[Classics] Anti-Dühring

Philosophy of Nature

5. Time and Space

We now come to philosophy of nature. Here again Herr Dühring has every cause for dissatisfaction with his predecessors.

“Natural philosophy sank so low that it became an arid, spurious doggerel founded on ignorance”, and “fell to the prostituted philosophistics of a Schelling and his like, rigging themselves out in the priesthood of the Absolute and hoodwinking the public”. Fatigue has saved us from these “deformities”; but up to now it has only given place to “instability”; “and as far as the public at large is concerned, it is well known that the disappearance of a great charlatan is often only the opportunity for a lesser but commercially more experienced successor to put out again, under another signboard; the products of his predecessor”. Natural scientists themselves feel little “inclination to make excursions into the realm of world-encompassing ideas”, and consequently jump to “wild and hasty conclusions in the theoretical sphere” {D. Ph. 56-57}.

The need for deliverance is therefore urgent, and by a stroke of good luck Herr Dühring is at hand.

In order properly to appreciate the revelations which now follow on the development of the world in time and its limitations in space, we must turn back again to certain passages in "world schematism" {15}.

Infinity — which Hegel calls bad infinity — is attributed to being also in accordance with Hegel (Encyclopaedia§ 93), and then this infinity is investigated.

“The clearest form of an infinity which can be conceived without contradiction is the unlimited accumulation of numbers in a numerical series {18} ... As we can add yet another unit to any number, without ever exhausting the possibility of further numbers, so also to every state of being a further state succeeds, and infinity consists in the unlimited begetting of these states. This exactly conceived infinity has consequently only one single basic form with one single direction. For although it is immaterial to our thought whether or not it conceives an opposite direction in the accumulation of states, this retrogressing infinity is nevertheless only a rashly constructed thought-image. Indeed, since this infinity would have to be traversed in reality in the reverse direction, it would in each of its states have an infinite succession of numbers behind itself. But this would involve the impermissible contradiction of a counted infinite numerical series, and so it is contrary to reason to postulate any second direction in infinity” {19}.

The first conclusion drawn from this conception of infinity is that the chain of causes and effects in the world must at some time have had a beginning:

“an infinite number of causes which assumedly already have lined up next to one another is inconceivable, just because it presupposes that the uncountable has been counted” {37}.

And thus a final cause is proved.

The second conclusion is

“the law of definite number: the accumulation of identities of any actual species of independent things is only conceivable as forming a definite number“. Not only must the number of celestial bodies existing at any point of time be in itself definite, but so must also the total number of all, even the tiniest independent particles of matter existing in the world. This latter requisite is the real reason why no composition can be conceived without atoms. All actual division has always a definite limit, and must have it if the contradiction of the counted uncountable is to be avoided. For the same reason, not only must the number of the earth's revolutions round the sun up to the present time be a definite number, even though it cannot be stated, but all periodical processes of nature must have had some beginning, and all differentiation, all the multifariousness of nature which appears in succession must have its roots in one self-equal state. This state may, without involving a contradiction, have existed from eternity; but even this idea would be excluded if time in itself were composed of real parts and were not, on the contrary, merely arbitrarily divided up by our minds owing to the variety of conceivable possibilities. The case is quite different with the real, and in itself distinguished content of time; this real filling of time with distinguishable facts and the forms of being of this sphere belong, precisely because of their distinguishability, to the realm of the countable {64-65}. If we imagine a state in which no change occurs and which in its self-equality provides no differences of succession whatever, the more specialised idea of time transforms itself into the more general idea of being. What the accumulation of empty duration would mean is quite unimaginable {70}.

Thus far Herr Dühring, and he is not a little edified by the significance of these revelations. At first he hopes that they will “at least not be regarded as paltry truths” {64}; but later we find:

“Recall to your mind the extremely simple methods by which we helped forward the concepts of infinity and their critique to a hitherto unknown import... the elements of the universal conception of space and time, which have been given such simple form by the sharpening and deepening now effected” {427-28}.

We helped forward! The deepening and sharpening now effected! Who are "we", and when is this "now"? Who is deepening and sharpening?

