Paul Lafargue

Social and Philosophical Studies

The Origin of Abstract Ideas

Inquiries Into the Origin of the Idea of Justice and the Idea of Goodness

I. Contradictory Opinions Regarding the Origin of Abstract Ideas

It often happens in the history of thought that hypotheses and theories, after having been the object of study and discussion, disappear from the field of intellectual activity to reappear only after a season of oblivion more or less prolonged. Then they are examined anew in the light of the know ledge accumulated during the interval, and some times they end by being included in the baggage of acquired truths.

The theory of the continuity of species – unconsciously admitted by the savage, who takes for his ancestors plants and animals endowed with human qualities, scientifically foreseen by the thinkers of antiquity and the Renaissance, brilliantly defined by the naturalists at the close of the eighteenth century – had sunk into so deep an oblivion after the memorable debate between Geoffrey Saint-Hilaire and Cuvier that its conception was attributed to Darwin when he revived it in 1859 in his Origin of Species. The proofs, which in 1831 had been lacking for Geoffrey Saint-Hilaire to bring victory for his thesis, Unity of Plan, had been accumulated in such abundance that Darwin and his disciples had been able to complete the theory and impose it on the scientific world.

The materialistic theory of the origin of abstract ideas had a similar experience: put forth and discussed by the thinkers of Greece, taken up in England by the philosophers of the seventeenth century, and in France by those of the eighteenth century – it has since the triumph of the Bourgeoisie been eliminated from philosophical preoccupations.

Alongside of the ideas which correspond to things and persons, there exist others which have no tangible counterpart in the objective world, such as the ideas of the Just, the True, the Good, the Evil; of Number, Cause and Infinity. If we are ignorant of the cerebral phenomenon which transforms the. sensation into an idea – just as we do not know how a dynamo transforms motion into electricity – we have no trouble in taking account of the origin of the ideas which are the conceptions of objects apprehended by the senses; while the origin of the abstract ideas which do not correspond to any objective reality, has been the object of studies which have not yet given definite results.

The Greek philosophers, whom we meet at the entrance of all the avenues of thought, have stated and tried to solve the problem of abstract ideas. Zeno (the founder of the Stoic School) looked upon the senses as the source of knowledge, but the sensation became a conception only after having undergone a series of intellectual transformations.

The savages and barbarians, who were the creators of the Latin and Greek languages, anticipating the philosophers, seemed to have believed that thoughts proceeded from sensations, since in Greek eidos, the physical appearance of the object, that which strikes the view, signifies “idea”; and in Latin sapientia, the taste of an object, that which strikes the palate, becomes “reason.” [1]

Plato, on the contrary, thought that the ideas of the Good, the True, the Beautiful, were innate, unchangeable, universal. “The soul in its journey in the track of God, disdaining what we improperly call beings, and raising its glances toward the one true Being had contemplated It and remembered what it had seen.” (Phaedrus). Socrates had also placed apart from humanity a Natural Right whose laws, nowhere written, are nevertheless respected by all the world, although men may have never assembled together to enact them by a common agreement. [2]

Aristotle does not seem to have so robust a faith in Natural Right, which he jests at pleasantly when he assures us that it was inviolable only for the gods, however, the immortals of Olympus were quite at their ease with this Natural Right, and their doings and practices were so grossly shocking to the morals current among mortals, that Pythagoras condemned to the torments of hell the souls of Homer and Hesiod for having ventured to relate them.

Right, Aristotle said, was not universal. According to him it could only exist between equal persons. The father of a family, for example, could not commit an injustice toward his wife, his children or his slaves, nor toward any person in dependence on him. He could strike them, sell them and kill them without thereby departing from the right. Aristotle, as is usually done, adapted his Right to the manners of his epoch; as he did not conceive of the transformation of the patriarchal family, he found himself obliged to erect its customs into principles of right. But instead of according to Right a universal and immutable character, he conceded to it only a relative value and limited its action to persons placed on an equal footing.

But, how is it that his teacher Plato, whose mind was so subtle, who had under his eyes the same customs and who had no idea of their abolition, since in his ideal republic he introduced slavery – had not the same opinions regarding the relativity of Justice? A word dropped by Aristotle gives room for the theory that Plato, like the priests of the Sacred Mysteries and a majority of the sophists, had not explained in his writings the whole of his philosophy, but had revealed it only to a small number of trusted disciples. He might have been intimidated by the condemnation of Socrates and the dangers incurred at Athens by Anaxogaras, who had imported thither from Ionia the Philosophy of Nature, and who escaped death only in flight.

This opinion is confirmed by an attentive and comparative reading of the dialogues of Plato, who, as Goethe remarks, often makes game of his readers. In any event, the teacher of Socrates and several of the disciples of the latter had but a slender idea of the immutability of Justice. Archelaus, who merited the surname of “Naturalist” (Phusikos), and who was the teacher of Socrates, denied Natural Right and maintained that civil laws were the only foundation for the notions of the Just and the Unjust. Aristippus, who, like Plato, was the disciple of Socrates, declared his profound contempt for Natural and Social Right, and professed that the wise man ought to put himself above civil laws and permit himself to do all they forbid when he could do so in safety: the action which they forbid being bad only in the vulgar opinion, invented to keep fools in check. [3] Plato, without having the boldness to put forth such doctrines, showed by his acknowledged respect for pederasty, the little importance he attached to the laws of Natural Right. This love against nature, forbidden to slaves, was the privilege of free citizens and virtuous men; in the Republic (Book 5) Socrates makes of this one of the rewards for warlike courage.

The quarrel over the origin of ideas was rekindled in the seventeenth and eighteenth centuries in England and France when the Bourgeoisie was setting itself in motion and preparing to grasp the dictatorship of society. There are no innate ideas, declared Diderot and the Encyclopedists. Man comes into the world as a blank tablet on which the objects of nature engrave their impressions as time passes. The Sensationalist school of Condillac formulated its famous axiom, “Nothing exists in the understanding which has not originally been in the senses.” Buffon advised the gathering of facts in order to procure ideas, which are nothing but compared sensations, or more accurately, associations of sensations.

