Let us leave the negation of the negation for a little and look at "the coexistent individual and social property." This will be called by Herr Duehring a "cloud realm," and, strange to say he is really right in this regard. But sad to say it is not Marx who is found to be in the cloud realm but on the contrary Herr Duehring himself. Since by virtue of his wonderful versatility in the vagaries of Hegel he does not experience any difficulty in telling us the necessary contents of the as yet unpublished volume of "Capital," so, after setting Hegel right, he is able to correct Marx without any trouble in that he ascribes to him a higher unity of a private property of which Marx has not said a word.

Marx says "It is the negation of the negation. This reestablishes private property but on the basis of the acquisitions of the capitalistic era, of the cooperation of free laborers and their common ownership of the land and the means of production. The transformation of the private property of individuals, depending upon the labor of individuals, into capitalistic property is naturally a process much more tedious, hard and difficult than the transformation of capitalistic private property, as it now exists, resting upon social production, into social property." That is all. The condition attained by the dispossession of the dispossessor is here shown as the restoration of individual private property resting however on a basis of social property in the land and means of production. For people who can understand English, the meaning of this is that social property extends to the land and means of production, and private property to the products, therefore to consumption. And that the matter should be evident even to infants Marx shows on page 56. "A society of free men who labor with social means of production, and consciously expend their individual labor power as social labor power," therefore a socialistically organised society, and he says further "The total product of the society is a social product. A portion of this product serves again as a means of production. It remains social. But another portion is consumed by the members of the society. It must therefore be distributed among them." And that ought to be clear, even to Herr Duehring, in spite of his having Hegel on the brain. The coexistent individual and social property, this confused and indefinite thing, this nonsense proceeding from the Hegelian dialectic, this misty world, this deep dialectic puzzle which Marx leaves his pupils to solve is merely a creation of Herr Duehring's imagination. Marx, as a so-called Hegelian, is obliged, as a result of the negation of the negation, to furnish a correct higher unity, and since he does not do this in accordance with the taste of Herr Duehring, the latter has to take a lofty stand and to smite Marx in the interests of the full truth of things upon which Herr Duehring holds a patent.

What attitude did Marx take to the negation of the negation? On page 761 and following he states the conclusion with respect to his economic and historical investigations into the so-called accumulation of original capital, extending over the fifty preceding pages. Before the capitalistic era in England, at least, small production existed, based upon the private property of the worker in his tools. The so-called accumulation of capital consists in the expropriation of these immediate producers, that is in the abolition of private property resting on the labor of individuals. This was possible because the aforesaid small production is only compatible with a narrow and primitive stage of production and of society and at a certain grade of development furnishes the means of its own suicide. This suicide, the transformation of individual and divided modes of production into social production, constitutes the early history of capitalism. As soon as the workers are transformed into proletarians and their means of labor into capital, as soon as the capitalistic methods of production are firmly established, the growing association of labor and the further transformation of the land and other means of production and hence the further expropriation of the owners of private property takes on a new form, "there is no longer the self-employing worker to expropriate, but the capitalist who expropriates many workers. This expropriation fulfils itself through the play of laws immanent in capitalistic production itself, through the concentration of capital. One capitalist kills many. Hand in hand with this concentration, or the expropriation of many capitalists by a few, there develop continually the conscious technical application of science, the deliberate organised exploitation of the soil, the transformation of the instruments of labor into instruments of labor which can only be employed collectively, and the economising of all means of production through their employment as the common means of production of combined social labor. With the constantly diminishing numbers of capitalist magnates who usurp and monopolise all the advantages of this process of transformation, grows the mass of misery, pressure, slavery, degradation and robbery but there grows also revolt and the constant progress in union and organisation of the working class brought about through the mechanism of the capitalistic process of production. Capitalism becomes an impediment to the methods of production developed with and under it. The concentration of the means of production and the organisation of labor reach a point where it comes into collision with its capitalistic covering. It is broken. The hour of capitalistic private property strikes. The expropriators are expropriated."

