So Marx has no other way of proving the necessity of the social revolution, of establishing the common ownership of land and of the means of production produced by labour, except by citing the Hegelian negation of the negation; and because he bases his socialist theory on these nonsensical analogies borrowed from religion, he arrives at the result that in the society of the future there will be dominant an ownership at once both individual and social, as Hegelian higher unity of the sublated contradiction. But let the negation of the negation rest for the moment and let us have a look at the ownership which is at once both individual and social . Herr D hring characterises this as a nebulous world , and curiously enough he is really right on this point. Unfortunately, however, it is not Marx but again Herr D hring himself who is in this nebulous world. Just as his dexterity in handling the Hegelian method of delirious raving {D. Ph. 227, 449} enabled him without any difficulty to determine what the still unfinished volumes of Capital are sure to contain, so here, too, without any great effort he can put Marx right la Hegel, by imputing to him the higher unity of a property, of which there is not a word in Marx. Marx says: It is the negation of negation. This re-establishes individual property, but on the basis of the acquisitions of the capitalist era, i.e., on co-operation of free workers and their possession in common of the land and of the means of production produced by labour. The transformation of scattered private property, arising from individual labour, into capitalist private property is, naturally, a process, incomparably more protracted, arduous, and difficult, than the transformation of capitalistic private property, already practically resting on socialised production, into socialised property. [K. Marx, Das Kapital, p. 793.] [Capital, volume I, Chapter 33, page 384 in the MIA pdf file.] That is all. The state of things brought about by the expropriation of the expropriators is therefore characterised as the re-establishment of individual property, but on the basis of the social ownership of the land and of the means of production produced by labour itself. To anyone who understands plain talk this means that social ownership extends to the land and the other means of production, and individual ownership to the products, that is, the articles of consumption. And in order to make the matter comprehensible even to children of six, Marx assumes on page 56 [Chapter 1, page 48 in the MIA pdf] a community of free individuals, carrying on their work with the means of production in common, in which the labour-power of all the different individuals is consciously applied as the combined labour-power of the community , that is, a society organised on a socialist basis; and he continues: The total product of our community is a social product. One portion serves as fresh means of production and remains social. But another portion is consumed by the members as means of subsistence. A distribution of this portion amongst them is consequently necessary. And surely that is clear enough even for Herr D hring, in spite of his having Hegel on his brain. The property which is at once both individual and social, this confusing hybrid, this nonsense which necessarily springs from Hegelian dialectics, this nebulous world, this profound dialectical enigma, which Marx leaves his adepts to solve for themselves is yet another free creation and imagination on the part of Herr D hring. Marx, as an alleged Hegelian, is obliged to produce a real higher unity, as the outcome of the negation of the negation, and as Marx does not do this to Herr D hring's taste, the latter has to fall again into his higher and nobler style, and in the interests of complete truth impute to Marx things which are the products of Herr D hring's own manufacture. A man who is totally incapable of quoting correctly, even by way of exception, may well become morally indignant at the Chinese erudition {D. K. G. 506} of other people, who always quote correctly, but precisely by doing this inadequately conceal their lack of insight into the totality of ideas of the various writers from whom they quote . Herr D hring is right. Long live historical depiction in the grand style {556}! Up to this point we have proceeded from the assumption that Herr D hring's persistent habit of misquoting is done at least in good faith, and arises either from his total incapacity to understand things or from a habit of quoting from memory a habit which seems to be peculiar to historical depiction in the grand style, but is usually described as slovenly. But we seem to have reached the point at which, even with Herr D hring, quantity is transformed into quality. For we must take into consideration in the first place that the passage in Marx is in itself perfectly clear and is moreover amplified in the same book by a further passage which leaves no room whatever for misunderstanding; secondly, that Herr D hring had discovered the monstrosity of property which is at once both individual and social {505} neither in the critique of Capital, in the Erg nzungsbl tter which was referred to above, nor even in the critique contained in the first edition of his Kritische Geschichte, but only in the second edition that is, on the third reading of Capital; further, that in this second edition, which was rewritten in a socialist sense, it was deemed necessary by Herr D hring to make Marx say the utmost possible nonsense about the future organisation of society, in order to enable him, in contrast, to bring forward all the more triumphantly as he in fact does the economic commune as described by me in economic and juridical outline in my Cursus {504} when we take all this into consideration, we are almost forced to the conclusion that Herr D hring has here deliberately made a beneficent extension of Marx's idea beneficent for Herr D hring. But what role does the negation of the negation play in Marx? On page 791 and the following pages he sets out the final conclusions which he draws from the preceding fifty pages of economic and historical investigation into the so-called primitive accumulation of capital.  