Descartes, reviving the method of introspection, and the “Know Thyself” of Socrates, and bringing again into use the Chinese puzzle of the Alexandrian School, “Given the Self, to find God,” isolated himself in his ego in order to know the universe, and dated from his ego the beginning of philosophy, for which he is reproached by Vico. As in his ego purified from beliefs that have been taught, or, so to speak, from the prejudices conceived from infancy by the senses, as well as from all truths taught by the sciences, Descartes found the ideas of Substance, of Cause, etc.; he supposed them to be inherent in the intelligence and not acquired by experience. They were, according to Kant s expression, universal and necessary ideas, rational concepts whose objects can not be furnished by experience, but existing incontestably in our mind; whether we know it or not, we hold at every moment certain necessary and universal judgments; in the simplest propositions are contained the principles of Substance, Cause and Being.

Leibnitz replied to those who with Locke affirmed that ideas were introduced by way of the senses, that in fact nothing existed in the understanding which had not originally been in the senses, except the understanding itself. Man according to him, brought with him at birth certain ideas and conceptions concealed in his understanding which the encountering of exterior objects brought to light. The intelligence is pre-formed before individual experience begins. He compared the ideas and conceptions anterior to experience to the different colored veins which streak a block of marble, and which the skillful sculptor uses to adorn the statues he chisels from it.

Hobbes, who, before Locke, had said in his treatise on Human Nature, that there were no .ideas which had not previously existed in sensation, and that the sensations are the origins of ideas – reproducing the thesis of Archelaus, maintained in his De Cive, that we must turn to the civil laws to know what was just and what was unjust. They indicate to us what must be called theft, murder, adultery or injury to a citizen; for it is not a theft simply to take away from someone that which he possesses, but that which belongs to him; now it is for the law to determine what is ours and what is another’s. Likewise, not every homicide is murder but rather when one kills one whom the civil law forbids putting to death; nor is it adultery to lie with a woman, but only to have to do with a woman whom the law forbids approaching. [4]

The patricians of Rome and Athens committed no adultery in having connection with the wives of artisans, in quas stuprum non committitur – “against whom a crime is not committed,” said the brutal legal formula. They were consecrated to the aristocratic debauch. In our days the husband who in England should kill his wife, taken in the act of adultery, would be summarily hanged as a vulgar assassin; while in France, far from being punished he becomes a hero, who has avenged his honor. The course of a river suffices to transform a crime into a virtuous act, so said, before Pascal, the skeptic Montaigne. (Book 2, Chapter 13.)

Locke maintained that ideas came from two sources, sensation and reflection. Condillac apparently deprived the English philosopher’s doctrine of one of its sources, reflection, leaving only sensation – which was transformed into attention, comparison, judgment, reason, and finally into desire and will.

His ex-disciple, Maine de Biran, casting sensation to the winds and restoring to honor the method of Descartes, who drew everything from his ego as from a well, found in the understanding the point of departure of his ideas. [5] The concepts of “Cause and Substance,” he said, “are antecedent in our mind to the two principles which contain them. We first think these ideas within ourselves, in our knowledge of the Cause and the Substance that we are; once these ideas acquired, induction carries them outside of us and makes us conceive of causes and substances wherever there are phenomena and qualities.” The principle of Cause and of Substance reduces itself to nothing but a phenomenon or rather a fiction of our understanding, to use Hume’s phrase. The introspective method of Descartes and Socrates, which the Bourgeois spiritualists abused so liberally, leads on one side to skepticism and on the other to impotence, for, “to pretend to illuminate the depths of psychological activity by means of the individual consciousness is like wishing to light the universe with a match,” says Maudsley.

The final victory of the Bourgeoisie in England and in France impressed a complete revolution upon philosophic thought. The theories of Hobbes, Locke and Condillac, after having occupied the center of the stage, were dethroned. People no longer deigned to discuss them and they were never mentioned unless truncated and falsified, to serve as examples of the wanderings into which the human spirit falls when it abandons the ways of God. The reaction went so far that under Charles X even the philosophy of the sophists of spiritualism fell under suspicion. An attempt was made to forbid their teaching in colleges. [6]

The triumphant Bourgeoisie re-established on the altar of its Reason the eternal truths and the most vulgar spiritualism. Justice, which the philosophers of Greece, England and France had reduced to reasonable proportions, which suited it to the conditions of the social environment in which it was manifested, became a necessary, immutable and universal principle. “Justice,” cried one of the most academic sophists of the Bourgeois philosophy, “is invariable and always present,” although it arrives only by degrees in human thought and in social facts. The limits of its field of action are ever extended and never narrowed; no human power can make it leave ground once acquired.

The Encyclopedists threw themselves with revolutionary enthusiasm into the quest of the origin of ideas, which they hoped to find by questioning the intelligence of children and savages. [7] The new philosophy scornfully rejected these inquiries which were of a nature to lead to dangerous results. “Let us set aside in the first place the question of origin,” exclaimed Victor Cousin, the master sophist, in his argument on the True, the Good and the Beautiful.

“The philosophy of the last century was too complaisant to questions of this sort. To what purpose shall we call on the region of darkness for light, or on a mere hypothesis for the explanation of reality; why go back to a pretended primitive stage in order to account for a present stage which can be studied in itself; why inquire into the germ of that which can be perceived and which needs to be known in its finished and perfect form? We deny absolutely that human nature should be studied in the famous savage of Aveyron or in his peers of the Islands of Oceanica or the American Continent. The true man is man perfect in his type; the true human nature is human nature arrived at its full development, as the true society is also the perfected society. Let us turn away our eyes from the child and the savage to fix them upon the actual man, the real and finished man.” (15th and 16th Lessons)

The ego of Socrates and Descartes could not but inevitably lead to the adoration of the bourgeois, the man perfect in his kind, real, finished, – the type of human nature arrived at its complete development and to the consecration of bourgeois society, the finished social order, founded upon the eternal and immutable principles of Goodness and Justice.

It is time to inquire into the value of this Justice and these eternal truths of Bourgeois spiritualism and to reopen the debate on the origin of ideas.