"Thesis: The world has a beginning in time, and with regard to space is also limited. — Proof: For if it is assumed that the world has no beginning in time, then an eternity must have elapsed up to every given point of time, and consequently an infinite series of successive states of things must have passed away in the world. The infinity of a series, however, consists precisely in this, that it can never be completed by means of a successive synthesis. Hence an infinite elapsed series of worlds is impossible, and consequently a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved. — With regard to the second, if the opposite is again assumed, then the world must be an infinite given total of co-existent things. Now we cannot conceive the dimensions of a quantum, which is not given within certain limits of an intuition, in any other way than by means of the synthesis of its parts, and can conceive the total of such a quantum only by means of a completed synthesis, or by the repeated addition of a unit to itself. Accordingly, to conceive the world, which fills all spaces, as a whole, the successive synthesis of the parts of an infinite world would have to be looked upon as completed; that is, an infinite time would have to be regarded as elapsed in the enumeration of all co-existing things. This is impossible. For this reason an infinite aggregate of actual things cannot be regarded as a given whole nor, therefore, as given at the same time. Hence it follows that the world is not infinite, as regards extension in space, but enclosed in limits. And this was the second thing" (to be proved).

These sentences are copied word for word from a well-known book which first appeared in 1781 and is called: Kritik der reinen Vernunft by Immanuel Kant, where all and sundry can read them, in the first part, Second Division, Book II, Chapter II, Section II: The First Antinomy of Pure Reason. So that Herr Dühring's fame rests solely on his having tacked on the name — Law of Definite Number — to an idea expressed by Kant, and on having made the discovery that there was once a time when as yet there was no time, though there was a world. As regards all the rest, that is, anything in Herr Dühring's exegesis which has some meaning, “We” — is Immanuel Kant, and the “now” is only ninety-five years ago. Certainly “extremely simple”! Remarkable “hitherto unknown import”!

Kant, however, does not at all claim that the above propositions are established by his proof. On the contrary; on the opposite page he states and proves the reverse: that the world has no beginning in time and no end in space; and it is precisely in this that he finds the antinomy, the insoluble contradiction, that the one is just as demonstrable as the other. People of smaller calibre might perhaps fuel a little doubt here on account of “a Kant” having found an insoluble difficulty. But not so our valiant fabricator of “from the ground up original conclusions and views” {D. Ph. 525}; he indefatigably copies down as much of Kant’s antinomy as suits his purpose, and throws the rest aside.

The problem itself has a very simple solution. Eternity in time, infinity in space, signify from the start, and in the simple meaning of the words, that there is no end in any direction neither forwards nor backwards, upwards or downwards, to the right or to the left. This infinity is something quite different from that of an infinite series, for the latter always starts from one, with a first term. The inapplicability of this idea of series to our object becomes clear directly we apply it to space. The infinite series, transferred to the sphere of space, is a line drawn from a definite point in a definite direction to infinity. Is the infinity of space expressed in this even in the remotest way? On the contrary, the idea of spatial dimensions involves six lines drawn from this one point in three opposite directions, and consequently we would have six of these dimensions. Kant saw this so clearly that he transferred his numerical series only indirectly, in a roundabout way, to the space relations of the world. Herr Dühring, on the other hand, compels us to accept six dimensions in space, and immediately afterwards can find no words to express his indignation at the mathematical mysticism of Gauss, who would not rest content with the usual three dimensions of space[37] {See D. Ph. 67-68}.

As applied to time, the line or series of units infinite in both directions has a certain figurative meaning. But if we think of time as a series counted from one forward, or as a line starting from a definite point, we imply in advance that time has a beginning: we put forward as a premise precisely what we are to prove. We give the infinity of time a one-sided, halved character; but a one-sided, halved infinity is also a contradiction in itself, the exact opposite of an “infinity conceived without contradiction”. We can only get past this contradiction if we assume that the one from which we begin to count the series, the point from which we proceed to measure the line is any one in the series, that it is any one of the points in the line, and that it is a matter of indifference to the line or to the series where we place this one or this point.

But what of the contradiction of “the counted infinite numerical series”? We shall be in a position to examine this more closely as soon as Herr Dühring has performed for us the clever trick of counting it. When he has completed the task of counting from (minus infinity) to 0 let him come again. It is certainly obvious that, at whatever point he begins to count, he will leave behind him an infinite series and, with it, the task which he is to fulfil. Let him just reverse his own infinite series 1 + 2 + 3 + 4 ... and try to count from the infinite end back to 1; it would obviously only be attempted by a man who has not the faintest understanding of what the problem is. And again: if Herr Dühring states that the infinite series of elapsed time has been counted, he is thereby stating that time has a beginning; for otherwise he would not have been able to start “counting” at all. Once again, therefore, he puts into the argument, as a premise, the thing that he has to prove.

The idea of an infinite series which has been counted, in other words, the world-encompassing Dühringian law of definite number, is therefore a contradictio in adjecto[“contradiction in definition” — ed.] contains within itself a contradiction, and in fact an absurd contradiction.

