The Spirituality of Culture

Updated: Apr 22

GENTILE, Giovanni. The Reform of Education, translated by Dino Bigongiari, 85–109. New York: Harcourt, Brace and Company, 1922.

The idealistic conception of culture enables us to get an initial understanding of the spirituality of the school. This spirituality is surely felt by all those who live within the class-room; but it should be understood in the most rigorous and absolute manner by those who wish to have a deeper consciousness of the extreme delicacy of the tasks performed and the words uttered by those who enter it with the sincere heart and the pure soul of the teacher.

The school is obviously not the hall which constraints the teacher and the pupils. These may have a hall, may even have the teacher, without yet possessing the school, which consists in the communication of culture. This culture, we have seen, is not really pre-existent to the act which communicates it; it is not to be found in books, not to be looked for in an ideal transcendent world, not to be demanded of the teacher. It is only in the spirit of the person who is in the act of learning. It is there in the manner in which it is possible for it to be there, not comparable to any presumed form of pre-existing culture. The school gains its existence entirely in the soul of the learner.

Knowledge is not to be found beyond the bounds of the human spirit. I insist on this conception because I am well aware that the minds of many rebel against this conclusion, no matter how irrefutable its grounds may be. For they ask: what then is the learning which we ascribe to the master minds of humanity, now indeed dead but still active in their works? They also ask how we are able to think and account for that learning which we feel we are not originating, which we know we are re-acquiring for ourselves after it has many times been in the domain of others.

Can we really consider as non-existent what we as yet do not know, may perhaps never know, but which is none the less capable of being known? When we are filled with reverence for the glory of men whose learning surpasses our powers, are we the victims of an illusion? Are we prevailed upon by ignorance and lack of reflection? And how then can we justify the cult which every civilised man consecrates to the mighty spirits—philosophers, poets, artists, and heroes—who added so much to the moral fund of humanity? Was there not a Dante six centuries back, who composed a lofty poem, which was admired by everybody, at a time when we, who now read it and bring it to life in our souls, were still so far removed from the entrance of this life?

The answer to all these questions is very simple, so simple that we must be careful lest we miss its significance. All this lore of the past which we strive to preserve surely does exist; it does contain all the names which are sacred to the memory of humankind. The Divine Comedy has been written and no longer awaits its Dante. But this lore of the past, as we for brevity’s sake call it, is nothing else than what we think as such. History, as it unfolds itself from century to century, is never compressed within a past which because of its completeness might be made to exist beyond the present and in opposition to it; but it exists in a past which is in the present as a plant that grows or an animal that lives, never adding anything new to the old, always transforming the old into the new; at no time, therefore, having anything but what is new, never being anything else but the new. In history, thus comprehended, we to-day are but one person with the men who thought before us, with the poets, the philosophers, the spiritual creators of the past. With them we are a person that grows and develops, ever acquiring, never losing; a single being that apprehends and recalls and constantly makes all his past bear fruit in the present. Our childhood has not completely passed away into nothing: it keeps returning to the ever-busy phantasy that tenderly fondles it, cherishes it, idealises it into poetry. If we consider this childhood as something that once was, that existed in utter ignorance of this poetry that was yet to be written, that could not then be written, surely this infancy is quite dead; we should rather say that it never existed. But it does live as the childhood which is a recollection, which arouses feelings, and such feelings as are at a given moment the actual sentiment of the adult. Once in the years long gone by a kindly word reached the depths of my soul. We all have heard in the years long gone by some such kindly words that in the mystery of our childish mind appeared as a revelation. Such words as fall from the lips of a mother and inspired by her tender affection have the secret power of appeasing us in a moment of rage, and of making us feel the gentle sweetness of that goodness which is made of love. We may since have forgotten that word, and the circumstances in which it was uttered: but it is none the less true that on that day our soul was modified and became endowed almost with a sixth sense. This sense has enabled us subsequently to perceive so many things that are beautiful in life, and it in turn grew stronger because of frequent use and increasing exercise, until it finally became the most potent organ of our moral personality. Here too our development has been a constant acquiring with no losing: a preserving of the past by which it was converted into the present, and therefore annulled as past pure and simple.