II. Formation of the Instinct and of Abstract Ideas

We may apply to the instinct of animals what the spiritualist philosophers call innate ideas. Beasts are born with an organic pre-disposition an intellectual pre-formation, according to Leibnitz’s phrase, which permits them to accomplish spontaneously, without going through the school of any experience, the most complicated acts necessary to their individual preservation and the propagation of their species. This pre-formation is nowhere more remarkable than in the insects which go through metamorphoses, as the butterfly and may-bug. According to their transformations, they adopt different kinds of life rigorously correlated with each of the new forms which they take on. Sebastien Mercier was altogether right when he declared that “instinct was an innate idea.” [8]

The spiritualists, not having the idea that instinct might be the result of the slow adaptation of a species of animals to the conditions of its natural environment, conclude stoutly that instinct is a gift of God. Man has never hesitated to put out of his reach the causes of the phenomena which escape him. But instinct is not like the Justice of the sophists of spiritualism, an immutable faculty, susceptible of no deviation, no modi fication. Domestic animals have more or less modified the instincts which God in his inexhaustible goodness bestowed on their savage ancestors. The chickens and ducks of our back yards have almost lost their instinct of flight, which became useless in the artificial environment in which man has placed them for centuries. The aquatic instincts has been obliterated in the ducks of Ceylon to such a degree that they have to be pushed to make them go into the water. Different varieties of chickens, Houdans, LaFleche, Campine, etc., have been robbed of the imperative instinct of maternity; although excellent layers they never think of sitting on their eggs. The calves in certain parts of Germany for generations have been taken from their mothers at birth, and among the cows a notable weakening of the maternal instinct has been observed. Giard thinks that one of the prime causes of that instinct in the mammals might be the organic need of relief from the milk, which makes the breasts swollen and painful. [9]

Another naturalist shows that the nest-building instinct of the stickleback must be attributed not to the Deity, but to a temporary inflammation of the kidneys during the mating season.

No very long time is necessary to reverse the best rooted instinct. Romanes cites the case of a hen which had been made to sit three times on duck's eggs and who conscientiously pushed into the water the true chickens which she had been permitted to hatch. Man has overturned the instincts of the canine race; according to his needs he has given it new instincts and afterwards has suppressed them. The dog in the savage state does not bark. The dogs of the savages are silent; civilized man has given the dog the instinct of barking and has afterwards suppressed it in dogs of certain breeds. When the hound encounters the game, he leaps upon it barking loudly, while the sight of game makes the setter mute and nails him to the spot. If the setter is of a good breed, he needs no individual education to manifest this instinct, which is relatively a new acquisition. The young dogs hunting for the first time stop mute and motionless in their path at the sight of stones, sheep, etc. The tendency is implanted in the brain, but it is blind and requires a special training. Since to modify or suppress the instincts of an animal and to develop new ones in in him, it is only necessary to place him in new conditions of existence, the instinct of the wild animals is then only the result of their adaptation to the conditions of the natural environment in which they live. It is not created all at once; it is developed gradually in the animal species under the action and reaction of external and internal phenomena, which may be unknown but which necessarily have existed.

Man can study in himself the formation of instinct. He can learn nothing mentally or physically without a certain cerebral tension which relaxes in proportion as the object of study becomes more familiar. When, for example, one begins to play the piano, one must watch attentively the movement of the hands and fingers in order to strike exactly the note desired, but with habit one reaches the point of touching it mechanically without looking at the keyboard, and while thinking of other things. Just so when one studies a foreign language one must constantly keep his attention on the choice of words, articles, prepositions, terminations, adjectives, verbs, etc., which come to mind instinctively when one becomes familiar with the new language. The brain and the body of man and the animal have the property of transforming into automatic actions what originally were voluntary and conscious, and the result of a sustained attention. Without this property of automatizing himself, man would be incapable of education, physically or intellectually; if he were obliged to watch over his movements in order to speak, walk, eat, etc., he would remain in everlasting childhood. Education teaches man to dispense with his intelligence. It tends to transform him into a machine more and more complicated. The conclusion is paradoxical.

The brain of an adult is more or less automatized according to the degree of his own education and that of his race. The abstract elementary notions of Cause, Substance, Being, Number, Justice, etc., are as familiar and instinctive to him as eating and drinking, and he has lost all remembrance of the manner in which he acquired them, for civilized man, like the setter, inherits at birth the traditional habit of acquiring them at the first occasion. But this tendency to acquire them is the result of a progressive ancestral experience prolonged through thousands of years. It would be as ridiculous to think that abstract ideas germinated spontaneously in the human head as to think that the bicycle or any other machine of the most improved type had been constructed at the first attempt. Abstract ideas, like the instinct of animals, were gradually formed in the individual and in the race. To seek their origin it is not enough to analyze the manner of thinking of the civilized adult, as Descartes does, but also, as the Encyclopedists would have had it to question the intelligence of the child and to re trace the course of the ages to study that of the barbarian and the savage, as we are obliged to do when we wish to find the origins of our political and social institutions, of our arts and our sciences. [10]

The sensationalists of the eighteenth century in making of the brain a tabula rasa, which was a radical way of renewing the “purification” of Descartes, neglected this fact of capital importance; namely, that the brain of the civilized man is a field worked for centuries and sown with concepts and ideas by thousands of generations and that, according to the exact expression of Leibnitz, it is pre-formed before individual experience begins. We must admit that it possesses the molecular arrangement destined to give birth to a considerable number of ideas and concepts. Some such admission is required to explain that extraordinary men, like Pascal, have been able to find out for themselves more than one series of abstract ideas, such as the theorems of the first book of Euclid, which have only been elaborated by a long procession of thinkers. In any case the brain possesses such an aptitude for acquiring certain concepts and elementary ideas that it does not perceive the fact of their acquisition. The brain is not merely limited to receiving impressions which come from outside, by way of the senses; it, of itself, does a molecular work, which the English physiologists call unconscious cerebration, which enables it to complete its acquisitions and even to make new ones without passing through experience. Students utilize this precious faculty when they learn their lesson imperfectly and go to bed leaving to their slumber the duty of fixing them in memory.

Indeed, the brain is full of mysteries. It is a terra incognita which the physiologists have scarcely begun to explore. It certainly possesses faculties which often find no outlet in the environment in which the individual and his race are evolving. These dormant faculties cannot therefore result from the direct action of the exterior environment upon the brain, but rather from its action upon other organs, which in their turn react upon the nervous centers. Goethe and Geoffroy Saint-Hilaire called this phenomenon the balancing of organs. Here are two historical examples.

Savages and barbarians are capable of a far greater number of intellectual operations than they accomplish in their daily life. During hundreds of years the Europeans have transported from the coast of Africa into the colonies thousands of savage and barbarian negroes, removed from civilized men by centuries of culture. Nevertheless at the end of a very short time they assimilated the crafts of civilization. The Guaranys of Paraguay, when the Jesuits undertook their education, were wandering naked in the forests, armed only with a wooden bow and club with no knowledge, except how to cultivate maize. Their intelligence was so rudimentary that they could not count beyond twenty, using their fingers and toes. Nevertheless the Jesuits made these savages skillful operatives, capable of difficult works – such as complicated organs, geographical spheres, paintings and decorated sculptures. These trades and arts with the ideas corresponding to them did not exist in the inborn state in the hands and brain of the Guaranys. They had been, so to speak, poured into them by the Jesuits as new airs are added to a street organ. The brain of the Guaranys, if it was incapable of discovering them by its own initiative was at least marvelously “predisposed” or “pre-formed,” according to Leibnitz’s phrase, for acquiring them.