Before the capitalist era, petty industry existed, at least in England, on the basis of the private property of the labourer in his means of production. The so-called primitive accumulation of capital consisted there in the expropriation of these immediate producers, that is, in the dissolution of private property based on the labour of its owner. This became possible because the petty industry referred to above is compatible only with narrow and primitive bounds of production and society and at a certain stage brings forth the material agencies for its own annihilation. This annihilation, the transformation of the individual and scattered means of production into socially concentrated ones, forms the prehistory of capital. As soon as the labourers are turned into proletarians, their conditions of labour into capital, as soon as the capitalist mode of production stands on its own feet, the further socialisation of labour and further transformation of the land and other means of production, and therefore the further expropriation of private proprietors, takes a new form. And now I ask the reader: where are the dialectical frills and mazes and conceptual arabesques; where the mixed and misconceived ideas according to which everything is all one and the same thing in the end; where the dialectical miracles for his faithful followers; where the mysterious dialectical rubbish and the maze in accordance with the Hegelian Logos doctrine, without which Marx, according to Herr D hring, is unable to put his exposition into shape? Marx merely shows from history, and here states in a summarised form, that just as formerly petty industry by its very development necessarily created the conditions of its own annihilation, i.e., of the expropriation of the small proprietors, so now the capitalist mode of production has likewise itself created the material conditions from which it must perish. The process is a historical one, and if it is at the same time a dialectical process, this is not Marx's fault, however annoying it may be to Herr D hring. It is only at this point, after Marx has completed his proof on the basis of historical and economic facts, that he proceeds: Thus, by characterising the process as the negation of the negation, Marx does not intend to prove that the process was historically necessary. On the contrary: only after he has proved from history that in fact the process has partially already occurred, and partially must occur in the future, he in addition characterises it as a process which develops in accordance with a definite dialectical law. That is all. It is therefore once again a pure distortion of the facts by Herr D hring when he declares that the negation of the negation has to serve here as the midwife to deliver the future from the womb of the past {D. K. G. 502-03}, or that Marx wants anyone to be convinced of the necessity of the common ownership of land and capital {503} (which is itself a D hringian contradiction in corporeal form) on the basis of credence in the negation of the negation {479-80}. Herr D hring's total lack of understanding of the nature of dialectics is shown by the very fact that he regards it as a mere proof-producing instrument, as a limited mind might look upon formal logic or elementary mathematics. Even formal logic is primarily a method of arriving at new results, of advancing from the known to the unknown and dialectics is the same, only much more eminently so; moreover, since it forces its way beyond the narrow horizon of formal logic, it contains the germ of a more comprehensive view of the world. The same correlation exists in mathematics. Elementary mathematics, the mathematics of constant quantities, moves within the confines of formal logic, at any rate on the whole; the mathematics of variables, whose most important part is the infinitesimal calculus, is in essence nothing other than the application of dialectics to mathematical relations. In it, the simple question of proof is definitely pushed into the background, as compared with the manifold application of the method to new spheres of research. But almost all the proofs of higher mathematics, from the first proofs of the differential calculus on, are from the standpoint of elementary mathematics strictly speaking, wrong. And this is necessarily so, when, as happens in this case, an attempt is made to prove by formal logic results obtained in the field of dialectics. To attempt to prove anything by means of dialectics alone to a crass metaphysician like Herr D hring would be as much a waste of time as was the attempt made by Leibniz and his pupils to prove the principles of the infinitesimal calculus to the mathematicians of their time. The differential gave them the same cramps as Herr D hring gets from the negation of the negation, in which, moreover, as we shall see, the differential also plays a certain role. Finally these gentlemen or those of them who had not died in the interval grudgingly gave way, not because they were