Philosophy is, according to Herr Duehring, the development of the highest forms of consciousness of the world and life, and embraces, in a wider sense, the principles of all knowledge and volition. Wherever a series of perceptions, or motives or a group of forms of life becomes a matter of consideration in the human mind the principles which underly these forms, of necessity, become an object of philosophy. These principles are single, or, up to the present, have been considered as single ingredients out of which are composed the complexities of knowledge and volition. Like the chemical composition of material bodies, the entire universe may be also resolved into fundamental forms and elements. These elementary constituents and principles serve, when once discovered, not only for the known tangible world but for that also, which is unknown and inaccessible. Philosophical principles therefore constitute the last complement required by the sciences in order that they may become a uniform system by means of which nature and human life are explained. In addition to the examination of the fundamental forms of all existence, philosophy has only two particular objects of investigation, Nature and Humanity. Hence our material may be classified into three main groups,—a general scheme of the universe, the teaching of the principles of nature and finally the principles which regulate Humanity. Thisarrangement at the same time comprises an inner logical order, for the formal principles which are true for all existence take precedence, and the concrete realms in which these principles display themselves follow in the gradation of their successive arrangements. So far, this is Herr Duehring's conception of things given almost in his very words.
He is therefore engaged with principles, formal conceptions, which are subjective and not derived from the knowledge of external phenomena, but which are applied to Nature and Humanity, as the principles according to which Nature and Humanity must regulate themselves. But how are these subjective principles derived? From thought itself? No, for Herr Duehring himself says: the purely ideal realm is limited to logical arrangements and mathematical conceptions (which latter as we shall later see is false). Logical arrangements can only be referred to forms of thought, but we are engaged here only with forms of existence, the external world, and these forms can never be created by thought nor derived from it but only from the external world. Hereupon the entire matter undergoes a change. We see that principles are not the starting point of investigation but the conclusion of it, they are not to be applied to nature and history but are derived from them. Nature and Humanity are not steered by principles, but principles are, on the other hand, only correct so far as they correspond with nature and history. That is just the materialistic conception of the matter, and the opposite, that of Herr Duehring is the idealistic conception, it turns things upside down and constructs a real world out of the world of thought, arrangements, plans and categories existing from everlasting before the world, just like Hegelianism.
As a matter of fact, we prefer Hegel's "Encyclopedia," with all its fever phantoms, to the "final truths of the last instance" of Herr Duehring. In the first place, according to Herr Duehring we have the general scheme of the universe which by Hegel is called "logic." Then according to both of them we have the application of this scheme to nature by means of the logical categories, the philosophy of nature, and finally their application to Humanity, by what Hegel calls "the Philosophy of the Spirit." "The inner logical arrangement" of Duehring's scheme brings us therefore logically back to Hegel's "Encyclopedia" from which it is taken with a fidelity which would move that Wandering Jew of the Hegelian school, Professor Michelet of Berlin, to tears.
Such a result follows if one takes it for granted that "consciousness," "thought," is something which has existed from the beginning in contradistinction to nature. It would then be of the greatest importance to bring consciousness and Nature, thought and existence, into harmony, to harmonise the laws of thought and the laws of Nature. But one enquires further what are thought and consciousness and whence do they originate. It is consequently discovered that they are products of the brain of man, and that Humanity is itself a product of nature which has developed in and along with its environment; wherefore it becomes self-apparent that the products of the brain of man being themselves, in the last instance, natural products, do not contradict all the rest of Nature but correspond with it.
But Herr Duehring cannot allow so simple a treatment of the subject. He thinks not only in the name of Humanity which would be quite a large affair, but in the name of the conscious and thinking beings of the whole universe. Indeed, it would be "a degradation of thefoundation concepts of knowledge and consciousness if one should wish to exclude or even to throw suspicion upon their sovereign value and undoubted claims to truth by means of the epithet 'human.'" In order that there may be no suspicion that upon some heavenly body or other twice two may make five, Herr Duehring does not venture to call thought a human attribute, and therefore he is obliged to separate it from the only true foundation on which it rests, as far as we are concerned, namely, from man and nature, and thereby falls, without any possibility of getting out, into an "ideology" which causes him to play baby to Hegel. It is self-evident that one cannot build materialistic doctrines on foundations so ideological. We shall see later that Herr Duehring is compelled to push nature to the front as a conscious agent and, therefore, as that, which people in plain English call God.