It is equally certain that the savage is as foreign to the abstract concepts of civilized men as to their arts and crafts, which is proved by the absence in their language of terms for general ideas. How then did the abstract ideas and concepts which are so familiar to the civilized man slip into the human brain? To solve this problem which has to so great an extent preoccupied philosophic thought, we must, like the Encyclopedists, start on the path opened up by Vico, and question language, the most important if not the first mode of manifestation of sentiments and ideas. [11] It plays so considerable a role that the Christians of the first centuries, reproducing the idea of primitive men, said, “The Word is God;” and that the Greeks designated by the same term, logos, the word and thought; and that from the verb phrazo (to speak), they derived phrazomai, to speak to one’s self, to think. Indeed the most abstract head cannot think without employing words – without speaking to himself mentally, if he does not do so really, like children and many adults who murmur what they think. Language holds too great a place in the development of the intellect for the etymological formation of words and their successive meanings to fail of reflecting the conditions of life and the mental state of the men who created and used them.

One fact strikes us at the outset; often one and the same word is used to designate an abstract idea and a concrete object. The words which in European languages signify material goods, and the straight line, have also the meaning of the moral Good and Right, Justice;

Here again are other examples chosen in the Greek language: Kalon, arrow, javelin, beauty, virtue; phren, heart, entrails, reason, will; kakos, man of plebeian origin, base, wicked, ugly; kakon, vice, crime. The word kakos contributes to the formation of a series of terms, employed for what is vile and evil; kakke, excrement; kakkia, vice, baseness; kakotheos, impious; kakophonia, unpleasant sound, etc.

The fact is worth attention, although little noticed. This is the way with daily phenomena; because they fill the eyes they are not seen. Nevertheless, it is worth considering how the vulgar tongue and the philosophic and legal tongue have joined under the same term the material and the ideal, the concrete and the abstract. Two questions are raised at the very outset: first, have the abstract and the ideal been degraded into the concrete and into the material, or have the material and concrete transformed themselves into the ideal and abstract? – and how has this transubstantiation been accomplished?

The history of successive meanings of words solves the first difficulty; it shows the concrete meaning always preceding the abstract meaning.

The link which attaches the abstract meaning to the concrete meaning is not always apparent. Thus it is difficult at first glance to perceive how the human mind could have linked pasturage to the abstract idea of law, the straight line to the idea of Justice, the share of a guest at a banquet to immutable destiny. I shall show the links which unite these different meanings in the article on the Origins of the Ideas, Justice and Goodness. It is only important at this moment to point out the fact.

The human mind ordinarily employs the same method of work in spite of the difference in the objects on which it operates: for example, the road which it has followed to transform sounds into vowels and consonants is the same as that which is traversed in rising from the concrete to the abstract. The origin of letters appeared so mysterious to the Bishop Mallinkrot, that in his De Arte Typographica, to put his mind at rest, he attributed their invention to God, who was already the author of instinct and abstract ideas. But the researches of philologists have torn away one by one the veils enveloping the alphabetical mystery. They have shown that letters did not fall ready-made from heaven, but man arrived only gradually at representing the sounds by consonants and vowels. I shall mention the first steps traversed, which are useful for my demonstration.

Man begins by picture-writing. He represents an object by its image, a dog by drawing of a dog. He passes then to symbolical writing, and pictures a part for the whole, the head of an animal for the entire animal. Then he rises to metaphorical writing: he portrays an object having some resemblance, real or supposed, with the idea to be expressed – the forepart of a lion to signify the idea of priority, a cubit for Justice and Truth, a vulture for maternity. The first attempt at phonetics was made by rebuses; the sound was represented by the image of an object having the same sound. The Egyptians, calling the pig’s tail deb, represented the sound deb by the picture of the curled tail of a pig. Finally a certain number of pictures are preserved more or less modified, no longer for the phonetic value of several syllables, but for that of the initial syllable, etc., etc. [12]

Writing had inevitably to pass through the metaphorical stage since primitive man thinks and speaks in metaphors. The Redskin of America to indicate a brave warrior said “he is like the bear;” the man with piercing glance is like the eagle; to affirm that he forgives an outrage he declares “he buries it in the earth,” etc. These metaphors are for us sometimes undecipherable; thus, it is difficult to understand how the Egyptians came to represent in their hieroglyphics Justice and Truth by the cubit, and maternity by the vulture. I shall disentangle the metaphor of the vulture. In the next article I will explain that of the cubit.

The matriarchal family had in Egypt an extraordinary longevity, as is shown in its religious myths by numerous traces of the antagonism of the two sexes; struggling, the one to preserve its high position in the family, the other to dispossess it. The Egyptian like Apollo in the Eumenides of Aeschylus, declares that it is man who fulfills the important function in the act of generation, and that woman, “like the pistil of a fruit, only receives and nourishes his germ.” The Egyptian woman returns the compliment and boasts that she conceives without the co-operation of man. The statue of Neith, the mother goddess, the “Sovereign Lady of the upper regions,” bore at Sais this arrogant inscription: “I am all that has been, all that is and all that shall be. No one has lifted my robe. The fruit I have borne is the Sun.” Her name, among other signs, has for its emblem the vulture and the first letter of the word mother (mou). [13]

Now the hieroglyphics of Horapollon teach us that the Egyptians believed that in the species of vultures there were no males and that the females were fertilized by the wind. They attributed to that bird, everywhere else regarded as ferocious, a motherly tenderness so extreme that it tore its breast to nourish its little ones. So, after having made of it, by reason of its strange generative property, the bird of Neith, the mother goddess, who herself also propagates without the co-operation of the male, they made of it the symbol of the mother, then of maternity.

This characteristic example gives an idea of the twists and turns through which the human mind passes to picture its abstract ideas through the images of concrete objects.

If in the metaphorical and emblematic writing the image of a material object becomes the symbol of an abstract idea, it is seen that a word created to denote an object or one of its attributes ends by serving to denote an abstract idea.