It is clear that an infinity which has an end but no beginning is neither more nor less infinite than that which has a beginning but no end. The slightest dialectical insight should have told Herr Dühring that beginning and end necessarily belong together, like the north pole and the south pole, and that if the end is left out, the beginning just becomes the end — the one end which the series has; and vice versa. The whole deception would be impossible but for the mathematical usage of working with infinite series. Because in mathematics it is necessary to start from definite, finite terms in order to reach the indefinite, the infinite, all mathematical series, positive or negative, must start from 1, or they cannot be used for calculation. The abstract requirement of a mathematician is, however, far from being a compulsory law for the world of reality.

For that matter, Herr Dühring will never succeed in conceiving real infinity without contradiction. Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case. The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. Hegel saw this quite correctly, and for that reason treated with well-merited contempt the gentlemen who subtilised over this contradiction.

Let us pass on. So time had a beginning. What was there before this beginning? The universe, which was then in a self-equal, unchanging state. And as in this state no changes succeed one another, the more specialised idea of time transforms itself into the more general idea of being. In the first place, we are here not in the least concerned with what ideas change in Herr Dühring's head. The subject at issue is not the idea of time, but real time, which Herr Dühring cannot rid himself of so cheaply. In the second place, however much the idea of time may convert itself into the more general idea of being, this does not take us one step further. For the basic forms of all being are space and time, and being out of time is just as gross an absurdity as being out of space. The Hegelian “being past away non-temporally” and the neo-Schellingian “unpremeditatable being” are rational ideas compared with this being out of time. And for this reason Herr Dühring sets to work very cautiously; actually it is of course time, but of such a kind as cannot really be called time, time, indeed, in itself does not consist of real parts, and is only divided up at will by our mind — only an actual filling of time with distinguishable facts is susceptible of being counted — what the accumulation of empty duration means is quite unimaginable. What this accumulation is supposed to mean is here beside the point; the question is, whether the world, in the state here assumed, has duration, passes through a duration in time. We have long known that we can get nothing by measuring such a duration without content just as we can get nothing by measuring without aim or purpose in empty space; and Hegel, just because of the weariness of such an effort, calls such an infinity bad. According to Herr Dühring time exists only through change; change in and through time does not exist. Just because time is different from change, is independent of it, it is possible to measure it by change, for measuring always requires something different from the thing to be measured. And time in which no recognisable changes occur is very far removed from not being time; it is rather pure time, unaffected by any foreign admixtures, that is, real time, time as such. In fact, if we want to grasp the idea of time in all its purity, divorced from all alien and extraneous admixtures, we are compelled to put aside, as not being relevant here, all the various events which occur simultaneously or one after another in time, and in this way to form the idea of a time in which nothing happens. In doing this, therefore, we have not let the concept of time be submerged in the general idea of being, but have thereby for the first time arrived at the pure concept of time.

But all these contradictions and impossibilities are only mere child”s play compared with the confusion into which Herr Dühring falls with his self-equal initial state of the world. If the world had ever been in a state in which no change whatever was taking place, how could it pass from this state to alteration? The absolutely unchanging, especially when it has been in this state from eternity, cannot possibly get out of such a state by itself and pass over into a state of motion and change. An initial impulse must therefore have come from outside, from outside the universe, an impulse which set it in motion. But as everyone knows, the “initial impulse” is only another expression for God. God and the beyond, which in his world schematism Herr Dühring pretended to have so beautifully dismantled, are both introduced again by him here, sharpened and deepened, into natural philosophy.

Further, Herr Dühring says:

“Where magnitude is attributed to a constant element of being, it will remain unchanged in its determinateness. This holds good ... of matter and mechanical force” {D. Ph. 26}.

The first sentence, it may be noted in passing, is a precious example of Herr Dühring's axiomatic-tautological grandiloquence: where magnitude does not change, it remains the same. Therefore the amount of mechanical force which exists in the world remains the same for all eternity. We will overlook the fact that, in so far as this is correct, Descartes already knew and said it in philosophy nearly three hundred years ago; that in natural science the theory of the conservation of energy has held sway for the last twenty years; and that Herr Dühring, in limiting it to mechanical force, does not in any way improve on it. But where was the mechanical force at the time of the unchanging state? Herr Dühring obstinately refuses to give us any answer to this question.

Where, Herr Dühring, was the eternally self-equal mechanical force at that time, and what did it put in motion? The reply:

“The original state of the universe, or to put it more plainly, of an unchanging existence of matter which comprised no accumulation of changes in time, is a question which can be spurned only by a mind that sees the acme of wisdom in the self-mutilation of its own generative power.” {78-79}.

