numbers, why there should be actual repetition of complexes of events, is for the moment greatly dark. It again concerns the empirical order of things, of which we know so little and of which philosophers can say even less. There are multitudes of atoms of gold, and multitudes of electrons from which a selection is made to constitute atoms, and many trees and dogs. The inorganic world spawns, like fishes in the organic world. The universe in its lower levels behaves apparently (does it do so really?) as if endowed with life. Knowledge of this kind we have, but what more have we? We accept repetition of things in their kinds as an empirical fact. To do so presents, it must be confessed, a problem of the gravest difficulty, which is only mitigated and not removed by the consideration that the multiplicity of individuals of one type, or that of types which fall under higher types, is not bare repetition, that the many specimens differ from one another however slightly, that even an atom is only a statistical conception, the conception of an average of individuals all varying about a mean. The fact of multiplicity remains. Supposing it to be true that no reason can be found in the nature of Space-Time itself why types should repeat themselves in many instances, we should have succeeded in overcoming the difficulty of how universals can be realised in particulars, only to be left with the problem, apparently insoluble, of how there come to be particulars at all. Later we shall see that quality is the distinctive empirical element in things, as contrasted with their a priori or categorial characters and with the relations of empirical things which arise from their being complexes of Space-Time. It may be that we must regard the multiplicity of nature in instances as something equally empirical. It may be that the problem though not now soluble, and I cannot see at present the solution of it, may ultimately admit solution, as I hope. I shall return to the matter at a later stage.16 At present we must insist that if there were no universals which as a matter of fact were repeated in their instances, we should not have reached the conception of universals. And more than that, if there were not the categorial possibility (that is the a priori possibility) of empirical repetition, not only would universality not be known (which after all concerns only human beings) but there would be no universality.
The distrust of repetition.
Several reasons exist which account for the tendency on the part of certain writers to push too far their reaction against the teaching of sheer empiricism which, not being empirical enough, disallows the reality of the non-empirical. They neglect the claims of repetition to be regarded as vital to universality and to be distinguished from the systematic nature of a universal. One reason is the fear of bare repetition, of instances which are not variations of a plan, but manufactured articles which exactly reproduce each other. If such repetition existed the use of instances would lie merely in their number. But as Mr. Bosanquet has so impressively taught us, the value of instances is that by their differences of character, not by their number, we are able to control one case by another and render precise the fundamental law which is involved and which may be masked by irrelevant circumstances or counteracted by others, “to purify” the law “by exceptions and finally limit it by negations.”17 When a single instance is of the right character it may be sufficient to establish a law; and the business of the logician is to define that Tightness of character. On the other hand, mere number of instances which we roughly call the same is only useful when analysis is impotent, and it can serve us because we can reason backwards from the relations between the number of various groups of instances to the probable character of the causes which are at work.
Now our conception of repetition renders this fear groundless; it means that repetition brings not exact identity but modifications within limits of an identical plan of construction. The more comprehensive is the plan, the greater the room left for variations which may themselves be specific variations of kind. Bare repetition it may be affirmed does not even exist. Manufactured articles are not identical though they may be identical within certain limits of precision. It is, however, true that the more closely instances reproduce each other the less useful they are for scientific discovery. But the mere difference of place and time which makes an instance numerically distinct may supply empirical conditions sufficient to lead to variation utilisable for scientific method.