Indeed, our philosopher had other motives in shifting the foundation of reality from the material world to that of thought. The knowledge of this general scheme of the universe, of these formal principles of being is just the foundation of Herr Duehring's philosophy. If we derive the scheme of the universe not from our own brain, but merely by means of our own brain, from the material world, we need no philosophy, but simply knowledge of the world and what occurs in it, and the results of this knowledge likewise do not constitute a philosophy, but positive science. In such a case, however, Herr Duehring's entire book would have been love's labor lost.
Further, if no philosophy, as such, is longer required there is no longer the necessity of any philosophy of nature even. The view that all the phenomena of nature stand in systematic mutual relations compels science toprove this systematic interconnection in all respects, in single cases as well as in the entirety. But an appropriate creative, scientific representation of this mutual connection in such a way as to show the composition of an exact thought-picture of the system of the universe in which we live remains not only for us but for all time an impossibility. Should such a final conclusive system of the interconnection of the various activities of the universe, physical, as well as intellectual and historical, ever be brought to completion at any point of time in the history of the human race, human knowledge would forthwith come to an end and future historical progress would be cut off from the very moment in which society was directed in accordance with the system, which would be an absurdity, mere nonsense.
Man is therefore confronted by a contradiction, on the one hand he is obliged to study the interconnections of the world-system exhaustively, and, on the other hand, he is unable to fully accomplish the task either as regards himself or as regards the system of nature. This contradiction, however, does not consist solely in the nature of the two factors World and Man; it is the main lever also of universal intellectual progress and is solved every day and for ever in an endless progressive development of humanity, just as mathematical problems find their solution in an endless progression of a recurring decimal. As a matter of fact also every concept of the universe is subject to objective limitations owing to the conditions of historical knowledge, and subjectively in addition owing to the physical and mental make up of the author of the concept. But Herr Duehring exhibits a mode of thought which is confined in its application to a limited and subjective idea of the universe. We saw earlier that he was omnipresent, in allpossible forms of the universe, now we see that he is omniscient. He has solved the final problems of science and has nailed up tight all future knowledge.
Herr Duehring considers that he can, as with the fundamental forms of existence, produce aprioristically by means of his own cogitations the whole of pure mathematics without making any use of the experience which is afforded us in the objective world. In pure mathematics the understanding is engaged "in its own free creations and imaginations"; the concepts of number and form are "self-sufficient objects proceeding from themselves" and so have "a value independent of individual experience and actual objective reality."
That pure mathematics has a significance independent of particular individual experience is quite true as are also the established facts of all the sciences and indeed of all facts. The magnetic poles, the formation of water from oxygen and hydrogen, the fact that Hegel is dead and that Herr Duehring is alive, are facts independent of my experience or that of any other single individual, and will be independent of that of Herr Duehring himself, as soon as he shall sleep the sleep of the just. But in pure mathematics the mind is not by any means engaged with its own creations and imaginings. The concepts of number and form have only come to us by the way of the real world. The ten fingers on which men count and thereby performed the first arithmetical calculations are anything but a free creation of the mind. To count not only requires objects capable of being counted but the ability, when these objects are regarded, of subtracting all qualities from them except number and this ability is the product of long historical development of actual experience. The concept form is, like that of number, derived exclusivelyfrom the external world and is not a purely mental product. To it things possessed of shape were necessary and these shapes men compared until the concept form was arrived at. Pure mathematics considers the shapes and quantities of things in the actual world, very real objects. The fact that these objects appear in a very abstract form only superficially conceals their origin in the world of external nature. In order to understand these forms and qualities in their purity it is necessary to separate them from their content and thus one gets the point, without dimensions, the line, without breadth and thickness, a and b, x and y, constants and variables, and we finally first arrive at independent creations of the imagination and intellect, imaginary magnitudes. Also the apparent derivation of mathematical magnitudes from each other does not prove their aprioristic origin, but only their rational interconnection. Before one attained the concept that the form of a cylinder was derived from the revolution of a rectangle round one of its sides, he must have examined a number of rectangles and cylinders even if of imperfect form. Like all sciences, mathematics has sprung from the necessities of men, from the measurement of land and the content of vessels, from the calculation of time and mechanics. But, as in every department of thought, at a certain stage of development, laws are abstracted from the actual phenomena, are separated from them and set over against them, as something independent of them, as laws, which apparently come from the outside, in accordance with which the material world must necessarily conduct itself. So, it has happened in society and the state, so, and not otherwise, pure mathematics though borrowed from the world is applied to the world, andthough it only shows a portion of its component factors is all the better applicable on that account.