Therefore: either you accept without examination my unchanging original state, or I, Eugen Dühring, the possessor of creative power, will certify you as intellectual eunuchs. That may, of course, deter a good many people. But we, who have already seen some examples of Herr Dühring's generative power, can permit ourselves to leave this genteel abuse unanswered for the moment, and ask once again: But Herr Dühring, if you please, what about that mechanical force?

Herr Dühring at once grows embarrassed.

In actual fact, he stammers, “the absolute identity of that initial extreme state does not in itself provide any principle of transition. But we must remember that at bottom the position is similar with every new link, however small, in the chain of existence with which we are familiar. So that whoever wants to raise difficulties in the fundamental case now under consideration must take care that he does not allow himself to pass them by on less obvious occasions. Moreover, there exists the possibility of interposing successively graduated intermediate stages, and also a bridge of continuity by which it is possible to move backwards and reach the extinction of the process of change. It is true that from a purely conceptual standpoint this continuity does not help us pass the main difficulty, but to us it is the basic form of all regularity and of every known form of transition in general, so that we are entitled to use it also as a medium between that first equilibrium and the disturbance of it. But if we had conceived the so to speak” (!) “motionless equilibrium on the model of the ideas which are accepted without any particular objection” (!) “in our present-day mechanics, there would be no way of explaining how matter could have reached the process of change.” Apart from the mechanics of masses there is, however, we are told, also a transformation of mass movement into the movement of extremely small particles, but as to how this takes place — “for this up to the present we have no general principle at our disposal and consequently we should not be surprised if these processes take place somewhat in the dark” {79-80, 81}.

That is all Herr Dühring has to say. And in fact, we would have to see the acme of wisdom not only in the “self-mutilation of our generative power” {79}, but also in blind, implicit faith, if we allowed ourselves to be put off with these really pitiable rank subterfuges and circumlocutions. Herr Dühring admits that absolute identity cannot of itself effect the transition to change. Nor is there any means whereby absolute equilibrium can of itself pass into motion. What is there, then? Three lame, false arguments.

Firstly: it is just as difficult to show the transition from each link, however small, in the chain of existence with which we are familiar, to the next one. — Herr Dühring seems to think his readers are infants. The establishment of individual transitions and connections between the tiniest links in the chain of existence is precisely the content of natural science, and when there is a hitch at some point in its work no one, not even Herr Dühring, thinks of explaining prior motion as having arisen out of nothing, but always only as a transfer, transformation or transmission of some previous motion. But here the issue is admittedly one of accepting motion as having arisen out of immobility, that is, out of nothing.

In the second place, we have the “bridge of continuity”. From a purely conceptual standpoint, this, to be sure, does not help us over the difficulty, but all the same we are entitled to use it as a medium between immobility and motion. Unfortunately the continuity of immobility consists in not moving; how therefore it is to produce motion remains more mysterious than ever. And however infinitely small the parts into which Herr Dühring minces his transition from complete non-motion to universal motion, and however long the duration he assigns to it, we have not got a ten-thousandth part of a millimetre further. Without an act of creation we can never get from nothing to something, even if the something were as small as a mathematical differential. The bridge of continuity is therefore not even an asses’ bridge[37a]; it is passable only for Herr Dühring.

Thirdly: so long as present-day mechanics holds good — and this science, according to Herr Dühring, is one of the most essential levers for the formation of thought — it cannot be explained at all how it is possible to pass from immobility to motion. But the mechanical theory of heat shows us that the movement of masses under certain conditions changes into molecular movement (although here too one motion originates from another motion, but never from immobility); and this, Herr Dühring shyly suggests, may possibly furnish a bridge between the strictly static (in equilibrium) and dynamic (in motion). But these processes take place “somewhat in the dark”. And it is in the dark that Herr Dühring leaves us sitting.

This is the point we have reached with all his deepening and sharpening — that we have perpetually gone deeper into ever sharper nonsense, and finally land up where of necessity we had to land up — “in the dark”. But this does not abash Herr Dühring much. Right on the next page he has the effrontery to declare that he has

“been able to provide a real content for the idea of self-equal stability directly from the behaviour of matter and the mechanical forces” {D. Ph. 82}.

And this man describes other people as “charlatans”!

Fortunately, in spite of all this helpless wandering and confusion “in the dark”, we are left with one consolation, and this is certainly edifying to the soul:

“The mathematics of the inhabitants of other celestial bodies can rest on no other axioms than our own!” {69}.


[37] A reference to the research carried out by the German mathematician Karl Friedrich Gauss into non-Euclidean geometry.

[37a] In the original a play on words: Eslesbrücke (asses' bridge) means in German also an unauthorised aid in study used by dull-headed or lazy students; a crib or pony.

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