Concerning the Conception of the Science of Knowledge Generally
CONCERNING THE CONCEPTION OF THE SCIENCE OF KNOWLEDGE GENERALLY.
§ 1.—Hypothetical Conception of this Science.
To unite divided parties it is best to proceed from the point wherein they agree. Philosophy is a science; in this all descriptions of philosophy are as agreed as they are divided in determining the object of this science. This division, may it not have arisen, because the conception of that science, which they unanimously asserted philosophy to be, had not yet been wholly developed? And may not the determination of this one characteristic, wherein they all agree, suffice to determine the conception of philosophy itself? A science has systematic form. All propositions in it are connected in one single fundamental proposition or principle, and unite with it to form a whole. This is universally conceded. But does this characteristic exhaust the conception of a science?
Supposing somebody were to build up ever so systematic a natural history of certain spirits of the air, on the unproven and unprovable assumption, that such creatures exist in the air, with human passions, inclinations, and conceptions, should we call such a system a science, no matter how closely its several parts might be connected with each other into a whole? On the other hand, supposing somebody were to utter a single proposition—a mechanic, for instance, the proposition that a pillar erected on a horizontal base in a right angle stands perpendicular, and will not incline toward either side, however far you extend it into infinity—a proposition which he may have heard at some time and approved as true in experience: would not all men concede that such a person had a scientific knowledge of the proposition, although he should not be able to evolve the deduction of his proposition from the first fundamental principle of geometry? Now, why do we call the fixed system, which rests on an unproven and unprovable first principle, no science at all, and why do we assert the knowledge of the mechanic to be science, although it does not connect in his reason with a system?
Evidently, because the first, in spite of its correct form, does not contain any thing that can be known; and because the second, although without a correct form, asserts something which is really known and can be known. The characteristic of science, therefore, seems to consist in the quality of its content and the relation thereof to the consciousness of the person of whom a knowledge is asserted; and the systematic form appears to be only accidental to the science; is not the object of science, but merely a means to attain that object.
This may, perhaps, be conceived in the following manner. If we suppose that from some reason or another the human mind can know only very little, and can have of every thing else only opinions, presentiments, or arbitrary meanings; and if we suppose, moreover, that from some reason or another the human mind can not well rest content with this limited or uncertain knowledge: then the only means of extending and securing that knowledge would be to compare all uncertain knowledge with the certain knowledge, and to draw conclusions from the equality or inequality of both as to the correctness or incorrectness of the former. If an uncertain knowledge were thus discovered to be equal to a certain knowledge, it might be properly assumed to be also certain; but if it were discovered unequal, it would now be definitely known as false, and could no longer deceive. We should be delivered from an error, although we might not have gained positive truth.
I speak plainer. Science is to be one and a whole. The proposition that a pillar erected in a right angle on a horizontal base occupies a perpendicular position, is doubtless a whole, and in so far a science for a person who has no connected knowledge of geometry.
But we also consider the whole geometry, which contains much more than that one proposition, a science. How then, and by what means do a multitude of very different propositions unite into one science, into one and the same whole?
Clearly by this, that the separate propositions are not science, but form a science only in the whole, and through their connection in the whole. But by a composition of parts you can not put something into the whole which is not to be found in one of the parts. Hence, if none of the connected propositions had certainty, there would also be no certainty in the whole formed by them. One of the propositions, at least, therefore, must be certain, and this one, perhaps, communicates its certainty to the others in this manner: that if the one is to be true, then the second must be true, etc. Thus a multiplicity of propositions would attain only one certainty, and result in only one science, for the very reason that they all have certainty and the same certainty. That one proposition which we have just now spoken of as positively certain, can not obtain its certainty from its connection with the others, but must have it beforehand; for by uniting parts you can not produce something which is in none of the parts. But all other propositions receive their truth from the first one. The first one must therefore be certain before all connection with the others; and all the others must receive their certainty only through and after the connection. From this it immediately appears that our above assumption is the only correct one, and that in a science there can only be one proposition which is certain before the connection with others. For if there were many such propositions, they would either be not at all connected with the former, and then they would not belong with it to the same whole; or they would be thus connected; but since they are only to be connected by one and the same certainty—that is, if the one theorem is true, then the other must be true—they can not have independent certainty; for in that case one proposition might have independent certainty, although others had no certainty, and hence they would not be connected through common certainty.
Such a proposition, which has certainty before and independent of all connection, is a fundamental principle. Every science must have a fundamental principle; nay, it might consist of simply such one principle, which in that case could not be called fundamental, however, since it would not be the foundation of others. But a science also can not have more than one fundamental principle, for else it would result in many sciences.
The other propositions which a science may contain get certainty only through their connection with the fundamental principle; and the connection, as we have shown, is this: If the proposition A is true, then the proposition B is also true; and if B is true, then must C be true, etc. This connection is called the systematic form of the whole, which results from the several component parts. Wherefore this connection? Surely not to produce an artistic combination, but in order to give certainty to propositions, which have not certainty in themselves. And thus the systematic form is not the object of science, but an accidence, a means, and on the condition that the science is to have a manifold of propositions. It is not the essence of science, but an accidental quality thereof
Let science be a building, and let the chief object of this building be firmness. The foundation is firm, and as soon as it is laid down, the object would therefore be attained. But since you can not live on the foundation, nor protect yourself by its means against the arbitrary attacks of enemies, or the unarbitrary attacks of the weather, you proceed to erect walls, and over the walls you build a roof. All the parts of the building you connect with the foundation and with each other, and thus the whole gets firmness. But you do not build a building in order to connect the parts; rather you connect the parts in order to make the building firm; and it is firm in so far as all its parts rest upon a firm foundation.
The foundation is firm, for it is not built on another foundation, but rests on the solid earth. But whereupon shall we erect the foundation of our scientific structure? The fundamental principles of our systems must and shall be certain in advance of the system. Their certainty can not be proven within the system; but every possible proof in the system presupposes already their certainty. If they are certain, then of course all their results are certain; but from what does their own certainty follow?
And even after we shall have satisfactorily answered this question, does not a new and quite different one threaten us? We are going to draw our conclusions thus: If the fundamental principle is certain, then another proposition also is certain. How do we get at this then? What is the ground of the necessary connection between the two, whereby the one is to have the same certainty which belongs to the other? What are the conditions of this connection, and whence do we know that they are the conditions and the exclusive conditions and the only conditions of this connection? And how do we get at all to assume a necessary connection between different propositions, and exclusive but exhausted conditions of this connection?