And now I ask the reader, where are the dialectic twists and twirls, the intellectual arabesques, where the confused thought the result of which is the identity of everything, where the dialectic mystery for the faithful, where the dialectic hocus pocus, and the Hegelian intricacies, without which, Marx, according to Herr Duehring, cannot develop his own ideas? Marx simply pointed to history and showed briefly that just as the small industry necessarily produced the conditions of its own downfall, by its own development, that is to say by the expropriation of the small holders of private property so now the capitalistic method of production has itself developed likewise the material circumstances which must cause its downfall. The process is a historical one and, if it is at the same time dialectic, it is not to the discredit of Marx, that it happens to be so fatal to Herr Duehring.

In the first place, since Marx is ready with his historical economic proof, he proceeds "The capitalistic method of production and method of appropriation, that is to say capitalistic private property is the first negation of individual private property founded on labor of individuals, the negation of capitalistic production will be self-produced with the necessity of a natural process, etc." (as quoted above).

Although Marx therefore shows the occurrence of this event as negation of the negation, he has no intention of proving by this means that it is a historical necessity. On the contrary "After he has shown that the actual fact has partially declared itself, and has, as yet partially to declare itself, he shows it also as a fact which fulfils itself in accordance with a certain dialectic law." That is all. It is therefore again merely supposition on Herr Duehring's part to assert that the negation of the negation must act as a midwife by whose means the future is brought out of the womb of the present, or that Marx wants to convince anyone of the necessity of social ownership of land and capital upon the credit of the negation of the negation.

It shows a complete lack of comprehension of the nature of the dialectic to regard it as Herr Duehring does, as an instrument of mere proof, just as one can after a limited fashion employ formal logic or elementary mathematics. Formal logic is itself more than anything else a method for the discovery of new results, for advancing from the known to the unknown, and so, but in a much more distinguished sense, is the dialectic, which, since it transcends the narrow limits of formal logic, attains a more comprehensive philosophical position. It is the same with mathematics. Elementary mathematics, the mathematics of constant quantities, proceeds within the limits of formal logic, at least as a rule: the mathematics of variable quantities which is peculiarly concerned with calculations running to the infinite, is substantially nothing but the application of the dialectic in mathematics. Mere proof becomes secondary before the manifold application of the method to new fields of investigation. But nearly all the proofs of higher mathematics from the first of the differential calculus, are, strictly speaking, false from the standpoint of elementary mathematics. This cannot be otherwise, if one, as is here the case, wishes to establish results won in the realm of dialectics by means of formal logic. For a crass metaphysician like Herr Duehring to want to prove anything by means of the dialectic would be the same wasted labor as Leibnitz and his pupils went through when they tried to establish the thesis of calculation to infinity by means of the mathematics of their time. The differential gave them the same spasms as the negation of the negation gives Herr Duehring and it played a role in it as we shall see. They admitted it at last, at least as many as did not die first, not because they were convinced but because it always worked out right. Herr Duehring, is, as he says, just in his forties, and if he attains old age, as we hope he will, he may also experience the same.