* * *

In the mind of the child and of the savage – “that child of the human race,” as Vico calls him – there exist only images of definite objects. When the little child says doll, he does not mean to speak of any doll no matter which but of one certain doll that he has held in his hands and that has already been shown him, and if another is offered him it results in his rejecting it with anger; so, every word is for him a proper name, the symbol of the object with which he has come in contact. His language, like that of the savage, possesses no generic terms embracing a class of objects of the same nature, but one series after another of proper names. Thus the savage languages have no terms for general ideas, such as “man,” “body,” etc., and for the abstract ideas, Time, Cause, etc. There are some which have not the verb “to be.” The Tasmanian had an abundance of words for every tree of the different species, but no term for saying tree in general. The Malay has no word for color, although he has words for every color. The Tbiponne has not words for man, body, time, etc. and he does not possess the verb to be. He does not say, “I am Abiponne,” but, “Me Abi-ponne.” [14] But by degrees the child and primitive man carry over the name and the idea of the first persons and things they have known to all the persons and things which present a real or fictitious resemblances with them. They elaborate after a fashion, by way of analogy and comparison, certain general and abstract ideas embracing groups of objects, more or less extended, and sometimes the proper name of one object becomes the symbolic term of the abstract idea representing the group of objects having analogies with the object for which the word had been coined. Plato maintains that the general ideas thus obtained, which classify objects without taking account of their individual differences, are “essences of divine origin.” Socrates in the Tenth Book of the Republic says that the idea of bed is an essence of divine creation, because it is immutable, always identical with itself, while the beds created by cabinet makers all differ among themselves.

The human mind has often brought together the most dissimilar objects having only a vague point of resemblance among themselves. Thus by a process of anthropomorphism man has taken his own members for terms of comparison, as is proved by the metaphors which persist in civilized languages although they date from the beginning of humanity, such as the “bowels of the earth,” the “veins of a mine,” the “heart of an oak,” “tooth of a saw,” the “gorge of a mountain,” the “arm of the sea,” etc. When the abstract idea of measure takes shape in his brain, he takes for a unit of measure his foot, his hand, his thumb, his arms (Orgyia a Greek measure equal to two arms extended). So every measure is a metaphor. When we speak of an object three feet, two inches in extent, we mean that it is as long as three feet two thumbs. [15] But with the development of civilization, people were forced to resort to other units of measure. Thus the Greeks took the stadion, the distance traversed in the footrace at the Olympic Games; and the Latins jugerum, the surface which could be plowed in one day by a jugum (a yoke of oxen).

An abstract word, as Max Muller remarks, is often only an adjective transformed into a substantive; – that is to say, the attribute of an object metamorphosed into a personage, into a metaphysical entity, into an imaginary being, and it is by way of metaphor that this metempsychosis is accomplished. The metaphor is one of the principal ways by which the abstract penetrates into the human brain. In the preceding metaphors, they speak of the mouth of a cavern, a tongue of land, because the mouth presents an opening and the tongue an elongated form. The same process has served to procure new terms of comparison in proportion as the need of them has made itself felt, and it is always the most salient property of the object, that which consequently impresses the senses most vividly which is made the term of comparison.

A great number of savage languages have no words for the abstract ideas of hardness, roundness, warmth, etc., and they are deprived of them because the savage has not yet succeeded m creating the imaginary beings or metaphysical entities which correspond to these terms. Thus, for hard he says “like stone,” for round “like the moon,” for hot, “like the sun;” because the qualities of hard, round and hot are in his brain inseparable from stone, moon and sun. It is only after a long process of brain work that these qualities are detached, abstracted from these concrete objects to be metamorphosed into imaginary beings. Then the qualifying term becomes a substantive and stands for the abstract idea formed in the brain.

No savage tribes have been found without the idea of number, the abstract idea par excellence, although the numeration of certain savages does not go beyond twenty. It is probable that even animals can count up to two. Here is an observation I have made, which is easy to repeat, and which would seem to prove it: the pigeon, although sitting on two eggs – with very rare exceptions – nevertheless has the property of laying eggs at will. If, after she has laid two eggs one is taken away, the female lays a third and even a fourth and fifth if the eggs are taken as fast as she lays them. She requires two eggs in the nest before she begins to sit. The domestic pigeon, overfed, may sometimes lay three eggs; when that happens she pushes one out of the nest, or else leaves it if she cannot push out the superfluous egg.

It would seem that the abstract idea of number, contrary to Vico’s opinion, is one of the first, if not the first, to be formed in the brain of animals and man; for if all objects have not the property of being round, hard or hot, etc., they have nevertheless one quality which is common to them, that of being distinct from one another, by their form and the relative position which they occupy, and this quality is the point of departure of numeration. [16] The brain substance must have the idea of number; that is to say, be able to distinguish the objects from each other, in order to carry on its function. This was recognized by the Pythagorian Philolaus, the first who, according to Diogenes of Laercia, affirmed that the motion of the earth described a circle, when he declared that number resides in all that is, and without it nothing can be known and nothing can be thought.

But the extension of numeration beyond the number two was one of the most painful of Herculean labors ever imposed upon the human brain, as is proved by the mystical character attributed to the first ten numbers [17]; and the mythological and legendary memories attached to certain figures: 10 (Siege of Troy and of Veii, which lasted exactly ten years); 12 (the 12 gods of Olympus, 12 labors of Hercules, 12 apostles, etc.); 50 (the 50 sons of Priam, the 50 Danaides; Endymion, according to Pausanius made Selene the mother of 50 daughters; Acteon hunted with 50 braces of hounds when Diana metamorphosed him; the boat constructed by Danaus according to the instructions of Minerva, had 50 oars, as had that of Hercules at the time of his expedition against Troy.) These numbers are so many stages at which the human mind halted after the efforts made to reach the points, and it has marked them with legends to preserve their memory.

The savage, when he arrives at the end of his numeration, says “many” to indicate the objects which remain over and which he cannot count for lack of numbers. Vico remarks that for the Romans 60, then 100, then 1,000 were innumerable quantities. The Hovas of Madagascar say for 1,000 “evening,” for 10,000 “night,” and the word tapitrisa, which they use to indicate a million, is literally translated by the end of counting. It was the same for us, but since the war of 1870-1871 it is a billion which marks the limit of our popular numeration.