In short, how shall the absolute certainty of the fundamental principle, and how shall the authority to draw from it conclusions as to the certainty of other propositions, be demonstrated? That which the fundamental principle is to have itself and to communicate to all other propositions which occur in the science, I call the inner content of the fundamental principle and of science generally; the manner in which it communicates this certainty to other propositions I call the form of science. The question is, therefore, How are form and content of a science possible? or how is science itself possible?
That which would give an answer to this question would be itself a science, and would be, moreover, the science of science generally.
It is impossible to determine in advance of the investigation whether such an answer is possible or not; that is, whether our whole knowledge has a cognizable, firm basis, or whether it rests, after all—however closely its separate parts may be connected—upon nothing, that is to say, upon nothing for us. But if our knowledge is to have a basis for us, then such an answer must be possible, and there must be a science which gives this answer. And if there is such a science, then our knowledge has a cognizable ground. Hence, in advance of the investigation, it is impossible to say whether our knowledge has a basis or has no basis at all; and the possibility of the science in question can only be demonstrated by its actual realization.
The naming of such a science, whereof the very possibility is as yet problematical, is altogether arbitrary. Still, if it should appear that all the territory hitherto considered useful for the cultivation of sciences has already been appropriated, and that only one piece of uncultivated land has been left vacant for the science of all other sciences; and if, moreover, it should appear that under a well-known name—the name of Philosophy—the idea of a science exists which pretends to be, or wishes to be, also a science, and is only in doubt where to settle down; then it might not be improper to assign this science to the empty and uncultivated place. Whether the word Philosophy has hitherto signified precisely that very same object is immaterial; and, moreover, if this science should really thus turn out to be a science, it would doubtless very justly discard a name which it has hitherto borne from a surely not over great modesty, namely, that of a Dilettanteism. The nation which shall discover this science is well worthy of giving it a name from its own language, and might name it simply Science, or the Science of Knowledge. What has been heretofore called philosophy would thus be the science of science generally.
§ 2.—Explanation of the Conception of the Science of Knowledge.
It is not allowable to draw conclusions from definitions. This rule signifies: from the fact that it is possible to think a certain characteristic in the description of a thing, which thing exists altogether independently of such a description, it is not allowable to conclude that this characteristic is therefore really discoverable in the thing; or, when we produce a thing after a conception formed of it, which conception expresses the purposes of the thing, it is not allowable to conclude from the thinkability of the purpose that it is actually realized. On no account, however, can the above rule signify that we must have no well-defined purpose in our bodily or mental labors, but must leave it to our fancy or to our fingers what the result of our labor shall be. The inventor of the aerostatic balls was perfectly warranted in calculating the relation of the gas in the balls to the weight of the atmosphere, and thus to discover the velocity of movement of his machine, although he did not know yet whether he would ever be able to discover a gas sufficiently lighter than air; and Archimedes was able to calculate the machine by which he could move the globe out of its place, although he knew well enough that he could find no place beyond the attraction of the earth from which to operate with his machine. Thus, also, with our science of knowledge. It is not as such something which exists independent of us, but rather something which must first be produced by the freedom of our mind, working in a certain direction, that is, if there is such a freedom, which, of course, can also not be known as yet. Let us determine this direction in advance, and obtain a clear conception of what is to be our work. Whether we can produce it or not will appear from the fact whether we do produce it, but this is not yet our purpose. We at present merely wish to see what it really is we intend to do.
1st. First of all, the described science is to be a science of science generally. Every possible science has one fundamental principle, which can not be proven in it, but must be certain in advance of it. But where, then, is this first principle to be proven? Evidently in that science which is to be the ground of all possible sciences. In this respect the science of knowledge would have a twofold object: Firstly, to show the possibility of fundamental principles generally; to show how, to what extent, and under what conditions, and perhaps in what degree something can be certain, and indeed to show what it really means to be certain; and, secondly, to prove particularly the fundamental principles of all possible sciences, which can not be proven in those sciences themselves.
Every science, which is to be a whole of component parts, has a systematic form. This form—the condition of the connection of the deduced propositions with the fundamental principle, and the ground which justifies us in drawing conclusions from this connection, that the deduced propositions have necessarily the same certainty which pertains to the fundamental principle—can also, like the truth of the fundamental principle, not be demonstrated in the particular science itself, but is presupposed as the possibility of its form. Hence, a general science of knowledge must, moreover, show up the ground for the systematic form of all possible sciences.
2d. The science of knowledge is itself a science. Hence it must also have one fundamental principle, which can not be proven in it, but must be presupposed for its very possibility as a science. But this fundamental principle can not be proven in another higher science, since otherwise this other higher science would be the science of knowledge. This fundamental principle of the science of knowledge, and hence of all sciences and of all knowledge, is, therefore, absolutely not to be proven; that is, it can not be deduced from a higher principle, the relation to which might demonstrate its certainty. Since, nevertheless, it is to be the basis of all certainty, it must be certain in itself, through itself, and for the sake of itself. All other propositions will be certain, because it can be shown that they are in some respect related to it, but this one must be certain merely because it is related to itself. All other propositions will only have a mediated certainty derived from it, but itself must have immediate certainty. Upon it all knowledge is grounded, without it no knowledge were indeed possible; but itself has its ground in no other knowledge, being, on the contrary, itself the ground of all knowledge. This fundamental principle is absolutely certain; that is, it is certain because it is certain. You can not inquire after its ground without contradiction. It is the ground of all certainty; that is, every thing which is certain is certain, because this fundamental principle is certain, and nothing is certain if it is not certain. It is the ground of all knowledge; that is, you know what it asserts, simply because you know any thing at all; you know it immediately when you know any thing at all. It accompanies all knowledge, is contained in all knowledge, and is presupposed by all knowledge. The science of knowledge, in so far as it is a science, and is to consist of more than its fundamental principle—which seems necessary, since it is to furnish the fundamental principles of all sciences—must have a systematic form. It is evident that it can not derive this form, either in regard to its determinateness or in regard to its validity, from any other science, since itself is to furnish all other sciences their systematic form. Hence, the science of knowledge must contain this form within itself, and must itself show up the ground of this form. Let us consider this a little, and it will directly appear what this assertion means. That whereof any thing is known we will, in the mean while, call the content, and that which is known thereof the form of a proposition. (In the proposition, gold is a body; that whereof is known is gold and the body; that which is known of them is, that they are in a certain respect equal, and might in so far replace each other. It is an affirmative proposition, and this relation is its form.)
