Chapter 11

[1]Eth.ii 7.

[2]Phenomenologiedes Geistes, p. 22.

[3]Gesetzt.

[4]Aufgehoben.

[5]Idee: Ideeller Weise.

[6]Potenz.

[7]'Nicht nur die Einsicht in die Abhängigkeit des Einzelnen vom Ganzen ist allein das Wesentliche; ebenso dass jedes Moment selbst unabhängig vom Ganzen das Ganze ist, und dies ist das Vertiefen in die Sache.' (HegelsLeben, p. 548.)

The ordinary logic-books have made us all familiar with the popular distinction between Abstract and Concrete. By a concrete term they mean the name of an existence or reality which is obvious to the senses, and is found in time and place;—or they mean the name of an attribute when we expressly or tacitly recognise its dependence upon such a thing of the senses. When, on the contrary, the attribute is forcibly withdrawn from its context and made an independent entity in the mind, the term expressing it becomes in the usual phraseology abstract. Any term therefore which denotes a non-sensible or intelligible object would probably be called abstract. And there is something to be said for the distinction, which, though unsuccessful in its expression, has some feeling of the radical antithesis between mere being and mere thought. It is true, that in the totality of sense and feeling, in the full sense-experience, there is a concrete fulness, as it were, an infinite store of features and phases waiting for subsequent analysis to detect. In the real kind of actual nature there is an inexhaustible mine of properties, which no artificial classification and description can ever come to the end of. Every qualitywhich we state, every relation which we predicate, is a partial and incomplete element in this presupposed reality, this implicit concrete; and as such is abstract, and comparatively unreal. It is something forcibly torn out of and held apart from its context. But on the other hand the concrete reality is not at first real, but implicit: it becomes really concrete only as it re-embraces, and re-constitutes in its totality the elements detected by analysis. But the popular distinction forgets this, and gives the title and rank of concrete to what very poorly deserves the name, viz. to the yet undiscerned reality denoted by a substantive name. Yet there can be little doubt that the popular use of these terms, or the popular apprehension of what constitutes reality,—for that is what it comes to,—is sufficiently represented by the ordinary logic-books. So that, if the whole business of the logician lies in formulating the distinctions prevalent in popular thought, the ordinary logic is correct.

Now the popular logic of the day,—the logic which has long been taught in our schools and universities—has three sources.—In the first place, but in a slight degree, it trenches upon the province of psychology, and gives some account of the operation by which concepts or general ideas are supposed to be formed, and of the errors or fallacies which naturally creep into the process of reasoning. This is the more strictly modern, the descriptive part of our logic-books.—But, secondly, the logic of our youth rests in a much higher degree upon the venerable authority of Aristotle. That logic, within its own compass, was a masterpiece of analysis, and for many centuries maintained an ascendency over the minds of men, which it well deserved. But it was not an analysis of thought or knowledge as a whole, and it treated its subject in fragments. Itgave in one place an analysis of science and in another an analysis of certain methods, which could be observed in popular discussions and practical oratory. As Lord Bacon remarked, it did little else than state and, it may be, exaggerate therationaleof argumentation. A high level of popular thought it unquestionably was, which Aristotle had to investigate,—a level which many generations of less favoured races were unable to reach. But there were defects in this Logic which fatally marred its general usefulness, when the limited scope of its original intention had been lost sight of. The thoughts of Greece, it has been said, were greatest and most active in the line of popular action for the city and the public interest, in the discussions, the quibbles, the fallacies, and rhetorical arts of the barber's shop and the 'agora.' The aim of such exercises was to convince, to demonstrate, to persuade, to overcome;—it might be for good and truth, but also it might not. And accordingly the Logic of Aristotle has been said to have for its end and canon the power to convince and to give demonstrative certainty. There is some ground, it may be, for this charge. The ancient logician seems to luxuriate in a rank growth of forms of sophism, and in an almost childlike fondness for variety of argumentative method. He seems resolved to trace the wayward tricks of thought and its phases through every nook and cranny, to exhaust all the permutations and complications of its elements. But let us be just, and remember that all this was in the main a speculative inquiry—for the sake of theory. It developed the powers of judgment and inference, just as the modern research for new metals, new plants, or new planets, develops the powers of observation. Both have some value in the material results they discover: but, after all, the mental culture they give is the main thing. Andthe talents quickened by deductive research are no whit less valuable than those owed to the other. Forms are essential, even if it be possible to make the terrible mistake of regarding them as all-important to the exclusion of matter.