Language shows us that man has taken his hand, his foot and his arms for units of length. He still uses his fingers and toes for counting. F. Nansen says the Esquimaux, with whom he lived more than a year, have no name for any figure beyond five. They count on the fingers of the right hand and then stop when all the fingers have been named and touched. For six they take the left hand and say the first finger of the other hand, for seven, the second finger, thus on to ten. Afterwards they count in the same fashion on the toes and stop at twenty, the limit of their numeration: but the great mathematicians go further and for twenty-one they say the first finger of the other man and begin again, passing over the hands and feet. Twenty is one man, one hundred is five men. The Roman figures which were used until the introduction of .the Arabic figures preserve the memory of this primitive mode of numeration; I is one finger, II is two fingers, V is a hand with the three middle fingers folded while the little finger and the thumb are straight; X is two Vs or two hands crossed. But when it was necessary to count beyond the hundred and the thousand, they were obliged to resort to other objects than the human members.

The Romans took pebbles, calculi, from which is derived the word calculus in modern languages. The Latin expressions calculum ponere (to place the pebble) and subducere calculum (to take away the pebble) indicate that it was by adding and taking away pebbles that they added and subtracted. At the Familistere of Guise I saw the first two arithmetical operations taught by a similar process to children of five and six years. Pebbles were the obvious things for this use; they had already served for drawing lots in the distribution of booty and land.

Savages cannot figure in their heads. They must have before their eyes the objects which they are counting. Thus, when they make exchanges they place on the ground the objects which they are giving opposite those they receive. This primitive equation, which in the last analysis is simply a tangible metaphor, is the only thing which can satisfy their minds. Numbers, in their heads, as in those of children, are concrete ideas. When they say two, three or five, they see two, three or five fingers, pebbles or any other objects. In many savage tongues the first five figures bear the names of the fingers; it is only by a process of intellectual distillation that the numbers come to strip themselves in the head of the civilized adult of any form corresponding to a certain object, and to keep only the form of conventional signs. [18] The most idealistic metaphysician cannot think without words nor calculate without signs, – that is to say without concrete objects. The Greek philosophers when they began their inquiries on the properties of numbers, gave them geometrical forms. They divided them into three groups: the group of linear numbers (mekos). the group of numbers of planes, squares (epipedon), the group of the numbers of three dimensions, cubes (triké auxé). The modern mathematicians have still preserved the expression linear number for a root number.

The savage for long, hard, round or hot, says “like the foot, stone, moon, sun;” but feet are of unequal length, stones are more or less hard, the moon is not always round, the sun is hotter in summer than in winter; so when the human mind felt the need of a higher degree of exactness, it recognized the insufficiency of the terms of comparison which it had till then used. It then imagined types of length, hardness, roundness and heat to be employed as terms of comparison. It is thus that in abstract mechanics, the mathematicians imagined a lever absolutely rigid and without thickness and a wedge absolutely incompressible in order to continue their theoretical investigations, arrested by the imperfections of the levers and wedges of reality. But the wedge and the lever of the mathematicians like the types of length, roundness, hardness although derived from real objects whose attributes had been submitted to intellectual distillation, no longer correspond to any real object but to ideas formed in the human head. Because the objects of reality differ among themselves and from the imaginary type, always one and identical with itself, Plato calls the real objects vain and deceptive images and the ideal type an essence of divine creation. In that case, as in a multitude of others, God, the creator, is man thinking.

Artists by an analogous process have given birth to chimeras, whose bodies, although com posed of detached organs abstracted from different animals, correspond to nothing real but to a fantasm of the imagination. The chimera is an abstract idea – as abstract as any idea you please of the Beautiful, the Good, the Just, Time or Cause – but Plato, himself, did not dare to class it in the number of his divine essences.

Man, probably when barbarous tribes began to differentiate into classes, separated himself from the animal kingdom and raised himself to the rank of a supernatural being, whose destinies are the constant preoccupation of the gods and the celestial bodies. Later on he isolated the brain from the other organs to make it the seat of the soul. Natural science reintegrates man in the animal series of which he is the sum and crown; the socialist philosophy will restore the brain to the series of organs. The brain has the property of thinking as the stomach has that of digesting. It cannot think but by the aid of ideas, which it fabricates with the materials furnished it by the natural environment and the social or artificial environment in which man evolves.


1. The Greeks seemed to have attached more importance to the sense of sight and the Latins to the sense of taste, as is proved by the following examples:

This difference, regarding the sense-sources of ideas, characterizes these two nations which played so great a historic role; the one in the evolution of thought and in its poetic and plastic manifestation, and the other in the elaboration of law, in the brutal manipulation of men and na tions, and in the unified organization of the ancient world.

The very young child and the savage carry to the mouth the object they wish to know; the chemists do the same. The French word savoir, to know, and its derivative savant, scientist, combine the two meanings. Voir indicates the function of the eye; and sa the last trace of the verb sapio, indicates the function of the palate.

(In this translation, as in the original French, the Greek words have been set in Roman type, since the book is intended for laborers rather than classical scholars, and the use of familiar letters makes the form of the words and the argument drawn from them plain to the ordinary reader. – Translator)

2. One of the unwritten laws of Socrates was the universal agreement to forbid sexual relations between the father or mother and their children. Xenophon, who had traveled in Persia and was not ignorant that the magi practiced this incest to honor the divinity and beget the high priests, claimed that it was contrary to natural and divine law because the children of such matings are puny. He reduced the law from the natural right of his master, Socrates, into nothing more than a physiological law based on experience.

Socrates would seem to have forgotten that Hesiod, following the religious legends of his epoch, gives to Uranus for wife his own mother, Gaia, the most ancient goddess, “the mother of all things,” according to Homer; in the religions of India, Scandinavia and Egypt we meet with cases of divine incest. Brahma marries his daughter Saravasty; Odin his daughter Frigga, and Amon in the Anastasy Papyrus in Berlin boasts of being the husband of his mother. These legends, which may be found in all primitive religions have a historical value: the legends and religious ceremonies preserve the memory of epochs long buried in oblivion. The bible story of the sacrifice of Abraham and the Christian communion, – that symbolic repast in which the devout Catholic eats his Incarnate God – are the distant echoes of the human sacrifices and the cannibal feasts of the prehistoric Semites.

Man to create his religious legends employs the same process as to elaborate his ideas – he uses as materials events of his dally life; in the course of the centuries the phenomena which gave birth to them are transformed and vanish, but the legendary or ceremonial form, which was their intellectual manifestation, survives: we need only interpret this intelligently to call up the customs of a past which was thought to be lost forever.