Such is the moral development of man, who believes himself an individual, but is in truth humanity considered momentarily in one of its fragments. Such is history: the unfolding of the spirit in its universality. It is not therefore difficult to determine what is the past culture in which we desire to graft our present one. It is our own actual culture in so far as it is not the patrimony, not the spiritual life of the isolated individual, of a particular being; but is instead the life of the spirit in its universality, the development of the human personality taken in its effective, historical concreteness.

The past with its entire content is a projection of our actual consciousness, i.e., of the present. But we must not give this proposition a sceptical sense. As I have already pointed out, the present neither in the particular individual nor in the universal history of the spirit, is sundered from the past by that abyss which is ordinarily seen from a materialistic point of view. The past is one and the same thing with the present. The past is the present in its inmost substance; and the present is the past that has matured. The grain of wheat which was buried in the furrow is now no longer to be found under the glebe. It lives, multiplied in the ear of wheat. The seed as such was decomposed and destroyed in the soil; it is there no more, it sprung thence as a blade of grass, it grew, was transformed, still is, still lasts, and will continue to endure in other forms. Where is it now? Why, in whatever form it may now have assumed. It is the past in the present, as the present.

So then, what is Dante the poet who towers over the centuries, the object of our admiration, the master of all who speak and use the Italian language? He is the lordly poet of the fourteenth century, not because he then lived his own individual life, but because he survives to-day in us who think him, who appreciate him even when we are not fully acquainted with him. In this sense he lives in us, as the seed does in the ear of corn.

I have just hinted at the possibility of appreciating something without fully understanding it. I wanted to make clear how impossible it is to separate, with a clean cut, knowledge from ignorance. It is far from true that before taking up a certain science we know absolutely nothing about,—that the boy who goes to school for the first time is completely devoid of all knowledge, or that he who is in quest of a book which he has never read can in no way whatever speak about it.

For fair renown begets love for the unseen person, as the poet reminds us and as experience often teaches. Frequently we know of the existence and the beauty of a woman whom we have never seen, but who is not therefore completely unknown to us. So also many of us desired to go to school long before we had seen the inside of a classroom. What is dearer than the joy foretasted at the first imagining of school? We look forward to that new life upon which we are about to enter in the company of our bigger brothers and of our older playmates. They have told us so many things about it. From their accounts and from the fond memories of our parents we already know the school before we approach it, and its pleasing aspects invite us into the classroom.

For the same reason we search for books we have never seen, and we are drawn towards new studies and pursuits. There is no leaping from ignorance to knowledge, as from pitch darkness to noon-tide brilliancy. The transition is imperceptible, as when the dim morning twilight merges into the first glimmerings of dawn, which in turn fade away under the dazzling flashes of sunrise. And even from the midst of darkness we yearn for a world which though unseen is somehow present to our consciousness, already illumined by our thought, warmed by our sentiments. Or, in other words, the culture which we do not yet possess, and which we expect to get at school, is already implanted in our mind, where it will sprout and grow and bear fruit, fused and confused with the life of our spirit.

Having now reached this point, can we define culture? I am inclined for a moment to assume the role of Don Ferrante in Manzoni’s novel. By pedantic ratiocinations he proved that the plague could not be a contagious disease: “for,” he said, “in nature everything is either a substance or an accident.” Contagion, he then went on to prove, could neither be the one nor the other; therefore the plague was but an influx of the stars, and there could be no use in taking precautions; and having proved this, he fell a victim to the epidemic, and died cursing the stars like an operatic hero. Let us follow for a moment in the footsteps of this pendant, whose method, ridiculous as it may seem, has had nevertheless a glorious history, and one which Manzoni himself admired.

I say: We can think only and we do think only two kinds of reality,—person or thing. Every one of us is naturally drawn to this distinction; and when we have formulated it, we feel more or less vaguely, more or less clearly, that every possibility is comprised within these two terms, that outside of them it is impossible to think any reality whatsoever. The reason is this: if we think, if we act, if we live, we inevitably place ourselves in a situation such that we on one side are as centre, as beginning, or as subject of our activity; and on the other side are the objects toward which our activity is directed and by which it is terminated. We therefore as subject of the entire surrounding world; and this world as the end of our thoughts and of our scientific inquiries, end of our desires and of our practical activity; the world which is represented in our consciousness, and which we strive to dominate by our labours, and our reason. Can there be anything else beside us and what we think?