And then, this is not the whole truth. There is a perfectly serious Greek science—Mathematics—a science of many branches: a science which, from Plato downwards, always stood in alliance with the studies of philosophy. Now, it might be said, perhaps with ground, that the conception of mathematical method too much dominated all attempts to get at the rationale of science, and led to the supremacy of syllogism. It would be fairer perhaps to put this objection in another shape. We should then say that the logic of Aristotle,—theAnalytics—is too much restricted to dealing with the most general and elementary principles of reasoning. But this is not in itself a fault. It becomes a fault only where there is no growth in philosophy—when it is merely handed on from master to pupil; and where there is a tendency to put philosophic doctrine to immediate use. To expend the whole energy of intellect in laying bare the general principles, the fundamental method, of knowledge and inference, is precisely what the founder of a science has a duty to do. But the beginning thus made requires development—and development which is fruitful must proceed by correction and antithesis, no less than by positive additions. It was not given to Aristotle's logic to be so carried on. His logic, like his system in general, had no real successor to carry it on in the following generation: and when in the less original ages of early Byzantine rule it again found students, it had become a quasi-sacred text which could only be commented on, not modified and developed. From the greatExegetaiof Greece itpassed westward to Boethius and eastward to the Syrian and Persian commentators in the early centuries of the Caliphate. From these, and from other intermediaries, it may be, it finally culminated in the work of the Latin Schoolmen of the later Middle Ages. But the very reverence which all these expositors felt for the text ofthePhilosopher rendered true development impossible.

Then, on the other hand, the lust of practical utility caused a grave misconception of what logic can do. For Aristotle, logic is a scientific analysis of the modes of inference; its uses are those which follow intrinsically from all noble activity freely and zealously prosecuted. But with the death of Aristotle the great days of knowledge for the sake of knowledge and divine wisdom were over. The Stoics into whose hands the chief sceptre of philosophy, directly or indirectly, passed never rose above the conception of life as a task and a duty, and of all other things, literature, science, and art, as subservient to the performance of that task. The conception is an ennobling one: but only with a relative or comparative nobility. It ennobles, if it is set beside and against the view that life is a frivolous play, a sport of caprice and selfishness. But it darkens and narrows the outlook of humanity, when it loses sight of life as a joy, a self-enlarging and self-realising freedom, of life as in its supreme phaseθεωρία—or the enjoyment of God. To the Stoic, therefore,—and to the dominant Christian theory which entered to some extent on the Stoic inheritance—logic, like the rest of philosophy, was something only valuable because ultimately it helped to save the soul.

It thus sunk into the position of an Organon or instrument. To the Stoic,—for instance to Epictetus—its value was its use to establish the doctrines of the Stoicfaith, by confuting the ill-arranged and futile inferences on which were founded the aims and approvals of ordinary worldly life. To the Christian, again, it served as a method for putting into systematic shape (under the guidance of certain supreme categories or principles also borrowed from Greek thought) the variety of fundamental and derivative aspects which successive minds, pondering on the power and mystery of the Christian faith, had set forward as its essential dogmas. It thus helped to build up (out of the leading ideas of Greek metaphysics, and the principles emerging in the earliest attempts to formulate the law of Christ) that amalgam of the power of a divine life with the reflective thought of the teachers of successive generations, which constitutes the dogmatic creed of Christendom. Such a reconstruction in thought of the reality which underlies experience—(in this case the experience of the Christian life), is inevitable if man is to be man, a free intelligence, and not a mere animal-like feeling. But its success is largely, if not entirely, dependent on the value of the logic and metaphysics which it employs: and it would be a bold thing to say that the subtle, abstract, and unreal system of Neo-Platonist and Neo-Aristotelian thought was an organon adequate to cope with the breadth and depth, latent if not very explicit, in the fulness and reality of the religious life.

Yet even as an Organon, Logic had to sink to a lower rank. As traditionalism grew supreme, and religion ossified into a stereotyped form of belief and practice, logic had less to do as an organiser of dogma. It sank, or seemed to sink (for it would be rash to speak too categorically of an epoch of thought so far removed from modern sympathy and understanding as the age of the Schoolmen), into a futile (and as it seemsoccasionally almost a viciously-despairing) play withproandcontra,—into a lust of argumentation which in masters like Ockam comes perilously close to scepticism or agnosticism. More and more, Scholastic thought, which, at one time, had been in the centre of such intellectual life as there was, came to be stranded on the shore, while the onward-flowing tide spread in other directions. These were the great days of logical sway, when it seemed as if logic could create new truth: as if forms could beget matter. So at least ran an outside rumour, which was probably based on some amount of real folly. But the more important point was that the old logic had lost touch with reality. New problems were arising, which it was—without a profound reconstruction—quite incapable of solving. Of these there were obviously two—not unconnected perhaps, but arising in different spheres of life. There was the revival of religious experience, growing especially since the thirteenth century with an ever-swelling stream in the souls of men and women, till it burst through all bounds of outward organisation in the catastrophe of the Reformation. Luther may have been historically unjust (as Bacon afterwards was) to the 'blind heathen master,' as he called Aristotle: but he was governed by a true instinct when (unlike the compromise-loving Melanchthon) he found the traditional system of logic and metaphysics no proper organon for the new phase of faith and theory. So, too, the new attempts at an inception and instauration of the sciences grew up outside the walls of old tradition, and were at first perhaps discouraged and persecuted as infidel and heretical, and were, even without that burden, pursued at much hap-hazard and with much ignorance both in aims and methods. Intelligent onlookers,—especially if inspired by an enthusiasm for the signs of an agehappier for human welfare—could not but sec how needful it was to come to some understanding on the aims and methods of the rising sciences.