convinced, but because it always came out right. Herr D hring, as he himself tells us, is only in his forties, and if he attains old age, as we hope he may, perhaps his experience will be the same. But what then is this fearful negation of the negation, which makes life so bitter for Herr D hring and with him plays the same role of the unpardonable crime as the sin against the Holy Ghost does in Christianity? A very simple process which is taking place everywhere and every day, which any child can understand as soon as it is stripped of the veil of mystery in which it was enveloped by the old idealist philosophy and in which it is to the advantage of helpless metaphysicians of Herr D hring s calibre to keep it enveloped. Let us take a grain of barley. Billions of such grains of barley are milled, boiled and brewed and then consumed. But if such a grain of barley meets with conditions which are normal for it, if it falls on suitable soil, then under the influence of heat and moisture it undergoes a specific change, it germinates; the grain as such ceases to exist, it is negated, and in its place appears the plant which has arisen from it, the negation of the grain. But what is the normal life-process of this plant? It grows, flowers, is fertilised and finally once more produces grains of barley, and as soon as these have ripened the stalk dies, is in its turn negated. As a result of this negation of the negation we have once again the original grain of barley, but not as a single unit, but ten-, twenty- or thirtyfold. Species of grain change extremely slowly, and so the barley of today is almost the same as it was a century ago. But if we take a plastic ornamental plant, for example a dahlia or an orchid, and treat the seed and the plant which grows from it according to the gardener s art, we get as a result of this negation of the negation not only more seeds, but also qualitatively improved seeds, which produce more beautiful flowers, and each repetition of this process, each fresh negation of the negation, enhances this process of perfection. With most insects, this process follows the same lines as in the case of the grain of barley. Butterflies, for example, spring from the egg by a negation of the egg, pass through certain transformations until they reach sexual maturity, pair and are in turn negated, dying as soon as the pairing process has been completed and the female has laid its numerous eggs. We are not concerned at the moment with the fact that with other plants and animals the process does not take such a simple form, that before they die they produce seeds, eggs or offspring not once but many times; our purpose here is only to show that the negation of the negation really does take place in both kingdoms of the organic world. Furthermore, the whole of geology is a series of negated negations, a series of successive chatterings of old and deposits of new rock formations. First the original earth crust brought into existence by the cooling of the liquid mass was broken up by oceanic, meteorological and atmospherico-chemical action, and these fragmented masses were stratified on the ocean bed. Local upheavals of the ocean bed above the surface of the sea subject portions of these first strata once more to the action of rain, the changing temperature of the seasons and the oxygen and carbonic acid of the atmosphere. These same influences act on the molten masses of rock which issue from the interior of the earth, break through the strata and subsequently cool off. In this way, in the course of millions of centuries, ever new strata are formed and in turn are for the most part destroyed, ever anew serving as material for the formation of new strata. But the result of this process has been a very positive one: the creation of a soil composed of the most varied chemical elements and mechanically fragmented, which makes possible the most abundant and diversified vegetation. It is the same in mathematics. Let us take any algebraic quantity whatever: for example, a. If this is negated, we get -a (minus a). If we negate that negation, by multiplying -a by -a, we get +a2, i.e., the original positive quantity, but at a higher degree, raised to its second power. In this case also it makes no difference that we can obtain the same a2 by multiplying the positive a by itself, thus likewise getting a2. For the negated negation is so securely entrenched in a2 that the latter always has two square roots, namely, a and a. And the fact that it is impossible to get rid of the negated negation, the negative root of the square, acquires very obvious significance as soon as we come to quadratic equations. The negation of the negation is even more strikingly obvious in higher analysis, in those summations of indefinitely small magnitudes {D. Ph. 418} which Herr D hring himself declares are the highest operations of mathematics, and in ordinary language are known as the differential and integral calculus. How are these forms of calculus used? In a given problem, for example, I have two variables,x and y, neither of which can vary without the other also varying in a ratio determined by the facts of the case. I differentiate x and y, i.e., I take x and y as so infinitely small that in comparison with any real quantity, however small, they disappear, that nothing is left of x and y but their reciprocal relation without any, so to speak, material basis, a quantitative ratio in which there is no quantity. Therefore, dy/dx, the ratio between the differentials of x and y, is dx equal to 0/0 but 0/0 taken as the expression of y/x. I only mention in