The world which we think and which we oppose to ourselves seems at first to contain different kinds of objects. There seem to be both persons and things; simple objects of cognition which we ordinarily call things which can never become subjects; and persons who at first are represented to us as objects of our knowing, of our love, and of our hatred, as ends of our activity; but who under a closer scrutiny are transformed before our eyes into knowing and acting subjects, who, in other words, become just exactly what we are. But when we really get to know these beings that surround us as subjects on an equal basis, then we cease to consider them as objects of our cognition, and as solely endowed with that material objectivity which at first put them in the same category with the inanimate things, with plants and animals. We then find them close to us, very close; fused with our own spiritual substance. We feel them to be our fellow men, our kinsmen, with whom we constitute that person of whose existence I am aware every time I say We: the person we must take into account whenever we wish to affirm our personality in a concrete manner, the only person, the one subject, the true subject of human knowledge and of human activity. The subject which knows and acts as a universal in the interests of all men, or rather in behalf of the one man in whom all single individuals are united and with whom they are all identified.

Then if we give a rigorous and exact meaning to the expressions, “We and what is before us,” “We and the objects,” “We and the World,” we have a correct classification of all thinkable reality differentiated into persons and things, but with the understanding that all persons are in reality one Person.

One person, and things innumerable! As we look about us, we find the horizon peopled with thousands and millions and infinite quantities of objects, which may one by one attract our attention, and may be gathered up in the vast, unbounded picture surveyed by the eye as it moves on from thing to thing, incessantly, without ever reaching the last. The world which we first discover is the world of matter, of things which strike our senses. This world rushes impetuously into our mind at the beginning of our natural experience. And these material objects are many not only de facto but also de jure. They must be, they cannot but be many if we are to consider them as material things. It is their peculiar nature, it is their very essence to be an indefinite multitude.

A material thing means a thing occupying space. And space is made up of elements, each one of which excludes all the others and is therefore conceived independently of the others, must so be conceived. For it is the very nature of space to be divisible. When it is narrowed down to a point and cannot be further subdivided, then it ceases to be space. Its divisibility signifies that space is nothing more than the sum of its parts; that it contains nothing in addition to these parts; that it therefore resolves itself into them without at all losing its being and without any of the parts being deprived of anything which was theirs in the whole. In fact, if anything were lost of the entire whole, this loss could not but be felt in each single part. A book, considered as a material thing, is composed of a certain number of printed leaves stitched together; and if the leaves fall apart, they may be brought together again so that they will compose the same book as before. An iron rod weighs the same before and after it has been broken up into parts.

Things cease to be exclusively and solely material when, though they may be divisible in a certain respect, they are nevertheless indivisible in another respect. Plants, animals, all living organisms, considered simply as objects occupying space and as therefore having certain dimensions, admit surely of being separated into parts. Trees are cut into logs, sawed into boards; animals are slaughtered and quartered. But considered from the point of view of its peculiar quality, of the essential property which distinguishes it from all other bodies, an organism is not divisible. If we do divide it, each component part ceases to be what it previously was when conjoined with the others. Such a part cannot be preserved; it withers, it decays, and is dispersed, so that the whole can never be reconstituted. The various parts of an organism, considered as such, are inseparable, because each of them is and maintains itself on the strength of its relations to the others, forming with them a true and essential unity. If we however try to find out what this unity is by which all the limbs are indissolubly held together, we shall discover nothing which can be observed and represented spatially, nothing endowed with dimensions, however small, after the manner of the several limbs which this unity fuses within itself and vivifies.

If unity which the life-giving principle of every organism could be spatially represented, or in other words, if it were something material, it would be one of those very limbs that have to be unified, and could not then be the unifying principle itself. Hence the vanity of the efforts on the part of materialistic physiologists who obstinately strive to explain life by observing the parts which compose the organic mass, by studying the concurrence of their processes, their chemical relationships, and their mechanism. A material being, organically constituted, is something more than a material thing pure and simple: it announces already a higher principle; it presages the spirit.