This want, which he keenly felt, Francis Bacon tried to satisfy. He pointed out, vaguely, but zealously and in a noble spirit, the end which that new logic had to accomplish. Bacon, however, could not do more than state these bold suggestions: he had not the power to execute them. He imagined indeed that he could display a method, by which science would make incredible advances, and the kingdom of truth in a few years come into the world. But this is a sort of thing which no man can do. Plato, if we take hisRepublicfor a political pamphlet, had tried to do it for the social life of Athens. What Plato could not do for the political world of Greece, Bacon could not do for the intellectual world in his time: for as the Athenian worked under the shadow of his own state, over-mastered even without his knowledge by the ordinances of Athens, so the Englishman was evidently enthralled by the medieval conceptions and by the logic which he condemned. What Aristotle had for ages been supposed to do, no philosopher could do for the new spirit of inquiry which had risen in and before the days of Bacon. That spirit, as exhibited in his great contemporaries, Bacon, as he has himself shown, could not rightly understand or appreciate. He failed, above all, to recognise the self-corrective, tentative, and hypothetical nature, of all open inquiry. But one need not for this disparage his work. It showed a new sense of the magnitude of the modern problem: it set prominently forward the comprehensive aim of human welfare: and by its conception of the 'forma' it kept science pledged to a high ideal. But Bacon could only play the part of the guide-post: he could nothimself lay down the road. And negatively he could warn against the belief that mathematics couldgenerateor do more indeed thandefinethe sciences. The spirit of free science, of critical investigation, of inductive inquiry, must and did constitute its forms, legislation, and methods for itself. For no philosopher can lay down laws or methods beforehand which the sciences must follow. The logician only comes after, and, appreciating and discovering the not always conspicuous methods of knowledge, endeavours to gather them up and give them their proper place in the grand total of human thought, correcting its inadequacies by their aid, and completing their divisions by its larger unities. Or rather this is a picture of what English logic might have done. But it does not do so in the ordinary and accepted text-books on the subject. What it does do, is rather as follows. To the second and fundamental part which it subjects to a few unimportant alterations,—i. e. to the doctrine of terms, propositions, and reasonings,—it subjoins an enumeration of the methods used in the sciences.

To the rude minds of the Teutonic peoples the logical system of Aristotle had seemed almost a divine revelation. From the brilliant intellect of Greece a hand was stretched to help them in the arrangement of their religious beliefs. The Church accepted the aid of logic, foreign though logic was to its natural bent, as eagerly as the young society tried for a while to draw support from the ancient forms of the Roman Empire. So with the advance of the Sciences in modern times some hopeful spirits looked upon the Inductive Logic of Mill in the light of a new revelation. The vigorous action of the sciences hailed a systematic account of its methods almost as eagerly as the strong, but untaught intellect of the barbarian world welcomedthe lessons of ancient philosophy. For the first time the sciences, which had been working blindly or instinctively, but with excellent success, found their procedure stated clearly and definitely, yet without any attempt to reduce their varied life to the Procrustean bed of mathematics, which had once been held to possess a monopoly of method. The enormous influence of the physical sciences saw itself reflected in a distinct logical outline: and the new logic became the dominant philosophy. Such for a while was the proud position of the Inductive Logic. Enthusiastic students of science in all countries, who were not inaccessible to wider culture, used quotations from Mill to adorn and authorise their attempts at generalisation and theory. A period of speculation in the scientific world succeeded the period of experiment, in which facts had been collected and registered. A chapter on Method became a necessary introduction to all higher scientific treatises. In our universities methodology was prodigally applied to the study of ancient philosophy. And so long as the scientific epoch lasts in its one-sided prominence, so long the theory of inductive and experimental methods may dominate the intellectual world.

But the Inductive Logic hardly rose to the due sense of its situation. It has not held to the same high ideal as Bacon set before it. It has planted itself beside what it was good enough to call the Deductive Logic, and given the latter a certain toleration as a harmless lunatic, or an old pauper who had seen better days. Retaining the latter with certain modifications, although it has now lost its meaning in the changed outlines of the intellectual world, Inductive Logic adds a methodology of the sciences, without however founding this methodology upon a comprehensive analysis ofknowledge as a whole, when enlarged and enlightened by the work of the sciences. Hence the two portions,—the old logic, mutilated and severed from the Greek world it grew out of, and the new Inductive or specially-scientific logic, not going beyond a mere classification of methods,—can never combine, any more than oil and water. And the little psychology, which is sometimes added, does not facilitate the harmony.

But Inductive Logic should have adopted a more thorough policy. There can only be one Logic, which must be both inductive and deductive, but exclusively, and in parts, neither. To achieve that task however Logic must not turn its back indifferently on what it calls metaphysics, and it must rise to a higher conception of the problems of what it calls psychology.