But what is this dreadful negation of the negation which makes life so bitter to Herr Duehring and which is to him what the unpardonable sin, the sin against the Holy Ghost, is to Christianity? It is a very simple process, and one, moreover, which fulfils itself every day, which any child can understand when it is deprived of mystery, under which the old idealistic philosophy found a refuge, and beneath which it will pay unprotected metaphysicians to take refuge from the stroke of Herr Duehring. Let us take a grain of barley. Millions of such grains of barley will be ground, cooked and brewed and then consumed. But let such a grain of barley fall on suitable soil under normal conditions; a complete individual change at once takes place in it under the influence of heat and moisture, it germinates. The grain, as such disappears, is negated, in its place arises the plant, the negation of the grain. But what is the normal course of life of this plant? It grows, blossoms, bears fruit and finally produces other grains of barley and as soon as these are ripe the stalk dies, and becomes negated in its turn. As the result of this negation of the negation, we have the original grains of barley again, not singly, however, but ten, twenty or thirty fold. Forms of grain change very slowly and so the grain of barley remains practically the same as a hundred years ago. But let us take a cultivated ornamental plant, like the dahlia or orchid. Let us consider the seed and the plants developed from it by the skill of the gardener, and we have in testimony of this negation of the negation, no longer the same seeds but qualitatively improved seed which produces more beautiful flowers, and every repetition of this process, every new negation of the negation, increases the tendency to perfection. Similarly this process is gone through by most insects, butterflies, for example. They come out of the egg by a negation of the egg, they go through certain transformations till they reach sex maturity, they copulate and are again negated, since they die as soon as the process of copulation is completed, and the female has laid her innumerable eggs. That the matter is not so plainly obvious in the case of other plants and animals, seeing that they produce seeds, plants, and animals not once but oftener, does not affect us in this case, we are now only concerned in showing that the negation of the negation actually does occur in both kingdoms of the organic world. Besides, all geology is a series of negated negations, one layer after another following the destruction of old and the establishment of new rock foundations. First, the original crust of the earth, through the cooling of the fluid mass, and through oceanic, meteorological, and chemical atmospheric action, being broken up into small parts, these broken masses form layers in the seas. Local elevations of the seas, through the ebb and flow of the waters, bring portions of these layers afresh under the influence of rain, the warmth of the seasons, and the oxygen and carbon in the atmosphere: melted and almost cooled masses of rock from the interior of the earth underlie these and break through the layers. Through millions of centuries new layers are continually being formed, always to a large extent destroyed and serving again as building materials for new layers. But the result of the process is always positive, the restoration of a piece of ground made up of exceedingly diverse chemical elements to a condition of mechanical pulverisation, which is the cause of a most abundant and diverse vegetation.

It is the same also in mathematics. Let us take an ordinary algebraic quantity a. Let us negate it, then we have-a (minus a). Let us negate this negation, that is let us multiply —a by —a and we have + a², that is the original positive quantity but in a higher form that is to the second power. It does not matter that we can attain the same a² by the multiplication of a positive by itself. The negated negation is established so completely in a² that under all circumstances it has two square roots a and —a. And this impossibility, the negated negation, the getting rid of the negative root in the square has much significance in quadratic equations. The negation of the negation is more evident in the higher analyses, in those "unlimited summations of small quantities," which Herr Duehring himself explains as being the highest operations of mathematics and which are usually called the differential and integral calculus. How do these forms of calculation fulfil themselves? I have for example in a given problem two variable quantities x and y, of which one cannot vary without causing the other to vary also under fixed conditions. I differentiate x and y, that is I consider x and y as being so infinitesimally small that they do not represent any real quantities, even the smallest, so that, of x and y nothing remains, except their reciprocal relations, a quantitative relation without any quantity; therefore dx/dy, the relation of the two differentials of x and y, is 0/0 but 0/0 is fixed as the expression of y/x. That this relation between two vanished quantities, the fixed moment of their vanishing, is a contradiction I merely mention in passing, it should give us as little uneasiness as it has given mathematics for the two hundred or so years past. What have I done except to negate x and y; not as in metaphysics so as not to trouble myself any further about them, but in a manner demanded by the problem? Instead of x and y, I have therefore their negation dx and dy in the formulæ or equations before me. I now calculate further with these formulæ. I treat dx and dy as real quantities, as quantities subject to certain exceptional laws, and at a certain point I negate the negation, that is, I integrate the differential formula. I get instead of dx and dy the real quantities x and y again, and am thereby no further forward than at the beginning, but I have thereby solved the problem over which ordinary geometry and algebra would probably have gnashed their teeth in vain.

It is not otherwise in history. All civilised peoples began with common property in land. Among all peoples which pass beyond a certain primitive stage the common property in land becomes a fetter upon production in the process of agricultural development. It is cast aside, negated, and, after shorter or longer intervening periods, is transformed into private property. But at a higher stage, through the development still further of agriculture, private property becomes in its turn a bar to production, as is to-day the case with both large and small land proprietorship. The next step, to negate it in turn, to transform it into social property, necessarily follows. This advance however does not signify the restoration of the old primitive common property, but the establishment of a far higher better developed form of communal proprietorship, which, far from being an impediment to production, rather, for the first time is bound to put an end to its limitations and to give it the full benefit of modern discoveries in chemistry and mechanical inventions.