A second reason is the fear lest laws or universals should be mistaken for the abstract generalities or generalisations which Berkeley demolished, which are derived or are supposed to be derived from their particulars by a process of omission. The specific features of individuals which give to things their ordered variety and richness of colouring are omitted; their common features are retained, and it is the business of thought to discover and arrange these generalities. Such abstractions are often spoken of, by those who justly repudiate them, as ‘class-concepts.’ Correspondingly, laws of nature have sometimes been conceived as abstractions of the common elements in the relations of things to the neglect of the variations of those relations. Now it is evident enough that useful as such abstractions may be and are for artificial or provisional purposes, they have nothing in common with universals as plans or laws of construction, for these so far from neglecting the wealth and variety of their particular instances are the formulae which hold the instances together, not merely in our thinking but in fact. But I cannot see from such acquaintance as I possess with science that these abstractions represent its practice. A class in the actual practice of the sciences is not a bare collection of particulars which happen to agree in certain important respects, but a group determined by their constitutive formula. Witness the displacement in biology of the artificial by the natural system of classification. Even the artificial system was inspired by a true scientific instinct, for all its faults. For the sexual parts on which the classification is founded are of the last importance in organic life, and supply a clue to, or in Mill's phrase are an index of, a vast number of other important properties. The constant effort of the physicist or chemist is to discover characters which are index characters to the real constitution of things. The atomic weights were a first approximation to this end. At present we are witnessing the attempt to resolve the atom into a planetary system of electrons in motion round their central nucleus. Where would it be possible to find a more flagrant example of the real striving of physical science after constitutive plans? It is true that so eminent a logician as Jevons has represented scientific procedure as founded on the ideal of perfect enumeration of instances. But it is hardly just that the sciences should be saddled with the errors of their interpreters. The most elementary acquaintance with simple mathematics is enough to show in them the same endeavour after systematising their facts that is verifiable in the less ‘abstract’ sciences. The idea that mathematical propositions are mere generalisations could only be entertained by the misunderstanding of empirical method to which Mill fell a victim. He attempted to set geometry on the level of the inductive sciences by regarding geometry and arithmetic as concerned not with Space and Time themselves but with the physical things which occupy them. Geometry is indeed an empirical and experimental science; but its empirical subject-matter is not the things which fill Space, but their spaces. It observes the behaviour of Space, and the variety of its empirical material supplied by complexes within Space are the figures whose properties it discovers and connects into a system. It is thus not the sciences themselves which in their spirit and purpose worship the idol of abstract generalities. A spectre has been conjured up by the fears of philosophers which is called the mechanical method of science. But so far as I can see, it is the offspring of mistaken philosophers, or of science playing the part, as it often rightly does, of a spectator of its own procedure, but failing to do it justice.
The ‘concrete’ universal.
A profounder reason for the distrust of universals, described as laws which are repeated in particular instances, is connected with the previous one. They seem to some to remove us from reality, whereas the aim of all thought and science is to preserve the most intimate contact with reality, and with reality in its sensible form. Such an aim is more surely, say they, embodied in a work of art where every part of the work is vivified by its meaning, which as it were penetrates into every corner of the statue or the picture or the poem. Laws are infected with the repetitive disease; and the infection is conveyed by Space and Time, which are for these thinkers the beau-ideal of endlessness without purpose, the splintering of things into dissipated elements without the stability of real existence. The duty of thought is to be organic, and even if there is something which can never be reduced to terms of thought, if a person for instance can never be exhausted in his personality by any organisation of predicates, yet thought aspires to be individual and in its own sphere to mirror reality so far as thought can. All thinking tends thus to the concrete, defining itself into complex individuality. The ‘mechanical principle’ neglects this purpose and misses the true concreteness of thought.