But the things that we all agree to regard as spiritual defy absolutely every attempt at division. A poem may be considered in a certain way as material, and may accordingly be divided into various parts,—stanzas, lines, words. But it is clear that such a separation cannot have the value which we assign to the divisions of things material. For in their case every part can stand by itself, and is in no way deprived of its characteristic being; whereas every part of a poem, stanza, verse, word, calls out and responds to every other part; and if isolated from them, loses the meaning which it had in the context; or rather it loses every meaning, and consequently perishes. It is true that by conjectures we interpret even very small fragments of ancient poems. But we do so only in so far as we claim the possibility of restoring approximately the entire poem in which the given fragment may live, by which it may be restored to life. Likewise all the words lined up in dictionaries are as so many bleeding limbs of living discourses, to which they must somehow or other be ideally reconnected, if we are to understand what they really were and what functions they had. Multiplicity of parts in things of the spirit is only apparent: it must be reduced to indivisible unity, from which every element of the multiplicity derives its origin, its substance, and its life, so that we may give to it a real meaning and a foundation.

Nor is this the only unity possessed by the things that are assumed to be spiritual. We have already considered the unity whereby, for example, the words of a poem cannot be separated from the poem itself, in which each of them acquires a particular accent, a particular expression, and therefore a particular individuality. We shall now consider another unity. He who really perceives a poem is not confronted by an observable thing, compact if you will, unseverable and united, but none the less independent of human personality. Poetry is only understood when in the flowering unity of its verses and in the continuous rhythm of its words we grasp a sentiment in its development, a soul’s throb in a moment of its life, a man, a personality. The poetry of Dante is very different from that of Petrarch, because each is the expression of a powerfully distinct personality. Any composition of these poets is understood and enjoyed only when we feel in it the personal accent which distinguishes one poetical personality from the other. A poet without individuality has no significance whatsoever, and therefore no existence as a poet. But the real artist leaves his imprint more or less markedly in all his productions, so that in every given instance, over and beyond the variety of the subject matter, we feel the living soul of the poet. A poem then is the poet; it is a person and not a thing. And the same can be said, as we can easily see, of all things that are commonly called spiritual.

But in addition to things material, it seems that there are immaterial ones which do not pertain as one’s own to any particular person. The ideas of which we had occasion to speak before,—immaterial entities, not perceptible by the sense, but thinkable by the intellect, and which severally correspond to all sorts or species of the various material things,—were once conceived as things by philosophers, and they are still so conceived to-day by the majority of men. It is not requisite that one actually think them; it is sufficient that they be in themselves thinkable. As a matter of fact, they may or may not be thought, no differently therefore from any of the material objects which are not created by our senses, but must already exist in order that our senses may perceive them. These ideas are many, in a manner corresponding to the material objects; and they are all different. The mirror, so to speak, the multiplicity of material things in whose semblance and likeness they were devised. There are horses in nature, and there is the idea of the horse by which we are able to recognise all the animals that belong to that species. There are dogs, and there is the dog which we rediscover in every one of them. And there are flowers and the flower; and pinks, roses, and lilies, as well as the pink, the rose, and the lily; and likewise iron, copper, silver, gold, lime, water, and so on, to infinity. It is impossible to set a limit to ideas, because it is not possible ever to stop dividing, distinguishing, subdividing that nature which unfolds itself throughout space.

This boundless multitude of ideas, through which our mind can rove, surely has no spatial extension. But because of the necessity of conceiving any multitude as existing in some kind of space, it was thought proper to posit an ideal space in addition to the physical one. In other words, metaphorical dimensions were added to dimensions properly so called. But whether spatially or not, we strive to conceive ideas as many, each one of them existing by itself, and susceptible of being thought independently of the others. In reality however we never succeed in thinking them except as bound together and forming a system, in such a way that no single one of them can be thought except by thinking the others with it. Take man as an instance: each one of us has intuitively the idea of man, but this idea is not possessed like a word of which we may not even know the meaning. In thinking the idea we must think something which is its content. If we know what man is, we must be able to attribute a content to the idea of man. We may say, as the ancients did, that man is the laughing animal, or the speaking animal, because he is the only animal capable of expressing the emotions of his soul by laughter or by the inflection of his voice; because, in other words, he is the only animal who is conscious of what goes on within him. Or perhaps we might say that man is the reasoning animal, and we think this idea when we have thought the idea of animal and the idea of reason. But can the idea of animal be thought by itself alone? It, as well as the idea of reason, must have a content; that is, each must be connected with other ideas, without which it would be deprived of all consistency.

