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 second conclusion is 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 D hring, 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  {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 D hring 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 D hring 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 D hringian 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 D hring 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 D hring 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 D hring's head. The subject at issue is not the idea of time, but real time, which Herr D hring 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 D hring 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 D hring 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 D hring 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 D hring pretended to have so beautifully dismantled, are both introduced again by him here, sharpened and deepened, into natural philosophy. Further, Herr D hring says: Where, Herr D hring, was the eternally self-equal mechanical force at that time, and what did it put in motion? The reply: Herr D hring at once grows embarrassed. 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 D hring 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 D hring, 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 D hring 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 D hring. Thirdly: so long as present-day mechanics holds good and this science, according to Herr D hring, 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 D hring 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 D hring 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 D hring much. Right on the next page he has the effrontery to declare that he has 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:
1877: Anti-Duhring - V. Time and Space