It is such reasons which have led to the doctrine of the ‘concrete universal,’ a doctrine derived from Hegel and nowhere expounded with more effect and enthusiasm than by Mr. Bosanquet in the second chapter of his Principle of Individuality and Value. For our hypothesis on which things are ultimately complexes of space-time, it seemed that thoughts, whose object is the plans of such configurations, never can be divorced from their particulars; that Space and Time, so far from being the least self-subsistent of things, are in truth in their indissoluble union the ultimate reality in its simplest and barest terms; that the plans which it admitted are therefore concrete. But they do not aspire to be ‘concrete universals’ in distinction from the alleged abstract ones which do not and cannot exist. The so-called ‘concrete universal’ is in fact not a universal but a universe. It is not a law but a system. The relation of the universal to its particulars ceases to be that of a plan to its participants, but becomes that of a society to its members or a world to its parts. “The true embodiment of the logical universal,” says Mr. Bosanquet, “takes the form of a world whose members are worlds.” “The universal in the form of a world refers to diversity of content within every member as the universal in the form of a class neglects it.” (The universal we have described has neither the form of a world nor of a so-called class, but of a plan or law.) In the end there can be but one true universal, and that is the world itself as a single individual. Hence the significance of the phrase “a world whose members are worlds.” “The test of universality which it (the concrete universal) imposes is not the number of subjects” (granted at once!) “which share a common predicate, but rather than this, the number of predicates that can be attached to a single subject” (for instance, the name of a person).18
The recognition of this logical form as the true type of universality, Mr. Bosanquet says, “is the key to all sound philosophy.” With all respect to the writer who defends it with such skill, I venture to think this doctrine combines into one two distinct notions. One is that of the union of different features into a plan or law which is realised with modifications in individual instances, the combination of many predicates which appears to be intended in the passage I have quoted. This is the universal as I have described it. But such a plan cannot be called a universe. The other notion is that of the union into a system of different individuals in or by or under such a plan. Such a union is indeed a universe, but its relation to its particulars is not that of an individual to its predicates, nor that of a plan to its embodiments. A universe of particulars is not the universal of them. It introduces in fact a different and important conception which it misnames universal, that of an individual substance or the totality of changing phases of an individual's life, every one of which follows a certain plan or universal. I find in the doctrine of the concrete universal these two notions intermixed.19
The distinction may be illustrated first from the case of an individual person, which is regarded as typical. Any fact as we have seen is universal in so far as it follows a plan of constitution and can be repeated according to that plan in time and space. As a particular determined according to a plan it is an individual. An individual substance or thing (to anticipate what belongs to a later chapter) is the continuum of these repeated instances of its universal plan. In a personality the various acts of the individual are highly organised, and in the phases of his life distinct activities become prominent, but always in subordination to the one plan. Thus when an individual follows the well-known rule of Sir William Jones:
Six hours to law, to soothing slumbers seven,
Ten to the world allot, and all to Heaven;
dedication to Heaven describes the universal plan, the individual person is the continuum of different conditions of life which follow this plan. The theory of the concrete universal would make him the universal of his acts as well as the universe of them.
This case is that of an organised individual, and is of great complexity. A simpler case is that of a parabola whose equation is y2 = 4ax, where a has some definite value. This individual parabola is the thing or substance composed of all the points which follow the plan so described, and is the universe of them. But their universal is not the parabola but what may be described by the phrase ‘any point which satisfies this equation.’ The parabola is not a universal. On the other hand, there is a universal parabola which is the plan of all such totalities of points, a plan symbolised by the, same equation when the parameter a may vary from curve to curve. This universal parabola is not, however, the universe of all parabolas, and in fact there is no such individual or universe.
This is still plainer when we pass to a species or genus, which can only be called the universal of its specimens as being their plan of construction. If it means their universe, where is such an individual whole to be found? There is only the collection of individuals, which have not even that approach to organisation that can be found in a parabola. It may indeed happen that instances of a species (or, if we prefer to say so, species of a genus) are connected together into an organic whole which is more than a mere whole of parts. This is the case as I believe with human societies; and wherever beings tend to communal life there is an approach to this state of things. The members of a society are instances of a type which is represented by the society as a whole, and the society is in fact a species which is itself an individual existence.20 But we are not entitled on the strength of such special (and perhaps disputable cases) to identify a universal with an organised individual because the plan of the individual members happens in these cases to be in some way embodied in the whole. We still need the notion of a plan or law, and this is what commonly is called a universal.
In avoiding abstract universals, which not true science uses but a false logic of science imagines, the theory we are commenting upon assigns the name of universal to something which is not a universal in the traditional sense, but something different which is yet blended with the older meaning of universal. If the matter were one of nomenclature alone, it would not signify so much. Its importance lies in the metaphysical consequences. If universals (on the discovery of which all science turns) are really universes, and not merely laws, there is in the end only one universe or individual which is self-existent; the minor universes are shadows. For if the universal is related to its particulars as a thing to its predicates they become “adjectival” to it, and in the end the minor universes are adjectival to the one universe or absolute individual. If on the other hand the reality is Space-Time, individual things, and minor universes which are groupings of them, are real with the reality of their parent, which is then “the nurse and mother of all becoming,” not the devouring maw which swallows all empirical things.
