Landmarks of Scientific Socialism: "Anti-Duehring"

by Friedrich Engels

Eternity is ascribed to existence, in agreement with Hegel, what Hegel calls "tiresome (schlecht) eternity," and this eternity is now investigated. "The plainest form of an incontrovertible idea of eternity is the piling up of numbers unlimitedly in arithmetical progression. Just as we can give a complete unity to each number without the possibility of repetition, so at every stage of its being it progresses still further and eternity consists in the unlimited manifestation of this condition. This sufficiently conceived eternity has but one single beginning with one single direction. Although it is not material to our concept to imagine a direction opposite to that in which the progression piles up, this notion of a backward moving eternity is only a hasty picture drawn by the imagination. Since it must necessarily run in a contrary direction, it would have behind it in each instance an endless succession of numbers. But this would be inadmissible as constituting the contradiction of a calculated infinity of numbers, and so it seems absurd to imagine a second direction of eternity."

The first conclusion to be drawn from this conception of eternity is that the chain of cause and effect in the universe must once have had a beginning: an endless number of causes which have followed one another endlessly is therefore unthinkable, "because innumerability is thus considered as enumerated," therefore a final cause is proved.

The second conclusion is "the law of the definite number: the accumulation of identical independent objects of an actual species is only thinkable as being made up of a definite number of these individual objects." Not only must the actual number of the heavenly bodies be definite at a given time, but the total number of all existent objects, the smallest independent particles of matter. This last necessity constitutes the real reason why no composite body is thinkable except as made up of atoms. All actual division has a fixed limit and must have it, if the contradiction of a numerated innumerability is to be avoided. On the same grounds not only must the revolutions of the sun and earth be fixed as they have occurred up to the present, even if they cannot be indicated, but all the periodical processes of nature must have had a beginning somewhere, and all the distinctions and complexities of nature which succeed each other must similarly have had an origin. This must indisputably have existed from eternity, but such an idea would be excluded if time consisted of real parts and was not arbitrarily divided to accommodate the possibilities of our understanding. It is different with time, self regarded, but the facts and phenomena of which time is made up being capable of differentiation can be enumerated. Let us conceive of a condition in which no change occurs and which undergoes no alteration in its stable identity; the time concept then becomes transformed into the general notion of existence. What is the result of piling up an empty duration of time is not discoverable. So far, Herr Duehring writes and he is not a little edified concerning the significance of these discoveries. He hopes that "it is perceived as a not insignificant truth," and later on says, "One should note the very simple phrases by which we have helped the concept of immortality and the criticism of it to a point at present unknown, through the sharpening and deepening of the simple elements of the universal conception of time and space."

We have helped! This deepening and sharpening! Who are we? In what are we manifest? Who deepens and who sharpens?

"Thesis—the world has a beginning in time and is bounded by space. Proof—If one suppose that the world has no beginning in time he is bound to grant infinity to each point of time, and so an infinite succession of things has passed away in the universe. But infinity of a series consists in the impossibility of its completion by successive syntheses. Therefore an eternal progression of the world is impossible. Hence a beginning of the world is a necessary condition of its existence, which was to be proved. Let us take the other concept. The world now appears as an eternal given whole consisting of things which have a simultaneous existence. Now we can conceive of the mass of a quantity, which can only be regarded under certain conditions, in no other way than by means of the synthesis of its parts, and we conceive the totality of the quantity by means of the completed synthesis or repeated additions of the unity to itself. Thus, in order to conceive of the universe as a whole which fills all space, the successive syntheses of the parts of an infinite universe must be regarded as being completed, that is an eternity of time must in calculating all coexisting things, be regarded as having existed, but this is impossible. Therefore an unending aggregate of actual things cannot be regarded as a given whole and therefore also not as coexistent. A world is therefore extension in space which is not unlimited and which has therefore bounds. And this was the second thing to be proved."

These statements are copied from a well-known book which made its appearance in 1781 and is entitled "The Critique of Pure Reason," by Immanuel Kant. They can be read there in Part I, Division 2, second section, second part. "First Antinomy of Pure Reason." To Herr Duehring alone remains the name and fame of having pasted the law of fixed numbers on one of the published thoughts of Kant and of having made the discovery that there was once a time when time did not exist but only a universe. For the rest, therefore, when we come across anything sensible in Herr Duehring's exposition "We" means Immanuel Kant, and the "present" is only ninety-five years old. Quite simple indeed, and unknown until now! But Kant does not establish the above statement by his proof. On the other hand, he shows the reverse, namely, that the universe has no beginning in time and no end in space, and he fixes his antinomy in this, the unsolvable contradiction that the one is just as capable of proof as the other. People of small calibre might be inclined to think that here Kant had found an insuperable difficulty, not so our bold author of fundamental results "especially his own." He copies all that he can use of Kant's antinomy and throws the rest away.

The matter solves itself very simply. Eternity in time and endlessness in space signify from the very words that there is no end in either direction, forwards or backwards, over or under, right or left. This infinity is quite different from an endless progression, since the latter always has some beginning, a first step. The inapplicability of this progression idea to our object is evident directly we apply it to space. Infinite progression translated in terms of space is a line produced continuously in a given direction. Is infinity in space expressed in this way, even remotely? On the contrary it requires six of these lines drawn from this point in three opposite directions to express the dimensions of space and we should have accordingly six of these dimensions. Kant saw this so plainly that he employed his progression merely indirectly in a round about way to express the extent of the universe. Herr Duehring on the contrary forces us to accept his six dimensions of space and at the same time has no words in which to express his contempt of the mathematical mysticism of Gauss who would not content himself with the three dimensions of space.

Applied to time, the series or row of objects, infinite at both extremities, has a certain figurative significance. But let us picture time as proceeding from unity or a line proceeding from a fixed point. We can say then that time has had a beginning. We assume just what we wanted to prove. We give a one-sided half-character to infinity of time. But a one-sided eternity split in halves is a contradiction in itself, the exact opposite of a hypothetical infinity, incapable of contradiction. We can only overcome this contradiction by assuming that the unity which we began to count the progression from, the point from which we measure the line, is a unity taken at pleasure in the series, a point taken at pleasure in the line. Hence as far as the line or series is concerned it is immaterial where we put it.

But as for the contradiction of the "counted endless progression" we shall be in a position to examine it more closely as soon as Herr Duehring has taught us the trick of reckoning it. If he has accomplished the feat of counting from minus infinity to zero, we shall be glad to hear from him again. It is clear that wherever he begins to count he leaves behind him an endless progression, and with it the problem which he had to solve. Let him only take his own infinite progression 1 + 2 + 3 + 4 etc. and try to reckon back to 1 again from the infinite end. He evidently does not comprehend the requirements of the problem. And furthermore, if he affirms that the infinite progression of past time is capable of calculation he must affirm that time has a beginning for otherwise he could not begin to calculate. Therefore he again substitutes a supposition for what he had to prove. The idea of the calculated infinite series, in other words Duehring's all-embracing law of the fixed number, is therefore a contradiction in adjecto, is a self contradiction, and an absurd one, moreover.

It is clear that an infinity which has an end but no beginning is neither more nor less than an infinity which has a beginning but no end. The least logical insight would have compelled Herr Duehring to the statement that beginning and end are mutually necessary to each other, like North Pole and South Pole, and that if one omit the end the beginning becomes the end, the one end which the series has and vice versa.