No proposition is possible without content or without form. It must contain something whereof we know, and something which is known thereof. Hence, the first principle of the science of knowledge must have both content and form. Now, this first principle is to be immediately and of itself certain, and this can only signify: its content must determine its form, and its form its content. Its form can only fit its content, and its content can only fit its form; every other form connected with that content, or every other content connected with that form, would cancel that principle itself, and thus annihilate all knowledge. Hence, the form of the absolute first principle of the science of knowledge is not only contained in that principle itself, but is also presented as absolutely valid for the content of that principle. Again: if there should be, besides this absolute first principle, still other fundamental principles of the science of knowledge—which in that case can only be partly absolute, and must be partly derived from the first principle, since otherwise in the first case they would not be fundamental principles, and in the latter case not connected with the first and highest principle—then the absolute part of these other fundamental principles could only be either the content or the form; and, likewise, the conditioned or derived part of these principles could only be either the content or the form. If the content of these other fundamental principles be their absolute or unconditioned part, then the absolute first principle of the science of knowledge must condition the form of those contents; or if the form of those other principles be the unconditioned part, then their content must be conditioned by the first principle of the science of knowledge; and thus indirectly also their form, that is, in so far as the form is to be form of the content. In either case, therefore, the form would be determined by the first absolute principle of the science of knowledge. And since it is impossible that there should be a fundamental principle not determined either in form or in content by the first absolute principle, (that is, if we are to have a science of knowledge at all,) it follows that there can only be three fundamental principles: one absolutely in and through itself determined both in form and in content; a second one determined through itself in form; and a third one determined through itself in content. If there are still other propositions in the science of knowledge, they must be determined both in regard to form and content by the fundamental principle. Hence, a science of knowledge must determine the form of all its propositions, in so far as they are separately considered. But such a determination of the separate propositions is only thus possible: that they reciprocally determine each other. But each proposition must be perfectly determined, that is, its form must suit only its and no other content, and its content must only suit its and no other form; for else such a proposition would not be equal to the first principle, in so far as that first principle is certain, and hence would not be certain. If, nevertheless, all the propositions of a science of knowledge are to be different, which they must be if they are to be many propositions and not one proposition, then no proposition can obtain its complete determination otherwise than through a single one of all propositions. And thus the whole series of propositions becomes determined, and no proposition can occupy another place in the system than that which it occupies. Each proposition in the science of knowledge has its position determined by a determined other proposition, and on its part determines the position of a determined third proposition. Hence, the science of knowledge establishes itself the form of its whole for itself
This form of the science of knowledge is necessarily valid for its content. For if the absolute first principle was immediately certain, that is, if its form was fit only for its content, and its content only for its form, and if through this first principle all possible subsequent propositions are determined, immediately or mediately, in form or content; if all subsequent theorems, in other words, are, as it were, contained already in the first one, then it follows that what holds good for the first must also hold good in regard to the others; that is, that their form is only fit for their content, and their content only for their form. It is true, this relates only to the separate propositions; but the form of the whole is nothing but the form of the separate propositions, thought in one; and what is valid for each separate must be valid for all, thought as one.
But the science of knowledge is to give not only itself its own form, but is also to give all other possible sciences their form; and is to make certain the validity of this form for all other sciences. This can only be thought possible on condition that every thing which is to be a proposition of any other science must be already involved in some proposition of the science of knowledge, and hence must have obtained its proper form already in that science. This opens to us an easy way of getting back to the content of the absolute first principle of the science of knowledge, of which we can now say something more than was possible before. If we assume for the present that to be certain means simply to have an insight into the inseparability of a determined content from a determined form, (which is to be only a definition of a name, since a real definition of knowledge is simply impossible,) then we might understand already to some extent how the fact that the fundamental principle of all knowledge determines its form only through its content, and its content only through its form, could determine the form of all the content of knowledge; that is to say, if all possible content were contained in the content of that first principle. If, therefore, there is to be an absolute first principle of all knowledge, this assumption must be correct; that is, the content of this first principle must contain all other possible content, but must itself be contained in no other content. In short, it must be the absolute content.
It is easy to remember that, in presupposing the possibility of a science of knowledge, and particularly of its first principle, we always presuppose that there is really a system in human knowledge. If such a system, however, is to be in it, it can be shown—even apart from our description of the science of knowledge—that there must be such an absolute first principle. If there is not to be any such system, two cases only are possible. Either there is no immediate certainty at all, and then our knowledge forms many series or one infinite series, wherein each theorem is derived from a higher one, and this again from a higher one, etc., etc. We build our houses on the earth, the earth rests on an elephant, the elephant on a tortoise, the tortoise again—who knows on what?—and so on ad infinitum. True, if our knowledge is thus constituted, we can not alter it; but neither have we, then, any firm knowledge. We may have gone back to a certain link of our series, and have found every thing firm up to this link; but who can guarantee us that, if we go further back, we may not find it ungrounded, and shall thus have to abandon it? Our certainty is only assumed, and we can never be sure of it for a single following day.
Or the second case: Our knowledge consists of finite series, but of many finite series, each series ending in a fundamental principle, which has its ground in no other one, but only in itself; all these fundamental principles having no connection among each other, and being perfectly independent and isolated. In this case there are, perhaps, several inborn truths in us, all more or less inborn, and in the connection of which we can expect no further insight, since it lies beyond these inborn truths; or there is, perhaps, a manifold simple in the things outside of us, which is communicated to us by means of the impression produced upon us by the things, but into the connection whereof we can not penetrate, since there can not be any thing more simple than the simplest in the impression. If this second case is the truth, if human knowledge is in itself such a piecework—as the real knowledge of so many men unhappily is—if originally a number of threads lie in our minds, which are or can be connected with each other in no point, then again we may not be able to alter this state of things, and our knowledge is, as far as it extends, certain enough; but it is no unit, it is a manifold knowledge. Our building stands firm, but, instead of being a connected structure, it is an aggregate of chambers, from none of which we can enter the other; a building wherein we always get lost, and never feel ourselves at home. There is no light in it; and in spite of our riches we always remain poor, because we can never calculate them, never consider them as a whole, and hence never know what we really possess; we can never use part of it to improve the rest, because no part is relatable to the rest. Nay, more: our knowledge will never be completed; we must expect every day that a new inborn truth may manifest itself in us, or that experience may furnish us with a new simple. We must always be prepared to build a new house for ourselves. No general science of knowledge will be possible as containing the ground of other sciences. Each will be grounded in itself. There will be as many sciences as there are separate immediately certain propositions. But if neither the first case is to be correct, namely, that there are one or more mere fragments of a system, nor the second, that there are to be a manifold of systems, then a highest and absolute first fundamental principle must exist as the basis of a complete and unit-system in the human mind. From this first principle our knowledge may expand into ever so many series, each of which again may expand into series, etc., still all of them must rest firm upon one single link, which is not dependent upon another one, which holds itself and the whole system by virtue of its own power. In this link we shall possess a globe, holding itself firm by virtue of its own gravitation, the central point whereof attracts with almighty force whatsoever we have but erected upon its surface and perpendicularly, and not in the air or obliquely, and which allows no grain of dust to be torn away from its sphere of power.