The ‘concrete universal’ then mistakes universality for system. It remains to add that the idea of system or organisation is of the highest value for understanding the problem of knowledge, and it is by this clue that Mr. Bosanquet himself has been able to render such service to logical theory. Organisation is a great empirical fact. It begins lower down than organic life and is perpetually overcoming the repetitive tendency which is equally empirical. As we ascend the scale of being in the order of time, aggregates are replaced by organic systems; and the higher a thing is in the scale, the greater it seems is its ordered complexity. But system in general exists in every complex even in the least organised, all disorder has its own complex plan. System is the coherence of elements, and the notion of system represents the essential continuity of Space-Time which it retains while it breaks up into its parts. The parts remain within the whole and are coherent with one another. Science investigates the particular forms of such coherence, and organisms are a highly-developed instance of it. The nature of an organism and still more a work of art is rightly exemplary in the methods which reason follows. Thought, in following the clue of coherence amongst its data, as science always does, is thus bringing back the scattered members of the universe into the spatio-temporal continuity out of which, in spite of their disguises of qualities higher than mere motion, they ultimately sprang. These considerations belong properly to the theory of truth, and the methods by which it is attained in science. Those methods are empirical rules by which we seek to bring order into the empirical material; and it may be surmised even at this stage that logic is an empirical science which deals with the interconnection of the isolated portions of our knowledge (that is, of reality) as presented in propositional form.21
This phrase, as I have had occasion to remark before, is inaccurate (see D. M. Y. Sommerville, The Elements of Non-Euclidean Geometry, London, 1914, ch. vi.). It is of course not used here with the assumption which the author imputes to many philosophers that three-dimensional geometry implies Space of four dimensions. That has been seen (Bk. I. ch. v.) in the first place not to be Space at all, in the next place to owe what reality it possesses to the work of thought. But the phrase is a convenient one. For the most part, however, I shall speak of the uniformity of Space. This is to be distinguished carefully from the supposed homogeneity or indifference of Space, which is declared to be characteristic of ‘conceptual’ in contrast with ‘perceptual’ Space. See before, Bk. I. ch. v. p. 152, and below, p. 216 n.
Doubtless this comparison has often been made, but it seems to me as suggestive and true now as when I first heard it from the late Hermann Grimm at Berlin more than thirty years ago.
There is now a large literature on imageless thinking. I may cite in particular the earlier work of Mr. Stout in Analytical Psychology, vol. i. Bk. I. ch. iv., and the researches by Messrs. Ach, Buehler, H. J. Watt of the Würzburg School of the late O. Külpe.
Bk. T. ch. iv. pp. 139 f.
Thus Mr. Bosanquet writes (Principle of Individuality, p. 40, note 3): “The universal is essentially a system or habit of self-adjusting response or reaction.” My difference from him lies in the phrase “system or habit.” A habit is for me not a system of its acts but the plan, or in extensional terms, the class of them. See below, pp. 233 ff.
More than one friendly critic has urged that if we can think of a Space of varying curvature, there must be at least one universal, that is the concept of the class of such curvatures; and consequently my contention that there are universals because there is uniformity or constant curvature breaks down in this instance. The answer which will be clearer from the ‘objections and elucidations’ which follow is from my point of view fairly clear. The notion of a variable curvature of Space is got from experience of Space with a constant one by a construction of thought, like four-dimensional Space. Because, being familiar with universals, we can universalise Space-curvature in thought, we are not therefore free to deny that universality as we know it in experience depends on constancy of curvature. Moreover, while there is a good meaning in the universal contained in the varying curvatures of curves in our Space, it is difficult to see what is the universal element in the varying curvatures of the supposed Space which itself varies in curvature. The supposed universal is rather comparable to colour in relation to the various colours, red, green, etc. There is no element colour in these of which red and green are variations. Colour is a collective name rather than a class one or a universal. Such a universal curvature is nothing then, as before, but a bare thought; and no conclusion can be drawn from the supposition of my critics. But, whether this last comparison be valid or not, I recall their attention to the real problem, which is how there can be sameness or generic identity at all. You may take these different entities, space-curvatures, however measured, and construct a new so-called ‘Space’ from them. But their generic identity is of your making. Unless they are the same in themselves there is no real universal of them. You may consider them as forming a class with the sameness called curvature. But you have still to ask the prior question how there can be classes of things at all. Sameness has to be accounted for before things can form a class. It is this fundamental question that the text endeavours to answer.
