Anti-Dühring by Frederick Engels 1877

Part I: Philosophy

III. Classification.

Philosophy, according to Herr Dühring, is the development of the highest form of consciousness of the world and of life {D. Ph. 2},and in a wider sense embraces the principles of all knowledge and volition. Wherever a series of cognitions or stimuli or a group of forms of being come to be examined by human consciousness, the principles underlying these manifestations of necessity become an object of philosophy. These principles are the simple, or until now assumed to be simple, constituents of manifold knowledge and volition {8}. Like the chemical composition of bodies, the general constitution of things can be reduced to basic forms and basic elements. These ultimate constituents or principles, once they have been discovered, are valid not only for what is immediately known and accessible, but also for the world which is unknown and inaccessible to us. Philosophical principles consequently provide the final supplement required by the sciences in order to become a uniform system by which nature and human life can be explained {9}. Apart from the fundamental forms of all existence, philosophy has only two specific subjects of investigation — nature and the world of man {14}. Accordingly, our material arranges itself quite naturally into three groups, namely, the general scheme of the universe, the science of the principles of nature, and finally the science of mankind. This succession at the same time contains an inner logical sequence, for the formal principles which are valid for all being take precedence, and the realms of the objects to which they are to be applied then follow in the degree of their subordination {15}.

So far Herr Dühring, and almost entirely word for word.

What he is dealing with are therefore principles, formal tenets derived from thought and not from the external world, which are to be applied to nature and the realm of man, and to which therefore nature and man have to conform. But whence does thought obtain these principles? From itself? No, for Herr Dühring himself says: the realm of pure thought is limited to logical schemata and mathematical forms {42} (the latter, moreover, as we shall see, is wrong). Logical schemata can only relate to forms of thought; but what we are dealing with here is solely forms of being, of the external world, and these forms can never be created and derived by thought out of itself, but only from the external world. But with this the whole relationship is inverted: the principles are not the starting-point of the investigation, but its final result; they are not applied to nature and human history, but abstracted from them, it is not nature and the realm of man which conform to these principles, but the principles are only valid in so far as they are in conformity with nature and history. That is the only materialist conception of the matter, and Herr Dühring's contrary conception is idealistic, makes things stand completely on their heads, and fashions the real world out of ideas, out of schemata, schemes or categories existing somewhere before the world, from eternity — just like a Hegel.

In fact, let us compare Hegel’s Encyclopaedia [30] and all its delirious fantasies with Herr Dühring»s final and ultimate truths. With Herr Dühring we have in the first place general world schematism, which Hegel calls Logic. Then with both of them we have the application of these schemata or logical categories to nature: the philosophy of nature; and finally their application to the realm of man, which Hegel calls the philosophy of mind. The “inner logical sequence” of the Dühring succession therefore leads us “quite naturally” {D. Ph. 15} back to Hegel’s Encyclopaedia, from which it has been taken with a loyalty which would move that wandering Jew of the Hegelian school, Professor Michelet of Berlin, to tears. [31]

That is what comes of accepting “consciousness”, “thought”, quite naturalistically, as something given, something opposed from the outset to being, to nature. If that were so, it must seem extremely strange that consciousness and nature, thinking and being, the laws of thought and the laws of nature, should correspond so closely. But if the further question is raised what thought and consciousness really are and where they come from, it becomes apparent that they are products of the human brain and that man himself is a product of nature, which has developed in and along with its environment; hence it is self-evident that the products of the human brain, being in the last analysis also products of nature, do not contradict the rest of nature's interconnections but are in correspondence with them. [32]

But Herr Dühring cannot permit himself such a simple treatment of the subject. He thinks not only in the name of humanity — in itself no small achievement — but in the name of the conscious and reasoning beings on all celestial bodies. Indeed, it would be

“a degradation of the basic forms of consciousness and knowledge to attempt to rule out or even to put under suspicion their sovereign validity and their unconditional claim to truth, by applying the epithet ‘human’ to them” {2}.

