It is only at this point, after Marx has completed his proof on the basis of historical and economic facts, that he proceeds: "The capitalist mode of production and appropriation, hence the capitalist private property, is the first negation of individual private property founded on the labour of the proprietor. Capitalist production begets, with the inexorability of a process of nature, its own negation. It is the negation of the negation"-- and so on (as quoted above).
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 Dühring 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 Dühringian contradiction in corporeal form) on the basis of credence in the negation of the negation {479-80}.
Herr Dühring'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 Dühring 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 Dühring 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 Dühring, 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 Dühring 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 Dühring'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.