There is a very instructive critical account of the various forms of the third man argument in a paper by Mr. A. E. Taylor on ‘Parmenides, Zeno and Socrates,’ in Proceedings Arist. Soc, 1915–16, N. S, vol. xvi. I do not enter into the question, which among these arguments the above objection corresponds to. I think it is the argument from infinite regress used in the Parmenides.
Cp. Lotze, Logic, § 117.
Below, p. 235.
Parmenides, 132 b. The argument is discussed fully in Mr. Taylor's paper just cited.
Cp. T. P. Nunn, The Teaching of Algebra, London, 1914, p. 542.
Mr. Bosanquet's Distinction of Mind from its Objects, p. 36, Manchester, 1913.
In a very interesting conversation, reported by M. Paul Gzell (Art, by Auguste Rodin, translated from the French by Mrs. Romilly Fedden, London, 1912), Rodin points out how the Greek statues, e.g. the Venus of Milo, or the Tanagra statuettes, secured the impression of repose by the opposite inclinations of the lines of the shoulders and the hips, so as to produce a balance of the body. Whereas in later art, as in the David of Michael Angelo, the lines are in the same direction, and the result is the impression of motion.
I can accept with equanimity the laughing charge of Aristophanes against one of the sophists of his time that “Vortex has expelled Zeus and reigns in his place.” Empirical things are vortices or eddies in the stuff of Space-Time, and universals are the laws of their construction. But I hope to show in the end how Vortex reintroduces Zeus in a more considered and worthier guise and to a securer throne.
I have made no attempt in the above to consider the bearing of the result on the teaching of Plato and the Pythagoreans; partly because it would be a matter of great length but mostly because I have not the required scholarship. I imagine that it is more in keeping with Pythagoreanism than with Plato himself. On the other hand, in describing universals as patterns of motion I do not go the length of one of the later Pythagoreans, Eurytus, of whom Mr. Burnet tells us that he represented the form of man (supposed identical with the number 250) by sticking pebbles to that number into wet plaster along the outlines of a human shape. This makes the form of man not merely a pattern of matter but actually a material thing. But exaggerated as the procedure is, the spirit of it is sound, and I delight in Eurytus. The Platonic doctrine of forms as numbers, that they are composed of limit and the unlimited or indeterminate dyad, represents within the world of forms what I am trying to say without any division of form from sensible things, allowance always being made for the absence of Time from Plato's conception of numbers or forms. But the separation of forms from sense which is common to Plato and the Pythagoreans disappears, as remarked above, when sensibles are regarded as spatio-temporal complexes. I have thought it best to use Plato for my purposes as a guide to my own inquiry without nice discussion of him for his own sake. For the same reason I do not enter into the question of how much in the above is in agreement with Aristotle's teaching when he is constructive and not merely critical of Plato. For Plato (with qualifications) as for him the forms were constructive laws. His doctrine that the species is the genus in energy or actualised appears to me of the greatest significance. On the other hand, what he adds to Plato in the matter is not very satisfying and certainly does not bridge the gap between sense and thought. For the actualisation of the species demands a prior individual of the same species: “man begets man.” But Aristotle though an evolutionist was necessarily only a logical and not a biological evolutionist—like Hegel after him. The whole controversy as to whether forms are beside particulars or in them loses its importance, as I have observed before, when both form and particulars are spatio-temporal.
Bk. III. ch. ix. F, ‘On values in general.’
Logic, vol. ii. ch. iv. p. 117, eds. i. and ii.
Loc. cit. pp. 37–40.
Thus Mr. Bosanquet himself, as before noted, compares a universal in the mind to a habit, and so far I seem to be repeating his view of the universal. But a habit is surely not related to its realisations as a thing to its predicates.
H. Spencer has, I believe, a remark somewhere to this effect, where I cannot remember.
For this topic see later, Bk. III. ch. ix. B, ‘Truth and Error.’