Landmarks of Scientific Socialism: "Anti-Duehring"

CHAPTER V

NATURAL PHILOSOPHY

We now come to natural philosophy. Here again Herr Duehring takes it upon himself to be dissatisfied with his predecessors. He says "Natural philosophy sank so low that it became barren dregs of poetry and had fallen into the degraded rubbish of the sham philosophy of a Schelling and the like, grubbing in priest-craft and mystifying the public." Disgust has rid us of these deformities, but up to the present it has been succeeded by instability, and "what is of concern to the public at large is that the disappearance of a particularly great charlatan merely gives an opportunity to a smaller but more expert successor who repeats the production in another form." Naturalists have little desire for "a flight into the kingdom of the universe-comprehending ideas," and therefore indulge too freely in speculations which "go to pieces." Thus complete salvation must be found, and, fortunately, Herr Duehring is at hand.

In order to comprehend aright the following conclusions respecting the unfolding of the universe in time and its limitation in space, we must again turn our attention to certain portions of the "scheme of the universe."

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.

The entire fallacy would not be possible if it were not for the mathematical practice of operating with an infinite series. Because in mathematics one must proceed from the given and finite to that which is not given and infinite, all mathematical series whether positive or negative, begin with a fixed point otherwise one cannot calculate. The ideal necessities of the mathematician however are very far from being a law compulsory upon the universe.

Besides Herr Duehring will never succeed in imagining an infinity without contradiction. In the first place, infinity is a contradiction and full of contradictions. For example it is a contradiction that infinity should be made up of finite things and yet such is the case. The notion of a limited universe leads to contradictions just as much as the notion of its unlimitedness, and each attempt to abolish these contradictions leads, as we have seen, to new and worse contradictions. But just because infinity is a contradiction, it is without end, endlessly developing itself in time and space. The abolition of the contradiction would be the end of infinity. Hegel saw that very clearly, and covers the people who entered upon intricate arguments about this contradiction with merited scorn.

Let us proceed. Now, time has had a beginning. What was before this beginning? The unchangeable universe incomparable with anything else. And as no changes occur in this condition the particular concept time is transformed into the general concept existence. In the first place we have nothing to do with the transformation which goes on in the brain of Herr Duehring. We are not engaged with a concept of time, but with actual time of which Herr Duehring cannot so easily dispose. In the second place no matter how much the concept of time is transformed into the general concept existence it does not bring us one step nearer the goal. For the fundamental forms of all existence are space and time, and a thing existing outside of time is as silly an idea as that of a being outside of space. The Hegelian "past existence in which there was no time" and the neo-Schelling "being beyond the scope of thought" are rational conceptions compared with this being outside of time. For this reason Herr Duehring goes to work very cautiously "intrinsically it may be called time, but one cannot really call it time, as time does not consist in itself of real parts but is merely divided by us into parts to suit our own convenience," only a real filling up of time with distinct facts makes it capable of calculation. It is impossible to see the significance of piling up an empty duration. But it does not matter anyway. The question is whether the universe in this presupposed condition continues, that is persists, through a period of time. We have long known that it is useless to try and measure such empty space and to calculate without plan or aim and just because of the tiresomeness of such a proceeding Hegel calls this infinity "miserable." According to Herr Duehring time exists only by virtue of change, not change in and through time. Because time is different from change and independent of it, we can measure it by the changes, because in order to measure we need something different from that which is to be measured. And the time in which no recognisible changes take place is very far from being no time, on the other hand since it is free from other ingredients, it is pure, that is to say, true time. Indeed if we want to contemplate time as a pure concept separated from all foreign admixture, we are obliged to eliminate all the various events which occur in time, either successively or simultaneously, and thus imagine a time in which nothing occurs. By this means we have not permitted the concept time to be overcome by the general concept of existence, but we have thereby arrived at a pure time concept. All these contradictions and impossibilities are mere child's play compared with the confusion into which he plunges the universe with its self-sufficient commencement. If the universe was in a condition in which no change occurred in it, how did it ever manage to get from that state to one of change? Moreover, an absolute condition of absence of change existing from eternity cannot possibly get out of that state unaided so as to pass over to a condition of progress and change. A first cause of motion must therefore have come from the outside, from beyond the universe, which caused the movement. This first cause of motion is clearly only another term for God, The God and the Beyond of which Herr Duehring fancied that he had so nicely settled in his scheme of the universe, return sharpened and deepened in his natural philosophy.

Further Herr Duehring says: "Where a fixed element of existence is capable of measurement, it will remain in unalterable stability. This is evident from material and mechanical force." The former quotation gives, it may be incidentally mentioned, a good example of Herr Duehring's axiomatic grandiloquence. Fixed quantities remain exactly the same, the quantity of mechanical force, once in the universe, is always the same. We will not dwell on this, so far as it is true, Descartes knew and said it three hundred years ago as regards philosophy, while in mechanical science the doctrine of the conservation of energy has been preached for the last twenty years. Herr Duehring has not improved upon it in so far as he limits it to mechanical energy. But where was mechanical energy at the period of unchangeableness? To this question Herr Duehring stubbornly refuses an answer.

Where was the unchangeable mechanical force then, Herr Duehring, and what was it busy about? Answer: "The original state of the universe, or, better, the existence of unchangeable matter, not allowing of any changes in time, is a question which no mind can pass except one which sees the acme of wisdom in the destruction of its own powers." Therefore you must either take my original condition with your eyes shut, or I, the lusty Eugene Duehring, brand you as an intellectual eunuch. Some people might be quite alarmed about this, but we who have seen a few examples of Herr Duehring's powers, can let the elegant abuse pass and reiterate the question, "But how about that mechanical energy, Herr Duehring, if you please?"

Herr Duehring is staggered at once. In fact, he stammers, "There is no proof of the actual existence of that original condition. Let us remember that this is also the case with each new step in the series with which we are acquainted. He therefore who will make difficulties in the foregoing case may see that he does not avoid them in the smaller apparent cases. Besides, the possibility exists that there are successively graduated intermediate states inserted, and thus there is a stable bridge by the means of which we can work backwards to the solution of the problem. As a matter of fact this notion of stability does not assist the main thought, but it is for us the fundamental form of regular progression, and of each transition known so far, so that we have a right to consider it as intermediate between the first original state and its disturbance. But if we consider the independent condition of equipoise from the point of view of mathematical concepts as, admittedly, without independent existence, there is no need of indicating the mode in which matter came into a dynamic condition." Outside of the mechanics of matter a change in movement of matter depends upon a change in the movement of the most insignificant particles. "Up to the present we have no universal principle of knowledge and we must therefore not be surprised if we are somewhat in the dark as to these matters."

That is all that Herr Duehring has to say, and we should seek the very pinnacle of wisdom not alone in a mutilation of the creative faculty, but in blind superstition, if we were to let the matter pass with these foolish evasions and statements. Absolute stability has no power of change in itself, Herr Duehring admits this. The absolute condition of equipoise possesses no means by which it can pass into a dynamic state. What have we then? Just three false and foolish phrases.