Whether such a system and its condition, a first principle, exist, can not be decided in advance of the investigation. This fundamental principle can neither be proven as mere principle, nor as the basis of all knowledge. Every thing depends upon the attempt. If we shall find a proposition which has the internal conditions of the fundamental principle of all human knowledge, we shall try to discover whether it has also its external conditions, whether every thing we know or believe to know can be traced back to it. If we succeed in this, we shall have proven by the realization of the science of knowledge that it is possible, and that there is a system of human knowledge, whereof it is the representation. If we do not succeed in this, there either is no such system or we have merely failed in discovering it, and must leave the discovery to more fortunate successors. To maintain that there is no such system merely because we have failed to discover it would be an assumption, the refutation whereof is beneath the dignity of earnest investigation.
§ 3.—Development of the Conception of the Science of Knowledge.
To develop a conception scientifically is to assign to it its place in the system of human sciences generally, that is, to show what conception determines its position in the system, and of which conception it determines the position. But the conception of the science of knowledge generally, as well as of knowledge generally, can evidently have no position in the system of all sciences, since it is itself rather the place for all scientific conceptions, and assigns to all their positions in itself and through itself. It is clear, therefore, that we can speak here only of a hypothetical development; that is, the question is, If we assume that there are sciences, and that there is truth in them, (which can not be known in advance of the science of knowledge,) how is the science of knowledge related to these sciences?
This question also is answered by the mere conception of that science. The latter sciences are related to it as the grounded is to its ground; they do not assign to it its place, but it assigns to them their places in itself and through itself. All we can, therefore, propose to ourselves here is a further explanation of this answer.
1. The science of knowledge is to be a science of all sciences. Here arises the question: How can the science of knowledge guarantee that it has furnished the ground, not only of all as yet discovered and known, but also of all discoverable and knowable sciences, and that it has completely exhausted the whole field of human knowledge?
2. As the science of all sciences, the science of knowledge is to furnish to all sciences their fundamental principles. Hence, all propositions, which are fundamental principles of the particular sciences, are at the same time inherent propositions of the science of knowledge; and thus one and the same propositions may be regarded both as a proposition of the science of knowledge, and as the fundamental principle of a particular science. The science of knowledge evolves from the same proposition further deductions; and the particular science whereof it is the fundamental principle also evolves from it further deductions. Hence, either the deductions of both sciences are the same—and then there is no such a thing as a particular science—or both sciences have a distinct and peculiar mode of deduction; and this is impossible, because the science of knowledge is to furnish the form of all sciences; or something is added to a proposition of the science of knowledge, which something must, of course, be derived from the same science, whereby it becomes fundamental principle of a particular science. Here the question arises: What is this which is added? or, since this additional is to frame the distinction, what is the definite boundary between the general science of knowledge and every particular science?
3. Again, the science of knowledge is to determine the form of all sciences. How this can be done we have shown above. But another science, under the name of logic, pretends to have this same object. Sentence must be passed upon the claims of both sciences, that is, it must be decided how the science of knowledge is related to logic.
4. The science of knowledge is itself a science. What it is to accomplish as such we have shown above. But in so far as it is a mere science, a knowledge, in the formal significance of the word, it is a science of a something; it has an object, and it is clear from the above that this object can be no other than the system of human knowledge generally. The question arises: How is the science of knowledge, as science, related to its object as such?
§ 4.—In How Far Can the Science of Knowledge Be Sure of Having Exhausted Human Knowledge Generally?
The hitherto true or imaginary human knowledge is not human knowledge generally; and, though a philosopher had really exhausted the former, and shown by a perfect induction that it were contained in his system, he would yet by no means have satisfied the task imposed upon philosophy; for how could he prove by his induction from present experience that in the future some discovery might not be made which would not fit into his system?
Quite as unsatisfactory would be the excuse that he only intended to exhaust the knowledge possible in the present sphere of human existence; for if his philosophy is only valid for this sphere, he clearly confesses that he knows no possible other sphere, and hence, also, not the limits of that sphere which his philosophy claims to exhaust. Hence, he has arbitrarily drawn a limit, the validity whereof he can only prove by past experience, and which may, therefore, be contradicted by any possible future experience even within his own posited sphere. Human knowledge generally is to be exhausted, signifies: it is to be absolutely and unconditionally determined what man can know not only on the present stage, but on all possible and conceivable stages of his existence.
This is only possible if it can be shown, firstly, that the accepted fundamental principle is exhausted; and, secondly, that no other fundamental principle is possible than the accepted one. A fundamental principle is exhausted when a complete system has been erected upon it, that is, when that fundamental principle necessarily leads to all the propositions deduced from it, and when, again, all deduced propositions necessarily lead back to it. When no proposition occurs in the whole system which could be true if the fundamental principle were false, or false if the fundamental principle were true; then this is the negative proof that no superfluous proposition has been accepted in the system; for the superfluous one, which did not belong to the system, might be true though the fundamental principle were false, or false though the latter were true. When the fundamental principle is given, all propositions must be given. Each particular one is given in and through the fundamental principle. This connection of the separate propositions of the science of knowledge proves that the science has the required negative proof in and through itself. This negative proof shows that the science is systematic, that all its parts are connected in a single fundamental principle.
Again, the science is a system, or is completed, if no further proposition can be deduced; and this furnishes the positive proof that all the propositions of the system have been admitted. Still, of this there must be other evidence; for the mere relative and negative assertion, I do not see what other deductions might be made, is not sufficient. Some one else might arise hereafter, and see what I did not see. We need, therefore, a positive proof that no other propositions could possibly follow, and this proof can only arise if the same fundamental principle from which we started shall also show itself to be the final result; since, then, we could not proceed without describing the same circle we should have already drawn. When the time comes to represent this science, it will be shown, also, that it really describes this circle, leaving the student precisely at the point from which it started, and thus furnishing also the second positive proof in and through itself. But although the fundamental principle be exhausted and a complete system erected upon it, it does not follow that thereby human knowledge generally is exhausted, unless we presuppose what ought first to be proven, namely, that this fundamental principle is the fundamental principle of human knowledge generally. Of course, nothing can be added or taken away from the completed system which has been erected; but why might not the future, through augmented experience, cause propositions to arise in human consciousness which can not be grounded upon that fundamental principle, and which, therefore, presuppose one or more other fundamental principles? In short, why could not one or more other systems coexist in the human mind with the first one? To be sure, they would be neither connected with the first one nor with each other in any common point; but neither is this required, if they are to form many systems. Hence, if the impossibility of new discoveries is to be satisfactorily proven, it must be shown that only one system can be in human knowledge. Now, since the proposition that all human knowledge results only in one in itself connected knowledge—is itself to be a component of human knowledge—it can not be grounded upon any other principle than the one assumed as the fundamental principle of all human knowledge, and can only be proven by it. By this we have gained, at least for the present, so much that we see how such a future proposition as we supposed might possibly arise in consciousness would not only be another one, different from the fundamental principle of our system, but would also be contradictory of the latter in form. For, according to all we have said, the fundamental principle of our system must involve the proposition that there is a unit-system in human knowledge. Every proposition, therefore, which is not to belong to this system must not only be a different system, but must be a direct contradiction of it, in so far as the former system asserts itself to be the only possible one. It must be a contradiction of the deduced proposition of the unity of the system; and, since all its propositions are inseparably connected, of each single theorem, and particularly of the fundamental principle thereof Hence, it would have to rest on a fundamental principle directly opposed to the first fundamental principle. If, for instance, the first fundamental principle should turn out to be: I am I; this second one would have to be: I am not I.