The incests practiced by the Persian priests, and the religious legends of peoples of such different races would therefore lead us to suppose that at a remote epoch sexual relations between parents and children were a customary thing. On this point Engels remarks that the savage tribes which first arrived at the point of forbidding them, must by this sole fact have acquired an advantage over their rivals and must consequently either have destroyed them or imposed their customs upon them. It is thus more than probable, that the prohibition of these incestuous marriages the most universal custom that is known, – so universal that Socrates thought it one of the laws of bis Natural Right – has not always prevailed, and that on the contrary those sexual relations were naturally practiced in the human species emerging from the animal. But experience having demonstrated their bad effects brought about their prohibition, as Xenophon thought. Breeders have also been obliged to prevent them among the domestic animals in order to get good results.

3. The anarchical opinions of Aristippus and the Cyrenaic School have been reproduced at various times in the course of history. Christian sects during the first centuries and during the middle ages; and political sects during the English Revolution of the seventeenth century and French Revolution of the eighteenth century have revived them, and in or days certain anarchistic sects propagate them. The lack of social equilibrium translates itself the brain by this cynical rejection of the notions of current and conventional ethics. I shall return to this aspect in the study devoted to the crisis of Greek philosophy.

4. De Cive, Sorbière’s translation, Amsterdam 1649.

Hobbes in the Leviathan takes up the same thesis, which he thought it best to entrust only to the Latin in De Cive:

“The desires and passions of man,” he said, “are not sins in themselves any more than the actions which result from these passions are faults, until a law forbids them.”

5. The intellectual evolution of M. de Biran is most interesting. It permits us to observe in the most remarkable French philosopher of the beginning of the nineteenth century the sudden and extraordinary veering of bourgeois thought, from the time when from being a revolutionary class, the Bourgeoisie became a ruling and conservative class. Biran in the manuscript of 1794, published after his death in 1824, declares that Bacon and Locke founded philosophical science and that Condillac “assigned its limits and dissipated forever those dreams which are termed ‘Metaphysics’.”

The National Institute, in which the sensationalism of Condillac was dominant, crowned in the month of Nivose of the year IX (1801) a study of Biran on the Influence of Custom Over the Faculty of Thought, which he had put up for competition. Biran there laid down as an axiom that the faculty of perception is the origin of all the faculties, and proposed to apply Bacon’s method to the study of man and to throw light on metaphysics by transporting physics into it. De Gerando, who also found it necessary to abjure Condillac and his philosophy, in his monograph on the Influence of Signs on the Faculty of Thought, crowned by the Institute in 1800, affirmed that the doctrine of Condillac was, as it were the last word of human reason on the doctrines which interested it the most.

The Institute crowned in 1805 a new monograph by Biran on the Decomposition of Thought. The political stage was transformed: the victorious Bourgeoisie was occupied in re-introducing and mustering into its service the Catholic religion, which it had ridiculed, despoiled and trampled under its feet when it was the maid-of-all-work of the aristocracy, its rival. While the men of politics were reorganizing the power, taking up and reinforcing the repressive forces of the ancient regime, the philosophers were taking up the task of clearing away the intellectual foundation of its “analytic and iconoclastic” philosophy of the Encyclopedists. The Institute, in crowning this monograph of Biran, and he himself in writing it, were conscientiously fulfilling the task imposed by the new social conditions. Biran’s monograph points out that there is somewhat of an illusion in the pretended analysis of Condillac, and in that sensation which transforms itself into judgment and will without one having taken the trouble to assign to it a principle of transformation, he makes the method of Bacon unseasonably applied to the study of the mind responsible for the aberrations of the eighteenth century philosophy, and takes his stand against any assimilation between the physical phenomena perceived by the senses and internal facts. The Sophists had succeeded to the Philosophers.

Cabanis himself, who was to die in 1808, still had time to make his change of front in his celebrated work on the Relations of the Physical and the Ethical In Man, which appeared in 1802, he had written:

“Medicine and ethics rest upon one common basis; upon a physical knowledge of human nature. * * * The source of ethics Is In the human organization. * * * If Condillac had understood animal economy he would have perceived that the soul is a faculty and not a being. We must consider the brain as a particular organ destined especially to produce thought, just as the stomach and intestines are destined to carry on digestion. Impressions are the food of the brain. * * * They get into the brain and set it at work. * * * They reach it isolated, without coherence, but the brain starts on its activity, acts upon them and soon sends them back metamorphosed into ideas. * * *”

Cabanis, who had written these materialistic horrors, proclaimed – in his letter to Fauriel, on First Causes, published sixteen years after his death – the existence of God; the intelligence governing the world, and the immortality of the soul by the persistence of tho ego after death. Fauriel had converted Cabanis, as Fontanes had metamorphosed Chataubriand from the atheistic follower of Rousseau, who wrote the Essays on Revolutions in 1797, into the reactionary and mystic Chataubriand who wrote the Genius of Christianity in 1802. There existed then a little clique of proselyters influential in the press and departments of government, who had undertaken to bring back the straying literary men and philosophers to sound doctrines.

It is useless to waste any accusations of recanting and treason against the men who had gone through the revolution and come out on the other side. These remarkable men would perhaps have preferred to keep the political and philosophic opinions which at their start in life had brought them to the front, but they were obliged to sacrifice them to retain their means of existence and the positions they had won, and to conquer the favors of the Bourgeoisie grown wise. They replaced these opinions by the politics and philosophy suitable to its material interests and satisfying its intellectual needs. Besides, they were bourgeois, following the influences of their social environment; they evolved with their class and they could make this change of skin without excessive pains. So it is not a case for moral indignation, but for investigation and analysis of the social causes which imposed upon them certain political changes of front and certain intellectual transformations. There are few moments in history where we can grasp better than in the first years of the nineteenth century, the direct action of social events upon thought. This epoch is all the more characteristic that it is then that were formulated almost all the economic, political, philosophical, religious, literary and artistic theories which were thenceforth to form the bulk of the intellectual baggage of the new ruling class.