In these circumstances the ordinary logic, in its fundamental terms, is more on the level of popular thought, than in a strictly scientific region, and does not attempt to unite the two regions, and examine the fundamental basis of thought on which scientific methods rest. The case of Concrete and Abstract will illustrate what has been said. To popular thought the sense-world is concrete: the intellectual world abstract. And so it is in the ordinary logic. To Hegel, on the contrary, the intellectual interpretation of the world of reality and experience is a truer and thus a more concrete description of it than that contained in a series of sense-terms. Now the difference between the two uses of the term is not a mere arbitrary change of names. When the philosopher denies the concreteness of the sense-world, and declares that it, as merely sensible, is only a mass of excluding elements, a 'manifold,' and in the second instance a series of abstractions, drawn out of thiscongeriesby perception, the change of language marks the total change of position betweenthe philosophic and the popular consciousness. Reality and concreteness as estimated by the one line of thought are the very reverse of those of the other. A mere sense-world to the philosopher is a world which wants unity, which is made up of bits imperfectly adjusted to each other, and always leading us to look for an explanation of them in sources outside them. The single things we say we perceive,—the here and the now we perceive them in—are found, upon reflection and analysis, to depend upon general laws, on relations that go beyond the single,—on what is neither here nor now, but everywhere and timeless. The reality of the thing is found to imply a general system of relations which make it what it is. Sense-perception in short is the beginning of knowledge: and it begins by taking up its task piecemeal. It rests upon a felt totality: and to raise this to an intelligible totality, it must at first only isolate one attribute at a time.

The apprehension of a thing from one side or aspect,—the apprehension of one thing apart from its connexions,—the retention of a term or formula apart from its context,—is what Hegel terms 'abstract.' Ordinary terms are essentially abstract. They spring from the analysis of something which would, in the first stage of the process, in strictness be described not as concrete, but as chaos:—as the indefinite or 'manifold' of sensation. But the first conceptions, which spring from this group when it is analysed, are abstract: they are each severed from the continuity of their reality. To interpret our feeling, our experience as felt, we must break it up. But the first face that presents itself is apt to impress us unduly, and seems more real, because nearer feeling: on the other it is more unreal, because less adequate as a total expression of the felt unity. In the same sense we call Political Economyan abstract science, because it looks upon man as a money-making and money-distributing creature, and keeps out of sight his other qualities. Our notions in this way are more abstract or more concrete, according as our grasp of thought extends to less or more of the relations which are necessarily pre-supposed by them. On the other hand, when a term of thought owns and emphasises its solidarity with others, when it is not circumscribed to a single relation, but becomes a focus in which a variety of relations converge, when it is placed in its right post in the organism of thought, its limits and qualifications as it were recognised and its degree ascertained,—then that thought is rendered 'concrete.' A concrete notion is a notion in its totality, looking before and after, connected indissolubly with others: a unity of elements, a meeting-point of opposites. An abstract notion is one withdrawn from everything that naturally goes along with it, and enters into its constitution. All this is no disparagement of abstraction. To abstract is a necessary stage in the process of knowledge. But it is equally necessary to insist on the danger of clinging, as to an ultimate truth, to the pseudo-simplicity of abstraction, which forgets altogether what it is in certain situations desirable for a time to overlook.

In a short essay, with much grim humour and quaint illustrations, Hegel tried to show what was meant by the name 'abstract,' which in his use of it denotes the cardinal vice of the 'practical' habit of mind. From this essay, entitled 'Who is the Abstract Thinker[1]?' it may be interesting to quote a few lines. A murderer is, we may suppose, led to the scaffold. In the eyes of the multitude he is a murderer and nothing more. The ladies perhaps may make the remark that he isa strong, handsome, and interesting man. At such a remark the populace is horrified. "What! a murderer handsome? Can anybody's mind be so low as to call a murderer handsome? You must be little better yourselves." And perhaps a priest who sees into the heart, and knows the reasons of things, will point to this remark, as evidence of the corruption of morals prevailing among the upper classes. A student of character, again, inquires into the antecedents of the criminal's up-bringing: he finds that he owes his existence to ill-assorted parents; or he discovers that this man has suffered severely for some trifling offence, and that under the bitter feelings thus produced he has spurned the rules of society, and cannot support himself otherwise than by crime. No doubt there will be people who when they hear this explanation will say "Does this person then mean to excuse the murderer?" In my youth I remember hearing a city magistrate complain that book-writers were going too far, and trying to root out Christianity and good morals altogether. Some one, it appeared, had written a defence of suicide. It was horrible! too horrible! On further inquiry it turned out that the book in question was theSorrows of Werther.

'By abstract thinking, then, is meant that in the murderer we see nothing but the simple fact that he is a murderer, and by this single quality annihilate all the human nature which is in him. The polished and sentimental world of Leipsic thought otherwise. They threw their bouquets, and twined their flowers round the wheel and the criminal who was fastened to it.—But this also is the opposite pole of abstraction.—It was in a different strain that I once heard a poor old woman, an inmate of the workhouse, rise above the abstraction of the murderer. The sun shone, as thesevered head was laid upon the scaffold. "How finely," said the woman, "does God's gracious sun lighten up Binder's head!" We often say of a poor creature who excites our anger that he is not worth the sun shining on him. That woman saw that the murderer's head was in the sunlight, and that it had not become quite worthless. She raised him from the punishment of the scaffold into the sunlit grace of God. It was not by wreaths of violets or by sentimental fancies that she brought about the reconciliation: she saw him in the sun above received into grace.'