Now, it would be wrong to conclude from this contradiction the impossibility of such a second fundamental principle. If the first fundamental principle involves the proposition that the system of human knowledge is a unit, it involves also, it is true, that nothing must contradict this system. But both these propositions are merely deductions from the first fundamental principle, and hence, by accepting the absolute validity of the deductions, we already assume that itself is the absolute first and only fundamental principle of human knowledge. Here, therefore, is a circle which the human mind can never get out of; and it is well to confess this circle plainly, lest its unexpected discovery at some time might confound men. This circle is as follows: If the proposition X is the first, highest, and absolute fundamental principle of human knowledge, then there is in human knowledge a unit-system, for the latter is the result of the proposition X. Now, since there is to be in human knowledge a unit-system, the proposition X, which really does establish such a system, is the fundamental principle of human knowledge, and the system based upon it is that unit-system of human knowledge.
It is unnecessary to be surprised at this circle. For to demand that it should be annihilated is to demand that human knowledge should be utterly groundless, that there should be no absolute certainty, and that all human knowledge should be only conditioned; in short, it is to assert that there is no immediate truth at all, but only mediated truth, and this without any thing whereby it is mediated. Whosoever feels thereunto inclined may investigate as much as he pleases what he would know if his Ego were not Ego; that is, if he did not exist, and if he could not distinguish a Non-Ego from his Ego.
§ 5.—What is the Limit which Separates the Science of Knowledge from the Particular Sciences?
We discovered above (§ 3) that one and the same proposition could not be in the same respect a proposition of the science of knowledge and of a particular science; and that to be the latter, it would be necessary to have something added to it. This character which is to be added can only be derived from the science of knowledge, since it contains all possible human knowledge; but can not, as is evident, be contained in that science in the same proposition which is to become fundamental principle of the particular science. Hence, it must be, perhaps, contained in another separate proposition of the science of knowledge, which is connected with the proposition which is to become the fundamental principle of a particular science. Since we have here to meet an objection which does not arise from the conception of the science of knowledge itself, but merely from the presupposition that there exist also other separate sciences, we can meet it also only by a presupposition, and shall have done enough for the present if we but show a possibility of the required limitation. That it will be the true limitation—although it may, nevertheless, turn out so—we neither care nor need to prove here.
Let it be, therefore, assumed that the science of knowledge contains those determined acts of the human mind which it—be it conditioned or unconditioned—enacts necessarily and under compulsion; but that it posits at the same time, as the highest explanatory ground of those necessary acts, a power to determine itself, (absolutely and without compulsion or necessity:) to act generally. Under this assumption the science of knowledge will result in a necessary and a not necessary or free acting. The acts of the human mind, in so far as it acts necessarily, will be determined by the science, but not in so far as it acts free.
Let it be further assumed that the free acts also are to be determined from some reason or another; then this determination can not occur in the science of knowledge. But since it is a determining, it must occur in sciences; hence in particular sciences. The object of these free acts can be no other than the necessary, furnished by the science of knowledge, since it furnishes every thing and since it furnishes only the necessary. Hence, in the fundamental principle of a particular science, an act which the science of knowledge left free would be determined. The science of knowledge would thus give to the act, that is, to the fundamental principle, firstly, its necessary character, and, secondly, freedom generally; but the particular science would give that freedom its determination; and thus the sharply drawn line of limitation would have been discovered. As soon as an in itself free act receives a determined direction, we leave the field of the science of knowledge generally, and enter the field of a particular science.
I shall illustrate this by two examples:
The science of knowledge furnishes, as necessary, space, and, as absolute limit, the point; but it leaves imagination perfectly free to posit the point wherever it chooses. As soon as this freedom is determined, for example, to move the point against the limit of the unlimited space, and thus to draw a line, we are no longer on the field of the science of knowledge, but on the field of a particular science, which is called geometry. The general problem, to limit space in accordance with a rule, or the construction in space, is fundamental principle of geometry, which science is thus clearly divided from the science of knowledge. Again: the science of knowledge furnishes as necessary a nature which, in its being and determinations, is to be considered as independent of us; and also furnishes as necessary the laws, according to which nature is to be and must be observed. But our power of judgment retains its full freedom to apply these laws or not, or to apply whatever law it chooses to any possible object; (for instance, to regard the human body as inorganic, or as organic, or as living matter.) But as soon as the power of judgment is required to observe a determined object by a determined law, (for instance, whether animal life can be explained from the mere inorganic; whether crystallization be the transition from chemical connections to organization; whether magnetic and electric powers are the same or not, etc.,) then it is no longer free, but obeys a rule; and hence we are no longer in the science of knowledge, but on the field of another science, which is called the science of nature. The general rule, to subsume every object of experience under a given law of nature in our mind, is fundamental principle of the science of nature. That science consists throughout of experiments, (not of a passive reception of the lawless influences of nature upon us,) which are arbitrarily undertaken, and with which nature may correspond or not; and by this characteristic the science of nature is abundantly separated from the science of knowledge.
Here, therefore, is already clearly seen why only the science of knowledge can have absolute totality, and why all particular sciences must be infinite. The science of knowledge contains only the necessary; if this is necessary in every respect, it is necessary also in respect to quantity, that is, it is necessarily limited. All other sciences are based upon freedom, freedom of our mind as well as of the absolutely independent nature. If this is to be truly freedom, subject to no law, it is impossible to prescribe for them a limited sphere, since this could only be done by a law. Hence, their spheres are infinite. Let no one, therefore, apprehend danger from an exhaustive science of knowledge for the infinite perfectibility of the human mind; on the contrary, instead of canceling that infinite perfectibility, the science of knowledge rather secures it against all doubt, and assigns to it a problem which can not be completed in all eternity,
§ 6.—How is the Science of Knowledge Related to Logic?