But as Herr Duehring imagines that the whole of pure mathematics can be derived from the mathematical axioms, "which according to purely logical concepts are neither capable of proof nor in need of any, and without empirical ingredients anywhere and that these can be applied to the universe, he likewise imagines, in the first place, the foundation forms of being, the single ingredients of all knowledge, the axioms of philosophy, to be produced by the intellect of man; he imagines also that he can derive the whole of philosophy or plan of the universe from these, and that his sublime genius can compel us to accept this, his conception of nature and humanity." Unfortunately nature and humanity are not constituted like the Prussians of the Manteuffel regime of 1850.
The axioms of mathematics are expressions of the most elementary ideas which mathematics must borrow from logic. They may be reduced to two.
(1) The whole is greater than its part; this statement is mere tautology, since the quantitatively limited concept, "part," necessarily refers to the concept, "whole,"—in that "part" signifies no more than that the quantitative "whole" is made up of quantitative "parts." Since the so-called axiom merely asserts this much we are not a step further. This can be shown to be a tautology if we say "The whole is that which consists of several parts—a part is that several of which make up a whole, therefore the part is less than the whole." Where the barrenness of the repetition shows the lack of content all the more strongly.
(2) If two magnitudes are equal to a third they are equal to one another; this statement is, as Hegel hasshown, a conclusion, upon the correctness of which all logic depends, and which is demonstrated therefore outside of pure mathematics. The remaining axioms with regard to equality and inequality are merely logical extensions of this conclusion. Such barren statements are not enticing either in mathematics or anywhere else. To proceed we must have realities, conditions and forms taken from real material things; representations of lines, planes, angles, polygons, spheres, etc., are all borrowed from reality, and it is just naive ideology to believe the mathematicians, who assert that the first line was made by causing a point to progress through space, the first plane by means of the movement of a line, and the first solid by revolving a plane, etc. Even speech rebels against this idea. A mathematical figure of three dimensions is called a solid—corpus solidum—and hence, according to the Latin, a body capable of being handled. It has a name derived, therefore, by no means from the independent play of imagination but from solid reality.
But to what purpose is all this prolixity? After Herr Duehring has enthusiastically proclaimed the independence of pure mathematics of the world of experience, their apriorism, their connection with free creation and imagination, he says "it will be readily seen that these mathematical elements (number, magnitude, time, space, geometric progression), are therefore ideal forms with relation to absolute magnitudes and therefore something quite empiric, no matter to what species they belong." But "mathematical general notions are, apart from experience, nevertheless capable of sufficient characterization," which latter proceeds, more or less, from each abstraction, but does not by any means prove that it is not deprived from the actual. In the scheme of theuniverse of our author pure mathematics originated in pure thought, in his philosophy of nature it is derived from the external world and then set apart from it. What are we then to believe?
"All-comprehending existence is sole. It is sufficient to itself and has nothing above or below it. To associate a second existence with it would be to make it just what it is not, a part of a constituent or all-embracing whole. When we conceive of our idea of soleness as a frame there is nothing which can enter into this, nothing which retains twofoldness can enter into this concept of unity. But nothing can alienate itself from this concept of unity. The essence of all thought consists in uniting the elements of consciousness in a unity. The indivisible concept of the universe has arisen by comprehending everything, and the universe, as the word signifies, is recognised as something in which everything is united into one unity."
So far Herr Duehring is quoted. The mathematical method, "Everything must be decided on simple axiomatic foundation principles, just as if it were concerned with the simple principles of mathematics," this method is for the first time here applied.
"The all-embracing existence is sole." If tautology, simple repetition in the predicate of what has been stated in the subject, if this constitutes an axiom, then we have a splendid specimen. In the subject Herr Duehring tells us that existence comprehends everything, in the predicate he explains intrepidly that there is nothing outside it. What a system-shaping thought. It is indeed system-shaping until we find six lines further down that Herr Duehring has transformed thesoleness of being by means of our idea of unity into its one-ness. As the work of all thought consists in the bringing together of all thought into a unity so is existence, as soon as it is conceived, thought of as a unity, an indivisible concept of the universe, and because existence so conceived is the sole universal concept, so is real existence, the real universe, just as much an indivisible unity, and consequently "the beings in the beyond have no further place as soon as the mind has learned to comprehend existence in the homogeneous universality."
That is a campaign with which in comparison Austerlitz and Jena, Koeniggratz and Sedan sink in insignificance. In a couple of expressions after we have set the first axiom moving we have abolished, put away, and destroyed all the inhabitants of the spirit-world, God, the heavenly hierarchies, heaven, hell and purgatory as well as the immortality of the soul.