[1]'Wer denkt abstrakt!' (Vermischte Schriften, vol. ii. p. 402.)

Induction and Experience are names to which is often assigned the honour of being the source of all our knowledge. But what induction and experience consist in, is what we are supposed to be already aware of; and that is—it may be briefly said—the concentration of the felt and sense-given fragments into an intimate unity. The accidents and fortunes that have befallen us in lapses of time, the scenes that have been set before and around us in breadths of space, are condensed into a mood of mind, a habitual shading of judgment, or frame of thought. The details of fact re-arrange themselves into a general concept; their essence gets distilled into a concentrated form. Their meaning disengages itself from its embodiment, and floats as a self-sustaining form in an ideal world. Thus if we look at the larger process of history, we see every period trying to translate the sensuous fact of its life into a formula of thought, and to fix it in definite characters. The various parts of existence, and existence as a whole, are stripped of their sensible or factual nature, in which we originally feel and come into contact with them, and are reduced to their simple equivalents in terms of thought. From sense and immediate feeling there is, in the first place, generated an image or idea which at least represents and stands for reality; and from that, in the second place, comesa thought or notion proper, which holds the facts in unity.

The phenomenon may, perhaps, be illustrated by the case of numbers. To the adult European, numbers and numbering are an obvious and essential part of our scheme of things that seems to need no special explanation. But the experience of children suggests its artificiality, and the evidence from the history of language corroborates that surmise. If number be in a way describable as part of the sense-experience, or total impression, it certainly does not come upon us with the same passivity on our part as the perception of taste or colour, or even of shape. It postulates a higher grade of activity. As Plato says, it 'awakes the intelligence': it implies a question and looks forward to an answer: it is thus the first appearance of what in its later fullness will be called 'Dialectic,' To put it otherwise: Numbering can only proceed where there is a unit, and an identity: it implies a one, and it implies an infinite repetibility of that one[1]It thus postulates the double mental act, first of reducing the various to its basis of identity, and, secondly, of performing a synthesis of the identical units thus created. In the highly artificial world in which we live all this seems simple enough. The products of machinery, articles of furniture, dress, &c., &c., are already uniform items: and the strokes of a clock seem almost to invite summation. But in free nature this similarity is much less obviously stamped on things: and the products of primitive art—of literalmanu-facture—display an individuality, an element of personal taste, even, which is necessarily lacking in things turned out by machinery. Thus it was necessary, before we could number, to reduce the qualitatively different to a quantitative equality orcomparability. There are indeed some instances, in that nearest of things to us, the human body, which might help. There is the obvious similarity of organs and limbs which go in pairs, and which might easily suggest a dual, as, so to speak, a sensuous fact amongst other facts. Again, there is the hand and its five fingers, or the two hands and the ten fingers. The five or ten, as a whole naturally given, suggest a grouping of numbers in natural aggregates. The fingers, again, (and here we may keep at first to the fingers proper, minus the thumb,) may be without much ingenuity said to give us a set of four, naturally distinct, yet naturally alike, and needing, so to speak, the minimum of intelligence to create the numerical scale from one to four. It is by them, indeed, that Plato, it may be unconsciously, illustrates the genesis of number. Here in short you have the natural abacus of the nations, but one restricted, first, perhaps to the group 1-4, secondly to the group 1-10.

We have seen how the dual was, in certain instances, almost a natural perceptive fact. But when it is so envisaged, it is hardly recognised as number strictly so called. It is only a fresh and peculiar sensuous attribute of things: a thing which has the quality of duplication, not a thought which is the synthesis of two identical units. It is a sort of accident, not part of a regular system or series. So again with the plural, which may appear in several shapes before it is assigned to its proper place as a systematic function of the singular. If the Malay, in order to say 'the king of all apes' has to enumerate one after another the several sub-species of ape, or if to express 'houses' he has to reduplicate the singular, to insert a word meaning 'all' or 'many,' we can see that the conception of number is for him still in the bonds of sense. It is nota synthetic category, but only a material multitude. But in other cases the plural proper is almost confounded with the so-called 'collective.' It is not an unfamiliar fact in Greek and Latin that the plural has acquired a meaning of its own,—not the mere multiple of its singular; as also that the collective term is occasionally used as an abstract, occasionally as the more or less indeterminate collection of the individuals. Such plurals and such collectives represent a stage of language and conception when the aggregate of singulars form a uniquely-qualified case of the object. And the peculiarity of them is seen in the way the plurality is immersed in and restricted to the special class of objects: as e. g. when in English the plurality of a number of ships is verbally stereotyped as against the plurality of a number of sheep, or of partridges (fleet, flock, covey). In such instances the category of number is completely pervaded and modified by the quality of the objects it is applied to. So, in the Semitic languages, the so-called 'broken plural' is a quasi-collective, which grammatically counts as a feminine singular (like so many Latin and Greek collectives): and whereas the more regular plural is generally shown by separable affix, this quasi-collective plural enters the very body of the word by vowel-change, indicating as it were by this absorption the constitution of a specifically new view of things. On the other hand, it may be said, there is in this collective a trace of the emergence of the universal and identical element through the generalisation due to the conjunction of several similars all acting as one[2]

