Landmarks of Scientific Socialism: "Anti-Duehring"

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.

But again; ancient philosophy was primitive naturalistic materialism. In the state of thought at that period it was, as such, incapable of clear conceptions of matter. But the necessity of clearness on this point led to the doctrine of a soul which could leave the body, then to the idea of the immortality of the soul, finally, to monotheism. The old materialism was therefore negated by idealism. But in the further development of philosophy idealism became untenable, and is negated by modern materialism. This, the negation of negation, is not the mere reestablishment of the old, but unites, with the surviving foundations, the whole thought content of a two thousand years' development of philosophy and science, as well as the history of these two thousand years. It is in a special sense no philosophy but a single concept of the universe which has to prove and realise itself not in a science of sciences apart, but in actual science. Philosophy is here also cast aside, that is "destroyed and preserved," destroyed as to its form, preserved as to its real content. Where Herr Duehring only sees word-jugglery a more real content is brought to light by the newer point of view.

Finally, even the Rousseau doctrine of equality, of which that of Herr Duehring is only a feeble and false plagiarism, has no existence unless the Hegelian negation of the negation serve it as a midwife, although it originated twenty years prior to the birth of Hegel. Far from being ashamed of this it bears in plain sight the stamp of its dialectic derivation in its earliest manifestation. In a state of nature and savagery men were equal, and, since Rousseau regards speech as a falsifying of natural conditions, he is quite right in predicating equality of animals of one species as far as this reaches, and the same also with regard to those speechless animal-men, recently hypothetically classified by Haeckel as Alali. But these equal animal men had one quality beyond the other animals, – perfectibility, the power of further development and this was the reason of inequality. Rousseau sees therefore in the existence of equality a step forward. But this advance was self contradictory, it was at the same time a retrogression. "All further advances (beyond the primitive stage) were so many steps, seemingly in the development of individual men, but actually in the decay of the species. Working in metals and agriculture were the two arts whose discovery brought about this great revolution" (the transformation of the primitive forests into cultivated lands, but also the introduction of poverty and slavery together with private property). "The poets hold that gold and silver, the philosophers that iron and corn have civilised men and ruined the human race." Each new advance of civilisation is at the same time an advance of inequality. All contrivances with which society endows itself by means of civilisation are in direct opposition to their original purpose. "It is beyond question and a foundation principle of the entire public law that people made rulers to defend their liberties, not to destroy them." And yet these rulers become of necessity the oppressors of the people and they carry the oppression to the point where inequality is brought to a climax and, then, transformed into its opposite, again becomes the reason of equality, for to despots all are equal, that is equally of no account. Here is the extreme of inequality, the crowning point which closes the circle, and touches the point from which we have proceeded; here all private individuals are equal, since they are of no account, and subjects have no law other than the will of their master. "But the despot is master only as long as he has the power, and for this reason he cannot complain of the use of force if he is banished… Force upholds him, force throws him down, everything goes according to a straight and naturally appointed path." And thus again inequality is transformed into equality, but not into the old materialistic equality of speechless, primitive men, but into the higher equality of organised society. The oppressor is oppressed, it is negation of the negation.

We have then, as regards Rousseau, not merely a method of thought which is quite analogous to that pursued in Marx's "Capital," but also a whole series of single dialectic turns of which Marx avails himself: Processes, which are antagonistic in their nature, containing a contradiction in themselves, are transformed from one extreme to its opposite, finally, as the quintessence of the whole, negation of the negation. Although Rousseau in 1754 could not speak the jargon of Hegel, he was then, at a period twenty-three years before the birth of Hegel, deeply infected with the Hegel contagion, the dialectic of contradiction, doctrine of logic, theology, etc. And if Duehring in his misapplication of Rousseau's theory of equality, operates with his two victorious men, he having lost his feet, falls, of necessity into the arms of the negation of the negation.