The science of knowledge is to determine the form for all possible sciences. According to current opinion, in which there may be something true, logic does the very same thing. How are these two sciences related to each other, particularly in respect to this problem, which each claims to solve?
By remembering that logic only pretends to determine the form of all possible sciences, whereas the science of knowledge is also to determine their content, an easy way is discovered to enter into this important investigation. In the science of knowledge the form is never separated from the content, nor the content from the form. In each of its propositions both form and content are inseparably united. If the propositions of logic are therefore to contain merely the form of possible sciences, they are not propositions of the science of knowledge; and hence the whole science of logic is not science of knowledge, nor even part of it. Curious as it may sound at the present state of philosophy, the science of logic is no philosophical science at all, but a peculiar, separate science; a fact, however, which is not to disparage the dignity of that science.
If the science of logic is such a separate science, it must be possible to show a determination of freedom by means of which the science of logic arises from the science of knowledge, and the limit of both may be ascertained. Such a determination of freedom is indeed clearly to be pointed out. In the science of knowledge, as we have said, form and content are necessarily united. Logic is to represent the pure form apart from the content; and this separation of form and content can only—since it is not an original separation—occur through freedom. Hence, it is by the free separation of form from the content that logic arises as a science. Such a separation is called abstraction; and hence logic consists essentially in abstraction from all content of the science of knowledge.
In this manner the propositions of logic would be merely form, which is impossible, for the conception of a proposition involves (see § 1) that it have both form and content. Hence, that which in the science of knowledge is mere form must be content in logic, and this content must again receive the general form of the science of knowledge, but which is now thought as the form of a logical proposition. This second act of freedom, whereby the form becomes its own content and returns into itself, is called reflection. No abstraction is possible without reflection, and no reflection without abstraction. Both acts, considered separately, are acts of freedom; and when, in this same separation, they are placed in relation to each other, one of them is necessarily the condition of the other. But in synthetical thinking both are only one and the same act, viewed from two sides.
From this results the determined relation of logic to the science of knowledge. The former is not the ground of the latter; but the latter is the ground of the former. The science of knowledge can not be proven from the science of logic, and no logical proposition, not even the proposition of contradiction, must be accepted in advance as valid by the science of knowledge; but, on the contrary, every logical proposition and the whole science of logic must be proven from the science of knowledge. It must be shown that all the forms contained in logic are really forms of a certain content in the science of knowledge. Thus, logic derives its validity from the science of knowledge, and not the science of knowledge its validity from logic.
Again, the science of knowledge is not conditioned and determined by logic, but logic is conditioned and determined by the science of knowledge. The science of knowledge does not derive its form from logic, but has that form in itself. On the contrary, the science of knowledge conditions the validity and applicability of logical propositions. The forms which logic establishes must, in the common way of thinking, and in all particular sciences, be applied to no other content than that which they are confined to in the science of knowledge; not necessarily to the whole of that content—for then we should have no particular sciences—but at least to what is part of that content. Without this condition the particular science to which such forms were applied would only be an air castle, however correct its logical deductions might be.
Finally, the science of knowledge is necessary; not necessary exactly in so far as it is a clearly conceived and systematically arranged science, but at least necessary as a natural gift; while logic is an artificial product of the human mind in its freedom. Without the former, no knowledge and no science would be possible; without the latter, all sciences would have been much later developed. The former is the exclusive condition of all science; the latter is a very beneficial invention to secure and facilitate the progress of sciences.
Let me exemplify this:
A = A is undoubtedly a correct logical proposition, and in so far as it is this it signifies: If A is posited, then A is posited. Two questions arise here: Is A really posited? and in how far and why is A posited if it is posited, or how are the if and the then connected?
Let us assume that A in this proposition signifies I, (Ego,) and that it has, therefore, its determined content, then the proposition would be this: I am I; or, if I am posited, then I am posited. But since the subject of this proposition is the absolute subject, in this single case the content is posited at the same time with the form; I am posited, because I have posited myself I am because I am. Hence, logic says: If A is, then A is; but the science of knowledge says: Because A (that is, this particular A = Ego) is, therefore A is. And thus the question: Is A (this particular A) really posited? is answered thus: It is posited, since it is posited. It is unconditionally and absolutely posited.
Let us assume that in the above proposition A does not signify I, (Ego,) but something else, then the condition can be clearly realized, under which it would be possible to answer: A is posited; and how we can be justified in drawing the conclusion: If A is posited, then it is posited. For the proposition A = A is valid originally only for the Ego; it has been abstracted from the proposition of the science of knowledge, I am I. Hence, all the content, to which it is to be applicable, must be contained in the Ego. No A can, therefore, be any thing else but an A posited in the Ego; and now the proposition reads: Whatsoever is posited in the Ego is posited; if A is posited in the Ego, then it is posited, (that is, in so far as it is posited as possible, actual, or necessary;) and thus the proposition is shown to be true, beyond contradiction, if the Ego is to be Ego. Again, if the Ego is posited because it is posited, then every thing which is posited in the Ego is posited because it is posited; and if A alone is posited in the Ego, then it is posited if it is posited; and thus our second question is also answered.
§ 7.—How is the Science of Knowledge, as Science, Related to its Object?
Let us first premise that this question has hitherto been utterly abstracted from, and that hence all the foregoing must be modified by the answering of this question.
Every proposition in the science of knowledge has form and content; something is known, and there is something whereof is known. But the science of knowledge is itself the science of something, and not this something itself. This would seem to prove that the science of knowledge, with all its propositions, is form of a content which existed in advance of it. How, then, is it related to this content, and what follows from this relation?
The object of the science of knowledge, we have seen, is the system of human knowledge. This exists independently of the science of it, and the science only shapes it into systematic form. What, then, may this new form be, how is it distinguished from the form which must exist in advance of the science, and how is the science generally distinguished from its object?
Whatever exists in the human mind, independently of science, we may also call the acts of that mind. These acts are the What which exists; they occur in a certain determined manner, and by this determined manner are they distinguished from each other. This is the How of the What. Hence, there is in the human mind originally, and in advance of our knowledge, form and content, and both are inseparably united; each act occurs in a determined manner, in accordance with a law, and this law determines the act. Nay, there may be, even for an outside observer, a system in these acts, if they are mutually connected with each other, and if they follow general, particular, and specific laws.