Hence, in order that no suspicion may arise that on some celestial body or other twice two makes five {30-31}, Herr Dühring dare not designate thought as being human, and so he has to sever it from the only real foundation on which we find it, namely, man and nature; and with that he tumbles hopelessly into an ideology [33] which reveals him as the epigone of the “epigone” Hegel {197}. By the way, we shall often meet Herr Dühring again on other celestial bodies.

It goes without saying that no materialist doctrine can be founded on such an ideological basis. Later on we shall see that Herr Dühring is forced more than once to endow nature surreptitiously with conscious activity, with what in plain language is called God.

However, our philosopher of reality had also other motives for shifting the basis of all reality from the real world to the world of thought. The science of this general world schematism, of these formal principles of being, is precisely the foundation of Herr Dühring's philosophy. If we deduce world schematism not from our minds, but only through our minds from the real world, if we deduce principles of being from what is, we need no philosophy for this purpose, but positive knowledge of the world and of what happens in it; and what this yields is also not philosophy, but positive science. In that case, however, Herr Dühring's whole volume would be nothing but love's labour lost.

Further: if no philosophy as such is any longer required, then also there is no more need of any system, not even of any natural system of philosophy. The perception that all the processes of nature are systematically connected drives science on to prove this systematic connection throughout, both in general and in particular. But an adequate, exhaustive scientific exposition of this interconnection, the formation of an exact mental image of the world system in which we live, is impossible for us, and will always remain impossible. If at any time in the development of mankind such a final, conclusive system of the interconnections within the world — physical as well as mental and historical — were brought about, this would mean that human knowledge had reached its limit, and, from the moment when society had been brought into accord with that system, further historical development would be cut short — which would be an absurd idea, sheer nonsense. Mankind therefore finds itself faced with a contradiction: on the one hand, it has to gain an exhaustive knowledge of the world system in all its interrelations; and on the other hand, because of the nature both of men and of the world system, this task can never be completely fulfilled. But this contradiction lies not only in the nature of the two factors — the world, and man — it is also the main lever of all intellectual advance, and finds its solution continuously, day by day, in the endless progressive development of humanity, just as for example mathematical problems find their solution in an infinite series or continued fractions. Each mental image of the world system is and remains in actual fact limited, objectively by the historical conditions and subjectively by the physical and mental constitution of its originator. But Herr Dühring explains in advance that his mode of reasoning is such that it excludes any tendency to a subjectively limited conception of the world. We saw above that he was omnipresent — on all possible celestial bodies. We now see that he is also omniscient. He has solved the ultimate problems of science and thus nailed boards across the future of all science.

As with the basic forms of being, so also with the whole of pure mathematics: Herr Dühring thinks that he can produce it a priori that is, without making use of the experience offered us by the external world, can construct it in his head.

In pure mathematics the mind deals “with its own free creations and imaginations” {D. Ph. 43}; the concepts of number and figure are “the adequate object of that pure science which it can create of itself” {42}, and hence it has a “validity which is independent of particular experience and of the real content of the world” {43}.

That pure mathematics has a validity which is independent of the particular experience of each individual is, for that matter, correct, and this is true of all established facts in every science, and indeed of all facts whatsoever. The magnetic poles, the fact that water is composed of hydrogen and oxygen, the fact that Hegel is dead and Herr Dühring alive, hold good independently of my own experience or that of any other individual, and even independently of Herr Dühring’s experience, when he begins to sleep the sleep of the just. But it is not at all true that in pure mathematics the mind deals only with its own creations and imaginations. The concepts of number and figure have not been derived from any source other than the world of reality. The ten fingers on which men learnt to count, that is, to perform the first arithmetical operation, are anything but a free creation of the mind. Counting requires not only objects that can be counted, but also the ability to exclude all properties of the objects considered except their number — and this ability is the product of a long historical development based on experience. Like the idea of number, so the idea of figure is borrowed exclusively from the external world, and does not arise in the mind out of pure thought. There must have been things which had shape and whose shapes were compared before anyone could arrive at the idea of figure. Pure mathematics deals with the space forms and quantity relations of the real world — that is, with material which is very real indeed. The fact that this material appears in an extremely abstract form can only superficially conceal its origin from the external world. But in order to make it possible to investigate these forms and relations in their pure state, it is necessary to separate them entirely from their content, to put the content aside as irrelevant; thus we get points without dimensions, lines without breadth and thickness, a and b and x and y, constants and variables; and only at the very end do we reach the free creations and imaginations of the mind itself, that is to say, imaginary magnitudes. Even the apparent derivation of mathematical magnitudes from each other does not prove their a priori origin, but only their rational connection. Before one came upon the idea of deducing the form of a cylinder from the rotation of a rectangle about one of its sides, a number of real rectangles and cylinders, however imperfect in form, must have been examined. Like all other sciences, mathematics arose out of the needs of men: from the measurement of land and the content of vessels, from the computation of time and from mechanics. But, as in every department of thought, at a certain stage of development the laws, which were abstracted from the real world, become divorced from the real world, and are set up against it as something independent, as laws coming from outside, to which the world has to conform. That is how things happened in society and in the state, and in this way, and not otherwise, pure mathematics was subsequently applied to the world, although it is borrowed from this same world and represents only one part of its forms of interconnection — and it is only just because of this that it can be applied at all.