The conditions under which the equality of the two men flourishes and which is set forth as an ideal condition is shown on page 271 of the Philosophy as the original condition. This original condition on page 279 is of necessity destroyed by the "robber system" – first negation. But we have now, thanks to the philosophy of reality, arrived at the point of abolishing the "robber system" and substituting for it the economic commune discovered by Herr Duehring – negation of the negation, equality on a higher plane.

What is the negation of the negation, therefore? It is a very far reaching, and, just, for this reason, a very important law of development of nature, human history and thought, a law which we see realised in the animal and vegetable kingdoms, in geology, in mathematics, in history, and philosophy, and which Herr Duehring himself, in spite of his opposition and resistance, must follow, after his own fashion. It is evident that I say nothing of the special development of the grain of barley from the germ to the crop bearing plant, if I say it is negation of the negation. Since the integral calculus is likewise negation of the negation, with the other assertion I should only affirm that the life process of a grain of barley is integral calculus or even socialism. But that is just the kind of thing which the metaphysicians push off on the dialectic. If I say that all these processes constitute negation of the negation, I embrace them all under this one law of progress, and leave the distinctive features of each special process without particular notice. The dialectic is, as a matter of fact, nothing but the science of the universal laws of motion, and evolution in nature, human society and thought.

At this point, however, the objection may be urged that the final negation is no true negation, I negate a grain of barley also when I grind it, an insect when I crush it, a positive quantity when I eliminate it, etc. Or I negate the statement "the rose is a rose" if I say "the rose is no rose" and what happens if I negate this negation again and say "but the rose is a rose"? These objection are, in fact, the chief arguments of the metaphysicians against the dialectic and are quite worthy of this idiotic method of reasoning. To negate in the dialectic is not simply to say "No," or to describe a thing as non-existent, or to destroy it after any fashion that you may choose. Spinoza says "omnis determinatio est negatio," every limitation or determination is at the same time a negation. Furthermore, the sort of negation here is shown first by means of the universal and in the second place by means of the distinctive nature of the process. I must not only negate but I must also restore the negation again. I must therefore so direct the first negation that the second remains possible or shall be so. How? Just according to the peculiar nature of each particular case. I grind a grain of barley, I crush an insect, I have certainly fulfilled the first act but have made the second impossible. Every species of things has therefore its own peculiar properties to be negated in order that a progression may proceed, and every species of properties and ideas is precisely the same in this regard. In infinitesimal calculations the negation is brought about after a different fashion than in the restoration of positive powers from negative roots. That has to be learnt like everything else. With the mere knowledge that the stalk of barley and infinitesimal calculation fall under the principle of the negation of the negation, I cannot cultivate more barley nor can I differentiate and integrate, just as I cannot play the violin by virtue of a mere knowledge of the laws of harmony. But it is evident that a merely childish negation of the negation such as writing down a and erasing it, or by affirming that a rose is a rose and that it is not a rose leads to no conclusion other than to show the silliness of the people who undertake processes so tedious. And yet metaphysicians would inform us that that is the right way to carry out the negation of the negation.

Herr Duehring is therefore a mystifier when he asserts that the negation of the negation was an analogy made by Hegel derived from religion and built up on the story of the Fall and the Redemption. Men thought dialectically a long time before they knew what the dialectic really was, just as they spoke prose a long time before the term "prose" was used. The law of the negation of the negation which operates in history and which until it is once learned goes on in our brains unconsciously to ourselves, was first clearly formulated by Hegel, and if Herr Duehring desires to employ it in secret but cannot stand the name, he should discover a better name. But if he insist on expelling it from the processes of thought, he must first be good enough to expel it from nature and from history, and find a system of mathematics in which – a multiplied by – a does not give us + a² and where the differential and integral calculus are both forbidden by law.

In this short section Engels leaves the general discussion in order to again pay his respects to the shortcomings and deficiencies of Herr Duehring. The matter possesses no general interest for Engels merely teases his opponent upon the magnificence of his claims and the slightness of his performances.