6. “In these last years.” a professor of philosophy writes in 1828, “authority has almost brought back the study of philosophy to the age of Scholasticism. * * * It has been ordered that lessons be given in Latin and under the form of ancient argumentation. This order is carried out in most of our colleges. * * * They are philosophizing in Latin from one end of France to the other, with the ceremonial and etiquette of the ancient syllogism: and on what are they philosophizing? On the thesis of the school and on the objecta which correspond to them; that is to say, that the argument is on logic, metaphysics and ethics.” (Essay on the History of Philosophy in France in the Nineteenth Century, by Ph. Damiron, Professor of Philosophy in the College of Bourbon, Paris, 1828)

7. La Societé des observateurs de l’homme (Society of the Observers of Man), of which Cuvier, the alienist Pinel, the philosopher Gerando, the jurist Portalis, etc., were members, voted in the month of Prairial VIII. (1800) a prize of 600 francs for the following study: To determine by the daily observation of one or several children in the cradle the order in which the physical intellectual and moral faculties are developed, and to what point this development is helped or hindered by the influence of objects and persons surrounding the child.

In the same Session, reported in the Décade Philosophique of the 30th day of Prairial, Gerando offered certain ideas on the methods to be followed in the observations of savage nations. Another member contributed an essay on the childhood of Massieu, deaf and dumb from birth.

The Society was greatly interested in the observation of the young savage from Aveyron brought to Paris about the end of the year VIII (1800). Three hunters found him in the forest where he lived naked, living on acorns and roots. He was apparently about ten years old.

8. On the seventh day of Nivose in the year VIII (1800), S. Mercier delivered in Paris, just emerging from the Revolution, the first lecture on innate ideas, in order to “dethrone Condillac, Locke and their metaphysics.” To Royer-Collard is attributed the first awakening of spiritualist philosophy, completely out of fashion for half a century. This honor, if honor there be, reverts to this unbalanced intellect, which opposed Kant to the Encyclopedists and noisily proposed to refute Newton, “that anatomist of light, who can imagine nothing more ridiculous than to make the earth turn like a turkey before the solar hearth.” Bourgeois spiritualism could not have in France a more worthy godfather.

The lectures of Mercier made a sensation; they were largely attended. The Décade Philosophique of the Tenth Floreal gives an account of the lecture on innate ideas.

“I admit them,” he exclaimed at the start, “and in this I obey my inmost reason. * * * Man thinks independently of objects and senses. * * Innate ideas explain everything. The picture of the ideas of a man would be the picture of celestial truths. * * * Instinct is an innate idea.”

Mercier had a precedent, the celebrated decree of Robespierre, which re-established God like an ordinary police commissioner who had been thrown out.

Art. 1. The French Nation recognizes the existence of the Supreme Being and the immortality of the soul.

Art. 4. Feasts shall be instituted to recall to man the thought of divinity and the dignity of his being.

A hymn recited at the feast of the restoration of the Supreme Being after the speech of Robespierre predicted the end of Atheism:

Where are they who dared threaten Thee
Who under the mantle of civism
Vile professors of Atheism
Hoped to efface Thee from the heart of man
*   *   *   *   *   *   *   *   *   *   *   *   *   *
   Did they think then * * * *
That in returning to nature
One would forget the Author of Nature?

9. The supplement of Figaro for January 1880 reproduced from the letters of a missionary, the native lamentations of an Indian woman at the equator over the corpse of her new-born child, which illustrates the part played by the milk in the primitive maternal love:

“Oh! my master, Oh! son of my vitals, my little father, my love, why have you left me? For you every day this breast with which you loved to play filled itself with warm milk. Ungrateful one! have I once forgotten you? Oh! woe is me; I have no longer any one to deliver my bosom from the milk which oppresses it”

10. The ancients were not afraid to go back to the animals to discover the beginnings of certain of our sciences: thus while attributing to the gods the origin of medicine, they admitted that several remedies and operations of minor surgery were due to the animals. The elder Pliny reports in his Natural History that the wild goats of Crete taught the use of certain healing herbs; the dog taught that of the couchgrass; and that the Egyptians asserted that the discovery of purging was due to the dog, that of bleeding to the hippopotamus and that of injection to the ibis.

11. Vico, in the preface to his little work on the Ancient Wisdom of Italy, says,

“I have resolved to find in the origins of the Latin language the ancient wisdom of Italy. We shall seek its philosophy in the origin of the words themselves.”

12. F. Lenormand’s Essay on the Propagation of the Phoenician Alphabet among the Nations of the Ancient World.

13. Champollion le Jeune: Pantheon Egyptian, 1825.

14. The idea of time was a long time in penetrating into the human brain. Vico remarks that the Florentine peasants of his epoch said so many harvests for so many years. The Latins for so many years said so many ears of corn (aristas), something still more concrete than harvests. The expression merely indicated their poverty of language (and of thought he might have added). The grammarians believe they see in it an attempt at art. Before having the concept of the year, – that is to say, of the sun’s revolution – man had the idea of the seasons and that of the revolutions of the moon. The elder Pliny said that the summer was counted for one year, the winter for another. The Arcadians, with whom the year was three months, measured it by the number of seasons and the Egyptians by the moon. That is why several of them are cited as having lived a thousand years.

15. The French word pouce has the double meaning of thumb and inch – Translator

16. Plato, who in the Timaeus represents an astronomer as speaking and who for the moment forgets his essences of divine origin, gives a materialistic origin of Number and Time.

“The observation of day and night, the revolutions of the months and the years have furnished us Number, re vealed Time and Inspired the desires of knowing Nature and the world.”

17. The decade had a sacred character for the Pythagorians and the Cabalists. The Scandinavians regarded the number three and its multiple nine as particularly dear to the gods. Every ninth month they made bloody sacrifices which lasted nine days, during which they sacrificed nine victims, man or animal. The Catholic Neuvaines, which are prayers lasting nine days, preserve the memory of this cult, and their holy trinity preserves the mystical character which all savage nations attach to the number three. It occurs in all primitive religions: three Parcae among the Greeks and the Scandinavians, three goddesses of life among the Iroquois.

18. The Greeks employed for figures the letters of the alphabet, preserving the ancient Cadmean letters which carried the numbers up to twenty-seven. The first nine letters were the units, the next nine the tens and the last nine the hundreds.

It must have been extremely painful and difficult to calculate with the figures of the Greeks and Romans, who did not possess the zero. The metaphysical abstractors of abstractions of Nirvana were the only ones capable of inventing this marvelous figure the symbol of nothing, which has no value and which gives value, and which according to the expression of Pascal, is a true indivisible of number as the indivisible is a true zero. The zero plays so considerable a part in modern numeration that its Arabic name sifr – which the Portuguese transformed into cifra, the English into cipher, the French into chiffre – after having first been employed for zero alone, serves to designate all the signs of number.

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Last updated on 14.9.2008