But just as Herr Dühring imagines that, out of the axioms of mathematics,

“which also in accordance with pure logic neither require nor are capable of substantiation” {34},

he can deduce the whole of pure mathematics without any kind of empirical admixture, and then apply it to the world, so he likewise imagines that he can, in the first place, produce out of his head the basic forms of being, the simple elements of all knowledge, the axioms of philosophy, deduce from these the whole of philosophy or world schematism, and then, by sovereign decree, impose this constitution of his on nature and humanity. Unfortunately nature is not at all, and humanity only to an infinitesimal degree, composed of the Manteuffelite Prussians of 1850. [34]

Mathematical axioms are expressions of the scantiest thought-content, which mathematics is obliged to borrow from logic. They can be reduced to two:

1) The whole is greater than its part. This statement is pure tautology, as the quantitatively conceived idea “part” is from the outset definitely related to the idea “whole”, and in fact in such a way that “part” simply means that the quantitative “whole” consists of several quantitative “parts”. In stating this explicitly, the so-called axiom does not take us a step further. This tautology can even in a way be proved by saying: a whole is that which consists of several parts; a part is that of which several make a whole; hence the part is less than the whole — in which the inanity of repetition brings out even more clearly the inanity of content.

2) If two quantities are equal to a third, they are equal to each other. This statement, as Hegel has already shown, is a conclusion, the correctness of which is vouched for by logic, and which is therefore proved, although outside of pure mathematics. The remaining axioms relating to equality and inequality are merely logical extensions of this conclusion.

These meagre principles do not cut much ice, either in mathematics or anywhere else. In order to get any further, we are obliged to bring in real relations, relations and space forms which are taken from real bodies. The ideas of lines, planes, angles, polygons, cubes, spheres, etc., are all taken from reality, and it requires a pretty good portion of naive ideology to believe the mathematicians that the first line came into existence through the movement of a point in space, the first plane through the movement of a line, the first solid through the movement of a plane, and so on. Even language rebels against such a conception. A mathematical figure of three dimensions is called a solid body, corpus solidum, hence, in Latin, even a tangible object; it therefore has a name derived from sturdy reality and by no means from the free imagination of the mind.

But why all this prolixity? After Herr Dühring, on pages 42 and 43, [35] has enthusiastically sung the independence of pure mathematics from the world of experience, its apriority, its preoccupation with the mind’s own free creations and imaginations, he says on page 63:

“It is, of course, easily overlooked that those mathematical elements (number, magnitude, time, space and geometric motion) are ideal only in their form, ... absolute magnitudes are therefore something completely empirical, no matter to what species they belong”, ... but “mathematical schemata are capable of characterisation which is adequate even though divorced from experience.”

The last statement is more or less true of every abstraction, but does not by any means prove that it is not abstracted from reality. In world schematism pure mathematics arose out of pure thought — in the philosophy of nature it is something completely empirical, taken from the external world and then divorced from it. Which are we to believe?