In a true plural, on the contrary, it is required that the sign of number be clearly eliminated from any peculiarities of its special object, and be distinctly separatedfrom the collective. And similarly the true numeral has to be realised in its abstractness, as a categoryper se.And to do this requires some amount of abstraction. In Greek, for example, we meet the distinction between numbers in the abstract, pure numbers (such as four and six), and bodily or physical numbers (such as four men, six trees)[3]. The geometrical aspect under which numbers were regarded by the Greeks, e. g. as oblong or square numbers, bears in the same direction. But another phenomenon in language tells the tale more distinctly[4]. Abundantly in Sanscrit and Greek, more rarely in Zend and Teutonic, and here and there in the Semitic languages, we meet with what is known as the dual number, a special grammatical form intended to express a pair of objects. The witty remark of Du Ponceau[5]concerning the Greek dual, that it had apparently been invented only for lovers and married people, may illustrate its uses, but hardly suffices to explain its existence in language. But a comparison of barbarian dialects serves to show that the dual is, as it were, a prelude to the plural,—a first attempt to grasp the notion of plurality in a definite way, which served its turn in primitive society, but afterwards disappeared, when the plural had been developed, and the numerals had attained a form oftheir own. If this be so, the dual is what physiologists call a rudimentary organ, and tells the same story as these organs do of the processes of nature.

The language of the Melanesian island of Annatom, one of the New Hebrides, may be taken as an instance of a state of speech in which the dual is natural. That language possesses a fourfold distinction of number in its personal pronouns, a different form to mark the singular, dual, trial, and plural: and the pronoun of the first person plural distinguishes in addition whether the person addressed is or is not included in the 'we-two,' 'we-three,' or 'we-many' of the speaker[6]. The same language however possesses only the first three numerals, and in the translation of the Bible into this dialect it was necessary to introduce the English words, four, five, &c. The two facts must be taken together: the luxuriance of the personal pronouns and the scanty development of numerals in such languages are two phenomena of the same law. The numeral 'four' to these tribes is said to bear the meaning of 'many' or 'several,' Another fact points in the same direction. In many languages, such as those of China, Further India and Mexico, it is customary in numbering to use what W. von Humboldt has called class-words. Here it is felt that an artificial unity has to be created, a common denominator found, and all reduced to it, before any summation can be carried out. Scholars and officials, in Chinese, can only be classed under the rubric of 'jewel' or dignity: and animals or fish by 'tails,' as if thereby only could one get a handle to holdthem and count them. (The idiom still lingers in western languages: as in English, heads of cabbage, or of cattle: or German,sechs Mann Soldaten.) So in Malay, instead of 'five boys' the phrase used is 'boy five-man': in other words, the numerals are supposed to inhere as yet in objects of a special kind or common occurrence[7]. And among the South Sea Islanders the consciousness of number is decidedly personal: that is to say, the distinction between one and two is first conceived as a distinction between 'I' and 'we two.' Even this amount of simplification surpasses what is found amongst some Australian tribes. There we find four duals: one for brothers and sisters: one for parents and children: one for husbands and wives: and one between brothers-in-law[8]. Each pair has a different form. We thus seem to see to what early language is applied: not to designate the objects of nature, but the members of the primitive family and their interests. The consciousness of numbers was first awakened by the need of distinguishing and combining the things that belonged to and specially interested men and women in the narrow circle of barbarian life[9]. It is not altogether imaginative in principle, though it may be occasionally surmise in details, to connect the rise of grammatical forms with the temperament and character of the people, and therefore with its social organisation. If the Bantoo or Caffir languages of Southern Africa instead of a single third personalpronoun and third personal termination to the verb use the separate forms corresponding to the ten class-prefixes of the nouns, it must be in accordance with the general spirit and system of these tribes. The various plural forms, if they persist, will reflect contemporary modes of life.

Numbers were at first immersed in the persons, and then, as things came to be considered also, in the things numbered. The mind seems to have proceeded slowly from the vague one to definite numbers. And the first decided step was taken towards an apprehension of numbers when two was distinguished from one, and the distinction was made part of the personal terminations. The plural was a further step in the same direction: the real value of which, however, did not become apparent until the numerals had been separately established in forms of their own. When that was accomplished, the special form of the dual became useless: it had outlived its purpose, and henceforth it ceased to have, any but that poetical beauty of old association which often adorns the once natural, but now obsolete growths of the past. When the numerals were thus emancipated from their material and sensuous environment, quantity was translated from outward being in its embodiments into a form of thought. At first, indeed, it was placed in an ethereal or imaginative space, the counterpart as it were of the sensuous space in which it had been previously immersed. It became a denizen of the mental region, as it had been before a habitant of the sense-world.