passing that this ratio between two quantities which have disappeared, caught at the moment of their disappearance, is a contradiction; however, it cannot disturb us any more than it has disturbed the whole of mathematics for almost two hundred years. And now, what have I done but negatex and y, though not in such a way that I need not bother about them any more, not in the way that metaphysics negates, but in the way that corresponds with the facts of the case? In place ofx and y, therefore, I have their negation, dx and dy, in the formulas or equations before me. I continue then to operate with these formulas, treating dx and dy as quantities which are real, though subject to certain exceptional laws, and at a certain point I negate the negation, i.e., I integrate the differential formula, and in place of dx and dy again get the real quantities x and y, and am then not where I was at the beginning, but by using this method I have solved the problem on which ordinary geometry and algebra might perhaps have broken their jaws in vain. It is the same in history, as well. All civilised peoples begin with the common ownership of the land. With all peoples who have passed a certain primitive stage, this common ownership becomes in the course of the development of agriculture a fetter on production. It is abolished, negated, and after a longer or shorter series of intermediate stages is transformed into private property. But at a higher stage of agricultural development, brought about by private property in land itself, private property conversely becomes a fetter on production, as is the case today both with small and large landownership. The demand that it, too, should be negated, that it should once again be transformed into common property, necessarily arises. But this demand does not mean the restoration of the aboriginal common ownership, but the institution of a far higher and more developed form of possession in common which, far from being a hindrance to production, on the contrary for the first time will free production from all fetters and enable it to make full use of modern chemical discoveries and mechanical inventions. Or let us take another example: The philosophy of antiquity was primitive, spontaneously evolved materialism. As such, it was incapable of clearing up the relation between mind and matter. But the need to get clarity on this question led to the doctrine of a soul separable from the body, then to the assertion of the immortality of this soul, and finally to monotheism. The old materialism was therefore negated by idealism. But in the course of the further development of philosophy, idealism, too, became untenable and was negated by modern materialism. This modern materialism, the negation of the negation, is not the mere re-establishment of the old, but adds to the permanent foundations of this old materialism the whole thought-content of two thousand years of development of philosophy and natural science, as well as of the history of these two thousand years. It is no longer a philosophy at all, but simply a world outlook which has to establish its validity and be applied not in a science of sciences standing apart, but in the real sciences. Philosophy is therefore sublated here, that is, both overcome and preserved {D. K. G. 503}; overcome as regards its form, and preserved as regards its real content. Thus, where Herr D hring sees only verbal jugglery , closer inspection reveals an actual content. Finally: Even the Rousseau doctrine of equality of which D hring's is only a feeble and distorted echo could not have seen the light but for the midwife s services rendered by the Hegelian negation of the negation {502-03} though it was nearly twenty years before Hegel was born.  And far from being ashamed of this, the doctrine in its first presentation bears almost ostentatiously the imprint of its dialectical origin. In the state of nature and savagery men were equal; and as Rousseau regards even language as a perversion of the state of nature, he is fully justified in extending the equality of animals within the limits of a single species also to the animal-men recently classified by Haeckel hypothetically as Alali: speechless. But these equal animal-men had one quality which gave them an advantage over the other animals: perfectibility, the capacity to develop further; and this became the cause of inequality. So Rousseau regards the rise of inequality as progress. But this progress contained an antagonism: it was at the same time retrogression. Already in Rousseau, therefore, we find not only a line of thought which corresponds exactly to the one developed in Marx s Capital, but also, in details, a whole series of the same dialectical turns of speech as Marx used: processes which in their nature are antagonistic, contain a contradiction; transformation of one extreme into its opposite; and finally, as the kernel of the whole thing, the negation of the negation. And though in 1754 Rousseau was not yet able to speak the Hegelian jargon {D. K. G. 491}, he was certainly, sixteen years before Hegel was born, deeply bitten with the Hegelian pestilence, dialectics of contradiction, Logos doctrine, theologies, and so forth. And when Herr D hring, in his shallow version of Rousseau s theory of equality, begins to operate with his victorious two men, he is himself already on the inclined plane down which he must slide helplessly into the arms of the negation of the negation. The state of things in which the equality of the two men flourished, which was also described as an ideal one, is characterised on page 271 of