How do we arrive at the idea of the unity of existence from that of its soleness? As a matter of fact, we generally conceive it. As we spread out our idea of unity as a frame around it the concept of existence becomes the concept of unity, for the existence of all thought consists in the bringing of elements of consciousness into unity.
This last statement is simply false. In the first place thought consists in the decomposition of objects of consciousness into their elements as well as in the uniting of mutually connected elements into a unity. There can be no synthesis without analysis. In the second place, thought can, without error, only bring those elements of consciousness into a unity in which or in the actual prototypes of which this unity already existed beforehand. If I comprehend a shoebrush under theclass mammal, it does not thereupon become a milk-giver. The unity of existence is therefore just the thing which had to be proved in order to justify his concept of thought as a unity, and if Herr Duehring assures us that he regards existence as a unity and not as twofold he tells us nothing more than that he himself personally thinks so.
To give a clear explanation of his method of reasoning, it is as follows, "I begin with existence. Therefore I think of existence. The idea of existence is an idea of unity. Thought and existence must therefore belong together, they answer one another, they mutually cover each other. Therefore existence is in reality a unity and there are no beings beyond." But if Herr Duehring had spoken thus plainly instead of entertaining us with oracular statements, the ideology of his argument would have been completely exposed. To attempt to undertake to prove from the identity of thought and existence the reality of the result of thought, that indeed were one of the fever-phantoms of a Hegel.
If his entire method of proof were really correct Herr Duehring would not have gained a single point over the spiritists. The spiritists would curtly reply, "The universe is simple from our standpoint also. The division into the hither and the beyond only exists from our special earthly original sin standpoint. In its essence, that is God, the entire universe is a unity." And they will take Herr Duehring with them to his beloved heavenly bodies, and will show him one or more where no original sin can be found, and where there is therefore no antagonism between the hither and the beyond, and the oneness of the universe is a demand of faith.
The most comical thing about the matter is that Herr Duehring in order to prove the non-existence of Godfrom his concept of existence, furnishes the ontological proof of God's existence. This runs as follows—If we think of God we think of Him as the concept of complete perfection. To the idea of perfection existence is a first essential, since a non-existent being is of necessity imperfect. We must therefore add existence to the perfections of God. Therefore God must exist. Thus Herr Duehring reasons exactly. If we think of existence we think of it as a concept. What is united into a concept is a unity, therefore existence would not correspond with its concept if it were not a unity. Therefore it must be a unity, therefore there is no God, etc.
If we speak of existence and merely of existence, the unity can only consist in this that all objects with which it is concerned are—exist. They are comprised under the unity of this common existence, and no other, and the general dictum that they all exist cannot give them any further qualities, common or not common, but excludes all such from consideration in advance. For as soon as we take a step beyond the simple fact that existence is common to all things, the distinctions between these separate things engage our attention, and if these differences consist in this that some are black, some white, some alive, others not alive, some hither and some beyond, we cannot conclude therefrom that mere existence can be imputed to all of them alike.
The unity of the universe does not consist in its existence, although its existence is a presumption of its unity, since it must first exist before it can be a unit. Existence beyond the boundary line of our horizon is an open question. The real unity of the universe consists in its materiality, and this is established, not by a pair of juggling phrases but by means of a long and difficult development of philosophy and natural science.
With respect to the subject in hand; the existence which Herr Duehring presents to us is "not that pure existence which is self sufficient and without any other qualities, in fact, only representing the antithesis of no-idea or absence-of-idea." Now we shall very soon see that the universe of Herr Duehring has its origin simultaneously with an existence which is without essential differentiation, progress or change, and is therefore merely in fact a contradiction of absence of thought, therefore really nothing. From this non-existence is developed the present differentiated, changeable universe which represents progressive growth; and when we grasp this idea, only by virtue of this eternal change do we arrive at "the concept of the self sufficing, universal existence." We have therefore now the concept of existence on a higher plane where it comprises within itself stability as well as change, being as well as development. Arrived at this point we find that "species and genera in fact the special and the general, are the simplest forms of differentiation, without which the constitution of things cannot be grasped."
But this is a means of distinguishing quality and after a discussion of this part of the subject we proceed "Over against the idea of species stands the idea of the whole, a homogeneity, as it were, in which no differentiation of species can longer be found," so we pass from quality to quantity and this is always "capable of measurement."