The mind was informed with quantity in the shape of number: but it does not follow from this, that the new product was comprehended, or the process of its production kept in view. Like all new inventions (and numeration may fairly be classed under that head), itwas laid hold of, and all its consequences, results, and uses estimated and realised by the practical and defining intellect. In one direction, it became, like many new inventions in the early days of society, a magic charm, and was invested with mystery, sacredness, and marvellous powers. But the intelligent mind,—the understanding,—resolved to make better use of the new instrument: and that in two ways, in practical work and in theory. On the one hand it was applied practically in the dealings of life,—in commerce, contracts, legislation, and religion. On the other hand, the new conception of number, which common sense and the instinctive action of men had evolved, was carried out in all its theory: it was analysed in all directions, and its elements combined in all possible ways. The result was the science of arithmetic, and mathematics in general. Such consequences did the reflective understanding derive from the analysis of its datum,—the fact of quantity freed from its sensuous envelope.

The general action of understanding, and of practical thought, is of this kind. It accepts the representative images which have emerged from sensation, as they occur: and tries to appreciate them, to give them precision, to carry them into details, and to analyse them until their utmost limits of meaning are explored. Where they have come from, and where they lead to,—the process out of which they spring, and which fixes the extent of their validity,—are questions of no interest to the understanding[10]. It takes its objects, as given in popular conception, as fixed and ultimate entities to be expounded in detail.

We have taken number as one example of the transference of a sensible or sense-immersed fact into a form of thought: but a form which is still placed in asuperior or mental space. One advantage of taking number as illustration, is that numbered things are distinguished from numbers in an emphatic and recognised way. Nobody will dispute that the abstraction, as it is called, has an existence of its own, and can be made a legitimate object of independent investigation. But if the process be more obvious in the case of the numerals, there must have been a similar course of development leading to the pronouns, the prepositions, and the auxiliary verbs—to what has been called the 'formal' or 'pronominal' or 'demonstrative' element, the connective and constructive tissue of language. Whether these pronominal 'roots' form a special and originally-distinct class of their own, or are derived from a transmutation of more material or substantial elements, is a question on which linguistic research casts as yet no very certain light. It is true that on the one hand etymology is mainly silent on the origin of pronouns, numerals, and the more fundamental prepositions (i. e. cannot refer them to roots significant of qualitative being): and one need not lay much stress on remarks, like that of Gabelenz[11], that in the Indo-Chinese languages the words forI, five, fishhave a like sound, as do those forthou, two, ear, or thatI am,originally meansI breathe. In all languages—though with immense diversities of degree, this formal element has attained a certain independence. And in many instances we can more or less trace the process by which there grew up in language an independent world of thought: we can see the natural existence passing out of the range of the senses into spiritual relations. Before our eyes a world of reason is slowly constituting itself in the history of culture: and we, who live now, enter upon the inheritance which past ages have laid up for us.

There is, however, a difference between the way in which these results look to us now, and the way in which they originally organised themselves. The child who begins to learn a language in the lesson-books and the grammars finds the members of it all, as it were, upon one level: adjectives, adverbs, prepositions, and verbs confront him with the same authority and rank. This appearance is deceptive: it may easily suggest that the words are not members in an organism, in and out of which they have developed. And this organism of thought has its individual types, expressed in the great families of human speech. Its generic form (as drawn out in a logical system) appears in different grades, with different degrees of fullness, in Altaic and Dravidian from what it does in Malay, or in Chinese, and these again have their own predominant categories as compared with those used in the American or African languages, or in Indo-Germanic and Semitic. If the Altaic languages e. g. are wanting in the verb proper, and manage with possessive suffixes and nouns; if the Semitic tenses display a poverty which contrasts with their wealth in Greek; and yet each group performs its function, we may infer that each speech has a complete organism, though it does not bring all its parts to adequate expression. All this distinction of 'parts of speech,' of forms, prefixes and suffixes, &c., is part of the life of language, embodying in more or less distinct organs the organisation of thought in the individual form it reached in that speech-type. Thus in Chinese there are strictly speaking no isolated words, nouns, or verbs: there are only abstract parts of a concrete sentence; and grammar in Chinese therefore has no accidence (no declensions, conjugations, &c.) but only syntax. Yet it is these abstract fragments which exist and seem to have independence andinherent meaning: whereas the unity in which they cohere to form a concrete context is the fleeting sentence of the moment. At the opposite extreme, again, the Mexican family of languages tend to incorporate relations to subject and object with the verb, in such a degree that the word almost becomes a sentence. Facts like these suggest that a science of the forms of language, in proportion as it generalises, tends to approach logic; and that logic will have a converse tendency to elevate to an unduly typical position the grammatical form of the languages with which the logician is best acquainted.