And so the mind that begins to think one single idea is compelled, almost dragged, to pass on to another, then to a third, and so on indefinitely. It finds itself in the condition of the man who tried to grasp a single link of a chain, just one, and found that he could not have it except on condition of taking the whole chain. So it is with ideas. We may not be capable of encompassing all of them in one single thought; but whenever we try to fix any one of them in our mind, it presents itself to us as a knot in which many other ideas are interlaced, twisted, and entangled. They form an infinite chain, in which it is not possible to think the first link or the last one, because the beginning is welded to the end, and we turn and turn and never reach the last. Is not this the nature of the ideas as we see them, as they constitute the field from which we must harvest all our possible thoughts?

Ideas are not, therefore, a true multiplicity, because they are not things, either material or ideal, and because they do not occupy any space whatsoever. Our imagination may present them to us as so many lights of an ideal sky; but our intelligence warns us that they cannot be separated one from the other and placed side by side. As I have already said: when we think one, we think them all. Or in any event we should, if we had mastered all that there is to be known. So that to our thought ideas appear as constituting one unique whole, a unity, that something which we call science, truth, knowledge. They are not a multitude, for the simple reason that in multiplicity they would be unthinkable. Their connection with and participation in an absolute unity come from the fact that they are the object of thought, and are therefore submitted to its activity, whereby they are ordered, correlated, organised, unified. In order that we may say that one idea contains another, or many others, we must analyse this first idea and define it. This first idea must be distinguished from the others, and they likewise among themselves. It is not therefore sufficient to say that there are these ideas, motionless, inert, lifeless, as they necessarily would be if they existed per se, as objects of mere possible contemplation. There must also be some one to analyse them, define them, and distinguish them. It is not enough to have the material of thought, we need thought also to mould and fashion this material, turn it effectively into thought stuff, reduce it to something susceptible of being thought. Ideas as things would in no way be related among themselves. But they do have that relationship which is generated by thought as it thinks them. Thought generates this relationship not as a fixed one, as would be the case if it were inherent in the things themselves; but as a relationship which is being formed by degrees, and which is continuously changing and developing. No ideal, abiding science, existing only as the object of a vague phantasy, can therefore result from this relationship. It constitutes instead a science which is ever re-formed and is never formed; it gives to the ideas an ever renewed aspect: it matures them, elaborates them, perfects them, by concentrating on each one of them the constantly increasing light of the system into which it closely binds them.

Ideas, then, as we really think them, are not a minutely fractioned and scattered multiplicity. Nor are they a mass of concurrent elements. They are Thought as it becomes articulate, and gains distinctness by these many Limbs, by these ideas, which exist, all of them, in the process by which they are gradually formed, developed, and complicated, and arrayed in an order which is constantly being renewed and which is never definitely perfected.

There are not then many ideas; there is one Idea, which is Thought. Only in a metaphorical sense can we consider them as things; and, properly speaking, they are the human person itself as actualised in thought, which is busily occupied in the construction of knowledge. They are an indivisible unity, in which each idea is found collaborating with every other one so as to answer the questions which Thought constantly propounds. They are the human person, not the persons; for we have already concluded that only in an abstract sense is it possible to speak of many persons; concretely there is but one universal Person which is not multiplicable.

There are not, then, going back to our original division, persons and things, material and spiritual. At the most there is one person, Man, and there are the material things which constitute this nature, as it occupies space, and in which we too believe we have a place, in as much as we consider ourselves beings of nature. Nothing beyond this can be conceived: on one side a sole immultiplicable reality, on the other a manifold reality, indefinitely divisible.

Here we might perhaps stop considering the special interest that called forth this inquiry. For no one could possibly suppose for a moment that culture could be placed in the midst of material things rather than in the spiritual reality which is a person. However, since the intimate nature of this spiritual reality which we call culture is not yet clearly revealed, we must continue our investigations, and give more attention to this division which for a moment we thought might be final. I mean the division of the world into persons and things: the equipoise of spirit and matter.

Do we really think this matter as we say we do, and which we believe we are justified in opposing to the spirit, in as much as the spirit is unity or universality, and matter, in its entirety, in every one of its parts, in everything, is an indefinite multiplicity? Matter can in truth be thought only on condition that it be possible to think multiplicity, that pure multiplicity which is the characteristic quality of matter.