But it is not at all necessary that they should actually occur (that is, in time) in that systematic form which the outside observer frames in positing them as dependent on each other; it is not at all necessary, for instance, that the act which comprises all others, and which furnishes the highest universal law, should actually occur first in our mind, and be followed by the one next in importance; not necessary at all that they should all occur in a pure and unmixed state, or that many of them might not appear as one. Let us assume, for instance, that the highest act of the Intelligence be this: to posit itself. It is not at all necessary that this act should be in time the first act of our mind which arises to clear consciousness; nor is it even necessary that it should ever occur in consciousness in its purity; that is, that the Intelligence should ever be able to think simply I am, without, at the same time, thinking another, which is Not I.
Now, herein lies the whole content of a possible science of knowledge, but not that science itself. In order to build up this science we need a new act of the human mind, not contained in all its other acts, namely, the power to become conscious of its manner of acting generally. And since this act is not to be contained in all the other acts, which are all necessary, and which are all the necessary acts, it must be an act of freedom. Hence, the science of knowledge, in so far as it is to be a systematic science, is built up in the same manner in which all possible sciences, in so far as they are to be systematic, are built up, that is, through a determination of freedom; which freedom is in the science of knowledge particularly determined: to become conscious of the general manner of acting of the intelligence. Hence, the science of knowledge is distinguished from other sciences only in this, that the object of the latter sciences is itself a free act, while the objects of the science of knowledge are necessary acts.
Now, by means of this free act, something, which is in itself already form, namely, the necessary act of the intelligence, is taken up as content and put into a new form, that is, the form of knowledge or of consciousness; and hence that free act is an act of reflection. Those necessary acts are separated from the order in which they may occur perchance, and are thus separated each free from all mixture; hence, that act is also an act of abstraction. It is impossible to reflect unless you have abstracted.
The form of the consciousness, wherein the necessary and general manner of acting of the intelligence is to be received, undoubtedly belongs itself to the necessary modes of acting of the intelligence. Hence, the manner of acting of the intelligence will undoubtedly be received in that consciousness like all its other contents; and the question whence the science of knowledge is ever to get this form would thus appear to involve no difficulty. But, if we escape the difficulty in the question about the form, the whole difficulty centres in the question about the content. If the necessary manner of acting of the intelligence is to be received into the form of consciousness, it must be already known as such, and hence must have already been received into this form. We are clearly in a circle.
This manner of acting is to be separated, according to the above, by a reflecting abstraction, abstracting from all that this manner of acting is not. This abstraction occurs through freedom, and in it the philosophizing judgment is not led by a blind compulsion. The whole difficulty, therefore, centres in this question: What rules does freedom follow in that separation? or how does the philosopher know what he is to accept as the necessary manner of acting of the intelligence, and what he is to pass by as accidental?
Now, this he can not possibly know, unless that which he is first to become conscious of is already in consciousness, which is a contradiction. There is, therefore, and can be, no rule for this procedure. The human mind makes many attempts; by blindly groping it first discovers dawn, and only from dawn does it emerge to the light of day. At first it is led by dark feelings, (the origin and reality of which the science of knowledge has to show up;) and if we had not begun to feel dimly what afterward we plainly recognized, we should be to-day yet the same lump of clay which arose from the earth, lacking all clear conceptions. This indeed the history of philosophy fully proves; and we have now stated the true ground why that which lies open in every human mind, and which every one can grasp with his hands, if it is clearly exposed to him, could only arise to the consciousness of a few, after much straying into error. All philosophers have proposed to themselves this same object, all have attempted to separate by reflection the necessary manner of acting of the intelligence from its accidental conditions; all have thus separated it more or less purely and perfectly; and, on the whole, the philosophizing judgment has steadily made progress, and drawn nearer to its final result.
But since that reflection—not in so far as it is undertaken or not undertaken, for in this respect it is free, as we have seen, but in so far as it is undertaken in accordance with laws, (that is, in so far as it is determined in character, if it is undertaken)—does also belong to the necessary manner of acting of the intelligence, its laws would necessarily occur in the system of that manner of acting; and thus one might well observe—after the science were finished—whether they were correct; that is, whether they agreed with the former or not. In other words, it would seem that it were possible to furnish an evident proof of the correctness of our scientific system after it had been finished.
But the laws of reflection, which we would thus discover in the course of the science of knowledge as the only possible ones whereby a science of knowledge could be possible, are, after all—even though they agree with those laws of reflection which we had presupposed as the rules of our investigation—the result of their previous application, and we thus discover here a new circle.
Certain laws of reflection have been presupposed by us; and now, in the course of the science of knowledge, we discover the same laws as the only correct ones; ergo, our presupposition has been true, and our science of knowledge is perfectly correct in form. If we had presupposed other laws, we doubtlessly should have discovered other laws in our science of knowledge as the only correct ones, and the only question would have been whether they agreed with the presupposed laws or not. If they did not, we should be sure either that the presupposed laws were wrong, or the discovered laws, or, which is most probable, both. It is, therefore, not allowable to draw such a conclusion in a circle. We merely conclude from the harmony of the presupposed and the discovered laws of reflection that the system is correct. This, to be sure, is only a negative proof, which gives simply probability. If the presupposed and the discovered laws do not agree, then the system is surely false. If they do agree, it may be correct. But it must not necessarily be correct; for although—if there is a system in human knowledge—such an agreement or harmony can only be discovered in one way, if the conclusions are rightly drawn, it always remains possible that the harmony may be the result of two incorrectly drawn conclusions, which cancel each other and thus produce harmony. It is as if I tested a calculation of division by multiplication. If I do not obtain the desired sum as product, I may be sure that I have made a mistake in calculating; but if I do obtain it, it is merely probable that I have calculated correctly; for I might have made both in division and multiplication the same mistake; for instance, might in both have counted 5 X 9 = 36. It is thus with the science of knowledge. That science is not only the rule, but, at the same time, the calculation. Whosoever doubts the correctness of our product, does not on that account doubt the ever-valid law that we must posit the one factor as many times as the other one has units; he only doubts whether we have correctly observed this law.