If these points were remembered, there would be less absurd employment of the grammatical categories of one group of languages to systematise another. Greek and Sanscrit grammar plays sad havoc with the organism of a Semitic tongue, and it is not less out of place as a schema for delineating e. g. South African dialect. Isolated words even in an Indo-Germanic language—even, we may say, in such a language as English—are still fractional, and do not get life and individuality except in their context. And it needs but a little experience to show how various that individuality may be. It needs perhaps still more meditation to realise that it is in this individuality that the real life of language lies: in the words said and written to express the thought of a personality. But, first, because language has its material and mechanical side, and secondly, because in civilised countries it further acquires a more stereotyped mechanism in written and printed language, its parts tend to gain a pseudo-independence. It is one aim of a philosophical dictionary to restore the organic interconnexion which in the mere sequence of vocables in juxtaposition is apt to be lost. What we call the meaning of a word issomething which carries us beyond that mere word,—which restores the connexions which have been broken off and forgotten. In the form of a dictionary, of course, this can only be done piece-meal: but if each piece is done thoroughly, it can hardly fail to bring out certain comprehensive connexions. The mere word seems a simple thing; and one is at first disposed to get rid of its difficulty by substituting a so-called synonym. But a deeper study reveals the fact that an exact synonym is a thing one can no more find than two peas which are absolutely indistinguishable. A synonym is only a practicalpis aller. But every word is really as it were a point in an infinitely complex organic life, with its essence or meaning determined by the currents to and fro which meet in it.

Words as we see themprima faciein a printed page do look separate entities. They stand, one here and another there, in a quasi-extension, with marks of direction and connexion pointing from one to another, but of connexion apparently extraneous to the more solid points which are represented by nouns and verbs, or names of substances, actions, and attributes. Results, as they are, of that practical analysis which the need of writing down language has led to, they are treated as complete wholes, which by the speaker are forced into certain temporary connexions. But this is an illusion which, because a thing changes its relationships, assumes that it can exist out of all relationships whatever. Every word of Language is such an abstraction, isolated from its context. But amid these contexts there are certain similarities: identical elements are detected: and these identical elements are the common names of language, the terms of general significance. In all cases, however, what an utterance of languagedescribes or expresses is a definite individual event or scene, conceived as a concrete of several parts. Each separate vocable is a contribution to the total: a step towards the real redintegration of the whole out of its several parts. But the total itself—the content of fact in any single sentence—is only an abstraction,—a part of the universe which human interest and need have isolated from the comprehensive scope of things. Thus, in two degrees, we may say, the picture produced in the sentence falls short of the truth of things. Each statement is an arbitrary or accidental cutting out of the totality: each element of the cutting is dependent on that abstraction, and relative to it. But—as in a given group of speech, the same sets of circumstances will naturally be selected, and tend to recur again and again,—the terms which describe them will acquire a certain association with the objects, and will come to be called the common names of these agents, acts, and qualities. They denote or 'represent' the things and acts, conceived however in certain aspects and relations, and not in their entirety and totality of nature.

In this product of intellectual movement above the limits of sensation we have the 'representation'[12]as Hegel calls it, on which the Understanding turns its forces. We have one product of the organic whole of thought taken by itself as if it were independent, set forth as a settled nucleus for further acquaintance: and this one point discussed fully and with precision, elaborated in all detail and consequence, to the neglect of its context, and the necessary limitations involved in the notion. The process of name-giving may illustrate this tendency in human thought to touch its objects only in one point. The names given to objects do notembrace the whole nature of these objects, but give expression only to one striking feature in them. Thus the name of the horse points it out as 'the strong' or 'the swift': the moon is 'the measurer' or 'the shining one'; and so in all cases. The object as expressed in these names is viewed from one aspect, or in one point: and the name, which originally at least corresponds to the conception, meets the object, properly speaking, on that side only, or in that relation. The object is not studied in its own nature, and in its total world, but as it specially enters the range of human interest, and serves human utilities. One can at least guess why it should be so: why a name should, in logical language, express an 'accidens' and not the 'essentia' of the object. For the investigation of primitive language seems to show that words, as we know them in separate existence, are a secondary formation: and that the first significant speech was an utterance intended to describe a scene, an action, a phenomenon, or complex of event. In point of time, the primary fact of language is an agglomeration or aggregate,—we may call it either word or clause (λόγος in short)—which describes in one breath a highly individualised action or phenomenon. The spirit or unifying principle in this group might be the accent. Such a word-group denotes a highly specialised form of being: and if we call it a word, we may say that the earliest words, and the words of barbarous tribes, are ingeniously special.[13]But it would be more correct to say, that in such a group the elements of the scene enter only froma single aspect or in a single relation. Accordingly when disintegration begins, the result is as follows. The elements of the group, having now become independent words held together by the syntax of the sentence, are adopted to denote the several objects which entered into the total phenomenon. But these words, or fragments of the word-group, 'represent' the objects in question from a certain point of view, and not in their integrity. The names of things therefore touch them only in one point, and express only one aspect. And thus, although different names will arise for the same thing, as it enters into different groups, in each case the name will connote only a general attribute and not the nature of the thing. These names are in the Hegelian sense of the term 'abstract.' In popular phraseology, they are only 'signs' of things: i. e. not 'symbols' (though they may have been in some cases symbolic in origin), for in a symbol there is anaturalcorrespondence or sensible analogy to the thing symbolised, but something 'instituted,' due to an 'understanding' or convention.

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