his Philosophie as the primitive state . This primitive state, however, according to page 279, was necessarily sublated by the robber system the first negation. But now, thanks to the philosophy of reality, we have gone so far as to abolish the robber system and establish in its stead the economic commune {504} based on equality which has been discovered by Herr D hring negation of the negation, equality on a higher plane. What a delightful spectacle, and how beneficently it extends our range of vision: Herr D hring's eminent self committing the capital crime of the negation of the negation! And so, what is the negation of the negation? An extremely general and for this reason extremely far-reaching and important law of development of nature, history, and thought; a law which, as we have seen, holds good in the animal and plant kingdoms, in geology, in mathematics, in history and in philosophy a law which even Herr D hring, in spite of all his stubborn resistance, has unwittingly and in his own way to follow. It is obvious that I do not say anything concerning the particular process of development of, for example, a grain of barley from germination to the death of the fruit-bearing plant, if I say it is a negation of the negation. For, as the integral calculus is also a negation of the negation, if I said anything of the sort I should only be making the nonsensical statement that the life-process of a barley plant was integral calculus or for that matter that it was socialism. That, however, is precisely what the metaphysicians are constantly imputing to dialectics. When I say that all these processes are a negation of the negation, I bring them all together under this one law of motion, and for this very reason I leave out of account the specific peculiarities of each individual process. Dialectics, however, is nothing more than the science of the general laws of motion and development of nature, human society and thought. But someone may object: the negation that has taken place in this case is not a real negation: I negate a grain of barley also when I grind it, an insect when I crush it underfoot, or the positive quantity a when I cancel it, and so on. Or I negate the sentence: the rose is a rose, when I say: the rose is not a rose; and what do I get if I then negate this negation and say: but after all the rose is a rose? These objections are in fact the chief arguments put forward by the metaphysicians against dialectics, and they are wholly worthy of the narrow-mindedness of this mode of thought. Negation in dialectics does not mean simply saying no, or declaring that something does not exist, or destroying it in any way one likes. Long ago Spinoza said: Omnis determinatio est negatio every limitation or determination is at the same time a negation.  And further: the kind of negation is here determined, firstly, by the general and, secondly, by the particular nature of the process. I must not only negate, but also sublate the negation. I must therefore so arrange the first negation that the second remains or becomes possible. How? This depends on the particular nature of each individual case. If I grind a grain of barley, or crush an insect, I have carried out the first part of the action, but have made the second part impossible. Every kind of thing therefore has a peculiar way of being negated in such manner that it gives rise to a development, and it is just the same with every kind of conception or idea. The infinitesimal calculus involves a form of negation which is different from that used in the formation of positive powers from negative roots. This has to be learnt, like everything else. The bare knowledge that the barley plant and the infinitesimal calculus are both governed by negation of negation does not enable me either to grow barley successfully or to differentiate and integrate; just as little as the bare knowledge of the laws of the determination of sound by the dimensions of the strings enables me to play the violin. But it is clear that from a negation of the negation which consists in the childish pastime of alternately writing and cancelling a, or in alternately declaring that a rose is a rose and that it is not a rose, nothing eventuates but the silliness of the person who adopts such a tedious procedure. And yet the metaphysicians try to make us believe that this is the right way to carry out a negation of the negation, if we ever should want to do such a thing. Once again, therefore, it is no one but Herr D hring who is mystifying us when he asserts that the negation of the negation is a stupid analogy invented by Hegel, borrowed from the sphere of religion and based on the story of the fall of man and his redemption {D. K. G. 504}. Men thought dialectically long before they knew what dialectics was, just as they spoke prose long before the term prose existed. [An allusion to Moli re's comedy Le Bourgeois gentilhomme, Act II, Scene 6 Ed.] The law of negation of the negation, which is unconsciously operative in nature and history and, until it has been recognised, also in our heads, was only first clearly formulated by Hegel. And if Herr D hring wants to operate with it himself on the quiet and it is only that he cannot stand the name, then let him find a better name. But if his aim is to banish the process itself from thought, we must ask him to be so good as first to banish it from nature and history and to invent a mathematical system in which -a x -a is not +a2 and in which differentiation and integration are prohibited under severe penalties.
1877: Anti-Duhring - XIII. Negation of the Negation