Let us compare this "clear analysis of the actual, universal scheme of things" and its "real, critical standpoint" with the fever-phantasies of a Hegel. We find that Hegel's "Logic" begins with existence as does that of Herr Duehring; that existence displays itself as nothing, as with Herr Duehring; that out of thisnot-being, a leap is made into being, and that existence is the result of this, that is a more complete and higher form of being, as with Herr Duehring. Being leads to quality, quality to quantity, just as with Herr Duehring. And in order that no essential shall be lacking Herr Duehring tells us elsewhere "from the realm of absence of sensation man leaps to that of sensation in spite of all the quantitative steps with but one qualitative leap ... from which we can show that he is entirely differentiated from the mere gradation of one and the same quality." This is just the Hegelian standard of measurement according to which mere quantitative expansion or contraction causes a sudden qualitative change at a given point, as for example with heated or cooled water, there are points where the spring into a new set of conditions is fulfilled under normal circumstances, and where therefore quantity suddenly changes into quality.
Our investigation has likewise sought to penetrate to the deepest roots, and discovers the rooted Duehring foundations to be the "fever-phantasies" of a Hegel, the categories of the Hegelian logic, in the first place, teachings in regard to existence after the antique Hegelian method, and an ineffective cloak of plagiarism.
And not content with purloining the whole scheme of existence from his despised predecessors, Herr Duehring after giving the above example of a change of quantity into quality has the coolness to say of Marx, "Is it not comical, this appeal (of Marx) to Hegelian confusion and mistiness, that quantity changes into quality." Confused mixture, who changes his ground, who is a comical fellow Herr Duehring?
All these pretty little statements are not only not "axiomatic utterances" according to label, but are simply taken from foreign sources, that is, from Hegel's"Logic." Of a truth there is not revealed in the whole chapter the shadow of any "inner connection," except so far as it is borrowed from Hegel, and the whole talk about stability and change finally runs out into mere garrulity on the subject of time and space.
From existence Hegel comes to substance, to the dialectic. Here he treats of reflex-movements, antagonisms and contradictions, positive and negative for example, and thence proceeds to causality, or the conditions of cause and effect and closes with necessity. Herr Duehring does not vary this method. What Hegel calls the "doctrines of existence" Herr Duehring has translated into "logical properties of existence." These exist, above all else in the antagonism of forces, in antithesis, Herr Duehring denies the antithesis in toto, but we shall return to this matter later. Then he proceeds to causality and thence to necessity. If Herr Duehring says of himself, "I do not philosophise from a cage," he must mean that he philosophises in a cage, the cage of the Hegelian arrangement of categories.
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. Allactual 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 theworld 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 thediscovery 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 atthe 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 aproceeding 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 fixedelement 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 whichwe 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.
In the first place, Herr Duehring says that to show the transition from each most insignificant step in the chain of things with which we are acquainted to the nextpresents the same difficulty. He seems to think that his readers are infants. The proof of the transitions and interrelations of the most insignificant links in the chain of existence is just what constitutes the subject matter of natural science. If there is an impediment anywhere, nobody, not even Herr Duehring, thinks to explain the development as proceeding from nothing, but on the other hand as only proceeding from transition, change, and forward movement from a completed evolutionary stage. Here, however, he undertakes to show with reference to matter that it proceeds from absence of movement and therefore from nothing.
In the second place, we have the "stable bridge." This does not help us appreciably over the difficulty, but we have a right to use it as a bridge between rigid stability and motion. Unfortunately stability consists in absence of motion, and the question as to the generation of motion remains as dark a secret as before. And if Herr Duehring shifts his no-movement at all to universal movement in infinitely small particles and ascribes to this ever so long a duration of time, we are still not the thousand part of an inch further from the place whence we started. Without a creative act we can get nothing from nothing, not even anything as small as a mathematical differential. The bridge of stability is therefore not even apons asinorum. Herr Duehring is the only person able to cross it.
Thirdly, as long as the present theories of mechanics prevail, this constitutes one of Herr Duehring's most reliable props, we cannot indicate how anything passes from a state of quiescence to one of motion. But the mechanical theory of heat teaches us that the movement of the mass depends upon the movements of the molecules, (so that even in this case movement proceeds fromother movement and not from lack of movement) and this Herr Duehring shyly points out might serve as a bridge between the entirely static (the state of equipoise) and the dynamic (self-movement). But here Herr Duehring leaves us entirely in the dark. All his deepening and sharpening has dug a pit of folly and we are brought up necessarily in "darkness." But Herr Duehring troubles himself very little about that. He says right on the next page, with considerable audacity that he has been able to endow the self contained stability with real significance by means of the properties of matter and the mechanical forces.
In spite of all these errors and confused statements we have still an inspiring faith remaining that "The mathematics of the inhabitants of other planets cannot rest on any axioms other than our own."