Hence, even the highest unity of the system, which is the negative proof of its correctness, leaves always something which can never be strictly proven, but only accepted as probable; namely, that this unity has not been the result of chance, or of incorrect conclusions. Various means may be devised to heighten this probability; the series of propositions may be gone over in thought again and again; one may reverse the method and compare the account from the result back to the fundamental principle; or one may reflect again upon the reflection, etc., etc.; the probability always becomes greater, but never becomes certainty. If one is only conscious of having investigated honestly, and not having had in mind the final results one wished to discover, this probability may well suffice, and an objector to the correctness of our system may well be required to show up the error in our conclusions; but it will never do to claim infallibility. The system of the human mind, whereof the science of knowledge is to be the representation, is absolutely certain and infallible; every thing grounded in it is absolutely true; it never errs, and whatever has ever necessarily been, or ever necessarily will be, in any human soul, is true. If men erred, the fault lay not in the necessary, but in the freedom of reflection, which substituted one law for another. And if our science of knowledge is a correct representation of this system, it is absolutely certain and infallible as that system; but the very question is, whether our representation is or is not correct, and of this we can never furnish a strict conclusion, but only a probable proof. Our science of knowledge has truth only on the condition and in so far as its representation is a correct one. We are not the legislators of the human mind, but its historians; not newspaper writers, it is true, but pragmatic history-writers.
Add to this the circumstance that a system may really be correct as a whole, though its separate parts have not complete evidence. Here and there an incorrect conclusion may have been drawn, suggestive propositions may have been left out, other propositions which can be proven may have been asserted without proof or established by incorrect proof; and yet the most important results may be correct. This seems impossible; it seems as if a hair-breadth deviation from the straight line would necessarily lead to infinitely increasing deviation; and thus indeed it would be if man had to produce all his knowledge by clear conscious thinking; whereas rather the fundamental genius of reason unconsciously guides him and leads him by new errors from the straight path of his formaliter and logically correct argument back to the materialiter only correct result, which he would never have reached again had he persisted in logically carrying out his wrong proposition.
Even, therefore, if a universally valid science of knowledge should be established, the philosophical judgment will still have an infinite field wherein to work its ultimate perfection; it will have to fill up blanks, to make more strict the proofs, and clearer to determine the determinations.
I have two more remarks to add:
The science of knowledge presupposes the rules of reflection and abstraction as well known and valid; it must do so necessarily, and need not be ashamed or make a secret of it. That science may express itself and draw conclusions like any other science, it may presuppose all logical rules and apply all conceptions which it needs. But these presuppositions are merely made to make itself intelligible; hence, without drawing any consequences therefrom. Every thing provable must be proven; with the exception of that first and highest fundamental principle, all propositions must be deduced. Hence, for instance, neither the logical proposition of opposition or contradiction, which is the ground of all analysis, nor the logical proposition of the ground, (nothing is opposite which is not related in a third, and nothing is related which is not opposed in a third, the proposition which is the ground of all synthesis,) is deduced from the absolute first principle, though they are deduced from the two fundamental principles which rest upon it. These two latter principles are also fundamental principles, it is true, but they are not absolute, only part of them is absolute; hence, these fundamental principles as well as the logical propositions which rest upon them need not be proven, but must be deduced. I explain myself clearer.
That which the science of knowledge establishes is a proposition, thought and put into words; that in the human mind which corresponds to it is an act of that mind, which in itself need not be thought at all. Nothing must be presupposed to this act than that without which the act as act would be impossible; and this is not tacitly presupposed, but the science of knowledge has to establish it clearly and distinctly as that without which the act would be impossible. Let the act be, for instance, D, the fourth in the series A, B, C, D; then the act C must be preposited to the act D, and shown as the exclusive condition of the act D; to the act C, again, the act B must be preposited, etc., etc. But the act A, the first act, is absolutely and unconditionally possible; and hence nothing is to be preposited as the condition of its possibility.
The thinking of this act A is, however, a quite different act, which presupposes far more. Suppose this thinking of A to be, in the series of acts about to be established, D, then A, B, and C must necessarily be presupposed as grounds of its possibility; and since that thinking (of A) is to be the first business of the science of knowledge. A, B, and C must be tacitly presupposed. It is not till you get to D that the presuppositions of the first can be proven; but as soon as you get this proof, you will have presupposed something else. The form of the science is thus always in advance of its content; and this is the reason why the science as such can only attain probability. The represented and the representation are in two different series. In the first series nothing is presupposed which is not proven; but for the possibility of the second you always must presuppose what can not be proven till later. The reflection which rules in the whole science of knowledge, in so far as it is a science, is a representing. But from this it does not follow that every thing about which it reflects must also be merely a representing. In the science of knowledge the Ego is represented; but from this it does not follow that the Ego is represented as merely representing; for other determinations of the Ego may be discovered in it. The Ego as philosophizing subject is undoubtedly merely representing; but the Ego as object of the philosophizing may be something more. Representing is the highest and absolute first act of the philosopher as such; but the absolute first act of the human mind may well be of another kind. That it will turn out to be so appears probable, in advance of all experience, from simply this reason: that the representation may be completely exhausted, and that its acting is altogether necessary, and must, therefore, have a final ground of its necessity, which, as final ground, can have no higher one. A science, therefore, which is erected on the conception of representation, might well be a very useful introduction to the science, but could not be the science of knowledge itself. But this much follows certainly from the above, that the collective modes of acting of the intelligence, which the science of knowledge is to exhaust, can be received in consciousness only in the form of representation; that is to say, only in so far as they are represented.
- The science of knowledge has absolute totality. In it one leads to all, and all to one. But it is also the only science which can be completed. Completion is, therefore, its distinguishing characteristic. All other sciences are infinite, and can not be completed, for they do not return to their fundamental principles. This the science of knowledge has to prove for all other sciences, and show up the ground of it.
- A question for mathematicians. Does not the conception of a line involve already the conception of straightness? Are there other lines than straight ones? And is the so-called curved line any thing but a combination of infinitely many and infinitely close connected points? The origin of the curved line as the line of limitation of the infinite space (from the Ego as central point an infinite manifold of infinite radii are drawn, to which our limited imagination posits an end-point, and these end-points, when thought as one, are the original line of the circle) seems to guarantee this; and from this it becomes clear that and why the problem of measuring it by a straight line is an infinite problem. It also appears from this why the straight line can not be defined.
- Curious as it may appear to many explorers of nature, it will nevertheless show itself to be the strict truth, that they themselves first put the laws into nature which they believe to have learned from her, and that the smallest as well as the most extensive law the structure of a leaf of grass as well as the motion of the heavenly bodies, can be deduced in advance of all observation from the fundamental principle of all human knowledge. It is true that no law of nature, and indeed no law whatever, arises to our consciousness, unless an object is given to which it can be applied; it is true that not all objects necessarily, and not all objects in the same degree, must or can agree with the laws; but for that very reason is it true that we do not learn them from observation, but posit them as the ground of all observation, and that they are not so much laws of independent nature as laws for ourselves how we have to observe nature.
- Hence it follows that the philosopher requires the dim feelings of the true, or requires genius in no less degree than the poet or the artist, only it is a genius of another kind. The artist requires the sense of beauty, the philosopher the sense of truth.