What then is the meaning of multiplicity? In absolute terms we call multiple that which consists of elements each one of which is quite independent of all the others, and absolutely devoid of any and every relationship with them. The materialist conceived the world as an aggregate of atoms, separated one from the other and having no reciprocal relevance of any sort whatsoever. In the world of pure quantity, which is the same as absolute multiplicity, mathematical science claims the knowledge of units indifferent to their nexus, and therefore susceptible of being united and separated, of being summed up and divided, without any alteration taking place within the individual unit itself. Numerical units are therefore preeminently irrelative.

But the concept itself of the multiplicity of irrelative elements is an absurd one. In order that we may conceive many unrelated elements we must, to start with, be able to conceive a couple of such elements. Let us take A and B, absolutely unrelated, and such that the concept of one will contain nothing of the other’s, and will therefore exclude it from itself. If A did not so exclude B, something of B would be found in A, and we could no longer speak of the two elements as irrelative. Irrelativity means reciprocal exclusion, a capacity by which each term is opposed to the other, and prevents the other from having anything in common with it. Without this reciprocal action whereby each term turns to the other and excludes it from itself, establishing itself as a negation of it, there would be no irrelativity. But this action by which each term is referred to the other so as to deny it, what is it but a relationship? Every effort therefore tending to break up reality into parts completely repugnant amongst themselves, mutually excluding one another, and therefore reciprocally indifferent, results in the very opposite of what was intended, viz.: the relative in place of the irrelative, unity instead of multiplicity.

Neither duality nor multiplicity is conceivable without that unity whereby the two engender that whole in which the two units are connected, even though they mutually exclude one another: without that unity which fuses and unifies every multiplicity determined in a number, which correlates among themselves the units which constitute the number. We could strip multiplicity of all unity only by not thinking it. But then in the gloom of what is not thought, multiplicity truly enough would not be unity, but it would not even be multiplicity, because it could not be anything at all. Or, if we prefer, it would be absolutely unthinkable.

Thought then establishes relationships among the units of the multiple, and thus constitutes them as the units of the manifold, and as forming multiplicity. It adds and divides, composes and decomposes, and variously distributes, materialising and dematerialising, so to speak, the reality which it thinks. For it materialises the reality when it conceives it as manifold: but it can conceive it as such only by unifying it, and therefore by dematerialising it and reabsorbing it into its own spiritual substance.

Matter is a manifold reality, without unity. What it is we already have seen: a material reality, and as such divisible into parts, placed in the world in the midst of a congeneric multitude. Now, since pure multiplicity is not conceivable except on condition that we abstract from that relationship to which the reciprocal exclusiveness of manifold elements is reduced, it is evident that matter and things are abstract entities. Thought stops to consider them, and regards them as existent, only because it withdraws the attention from that part of itself which it contributes to the making of the object represented. Thought therefore prescinds from that unity which material things could not by themselves contain, but from which it is impossible to prescind absolutely unless we wish to be reduced to an absurd conception.

Objective things then, the world of matter itself which we are wont to oppose in equipoise to the person, are in truth not separable from it. For matter has its foundation in thought by which the personality is actualised. Things are what we in our own thought counterpose to ourselves who think them. Outside of our thought they are absolutely nothing. Their material hardness itself has to be lent to them by us, for it ultimately is to be resolved into multiplicity, and multiplicity implies spiritual unity.

This then is the world: an infinity of things all of which have however their root in us. Not in “us” as we are represented ordinarily in the midst of things; not in the empirical and abstract “us” which feeds the vanity of the empty-headed egoist, of him who has not the faintest notion of what he really is, who can therefore think of himself only as enclosed within the tight husk of his own flesh and of his particular passions. No! they are rooted in that true “us” by which we think, and agree in one same thought, while thinking all things, including ourselves as opposed to things. And he who fails to reach this profound source, this root from which all reality receives its vitalising sap, may indeed get a blurred glimpse of a blind, inert, material mechanism, but he cannot even fix and determine this mechanism. He cannot upon further reflection stop at the conviction that it is in truth, as it appears in semblance, something real, for it reveals itself to him as so absurd as to become unthinkable. The world then is in us; it is our world, and it lives in the spirit. It lives the very life of that person which we strive to realise, sometimes satisfied with our work, but oftener unsatisfied and restless. And there is the life of culture.

It is not possible to conceive knowledge otherwise than as living knowledge, and as the extolment of our own personality. This is our conclusion. We shall, later on, derive from it two corollaries that are very important for teachers, in as much as they bear directly on the problems of education.

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