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 know ledge, since it furnishes every thing and since it furnishes only the necessary. Hence, in the fun damental principle of a particular science, an act which the science of knowledge left free would be INTRODUCTION. 41 determined. The science of knowledge would thus give to the act, that is, to the fundamental prin ciple, 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 wher ever it chooses. As soon as this freedom is de termined, 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 con- * A question for mathematicians. Docs not the conception of a line involve already the conception of srraightness? 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 lim itation of the infinite space (from the Ego as central point an in finite manifold of infinite radii are drawn, to vhich our limited im agination 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 thai and why the problem of mea suring it by a straight line is an infinite problem. It also appears from this why the straight line can not be defined, 42 INTRODUCTION.
42 INTRODUCTION.
struction in space, is fundamental principle of geom etry, 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 neces sary the laws, according to which nature is to be and must be observed.* But our power of judg ment retains its full freedom to apply these laws or not, or to apply whatever law it chooses to any pos sible object; (for instance, to regard the human body as inorganic, or as organic, or as living mat ter.) But as soon as the power of judgment is re quired to observe a determined object by a deter mined law, (for instance, whether animal life can be explained from the mere inorganic; whether crys tallization be the transition from chemical connec tions to organization; whether magnetic and elec- • Curious as it may appear to many explorers of nature, it tviil 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 fun damental principle of all human knowledge. It is true that no law of nature, and indeed no law whatever, arises to cur consciousness, unless an object is given to which it can be app'.ied;:t is true that not all objects necessarily, and not all objects hi 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 Lave to ob- •erve nature.
INTRODUCTION. 43 INTRODUCTION. 43 trie 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 ob ject of experience under a given law of nature in our mind, is fundamental principle of the science of nature. That science consists throughout of ex periments, (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 neces sary; 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 perfecti bility, the science of knowledge rather secures it £ M INTRODUCTION.
against all doubt, and assigns to it a problem which can not be completed in all eternity.
§ 6. — HOW IS THE SCIENCE OF KNOWLEDGE RE LATED TO LOGIC?
The science of knowledge is to determine the form for all possible sciences. According to cur rent opinion, in which there may be something true, logic does the very same thing. How are these two sciences related to each other, particu larly in respect to this problem, which each claims to solve?
By remembering that logic only pretends to de termine 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 insep arably 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.
INTRODUCTION. 45 INTRODUCTION. 45 If the science of logic is such a separate science, it must be possible to show a determination of free dom 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 free dom 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 repre sent 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 free dom. 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 concep tion of a proposition involves (see § *) 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 be comes its own content and returns into itself, is called reflection. No abstraction is possible with out 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 46 INTRODUCTION.
the condition of the other. But in synthetical think ing 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 con tradiction, 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 con fined to in the science of knowledge; not neces sarily to the whole of that content — for then we should have no particular sciences — but at least to INTKODUCTJON. 47 what is part of that content Without this condi tion 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 con ceived 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 for mer 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 proposi tion, 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 //"it is posited, or how are the ^"and the that 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 48 JA'TA'ODUCTfOA'.
knowledge says: Because A (that is, this particular A==Ego) is, therefore A is. And thus the ques tion: Is A (this particular A) really posited? is an swered 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 propo sition 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 pos sible, actual, or necessary;) and thus the proposi tion is shown to be true, beyond contradiction, if the Ego is to be Ego. Again, if the Ego is posit ed 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 pos ited if it is posited; and thus our second question is also answered.
49 § 7. — HOW IS THE SCIENCE OF KNOWLEDGE, AS SCIENCE, RELATED TO ITS OBJECT?
Let us first premise that this question has hith erto been utterly abstracted from, and that hence all the foregoing must be modified by the answer ing 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 some thing, 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 ex isted 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 ex ists independently of the science of it, and the sci ence 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 distin guished 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 deter mined manner are they distinguished from each other. This is the How of the WJiat. Hence, there is in the human mind originally, and in ad- 5O INTRODUCTION.
vance 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 com prises all others, and which furnishes the highest universal law, should actually occur Jirst in our mind, and be followed by the one next in impor tance; 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 in stance, 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 man- INTRODUCTION. 5 1 INTRODUCTION. 5 1 ncr of acting generally. And since this act is not to be contained in all the other acts, which are all ne cessary, and which are all the necessary acts, it must be an act of freedom. Hence, the science of know ledge, in so Tar 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 free dom; which freedom is in the science of know ledge 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 ob jects 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 ne cessary and general manner of acting of the intelli gence is to be received, undoubtedly belongs* itself to the necessary modes of acting of the intelligence. Hence, the manner of acting of the intelligence 52 INTRODUCTION.
52 INTRODUCTION.
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, ac cording 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 philoso pher 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 blind ly 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 * Hence it follows that the philosopher requires the dim feeling* INTRODUCTION. 53 which the science of knowledge has to show up;) and if we had not begun to feel dimly what after ward 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 ex posed to him, could only arise to the consciousness of a few, after much straying into error. All phi losophers 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 se parated 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 under taken in accordance u'it/i lau>st (that is, in so far as it is determined in character, if it is undertaken) — does also belong to the necessary manner of act ing 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 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 ixauty, the philosopher the sense of truth.
54 INTRODUCTION.
finished — whether they were correct; that is, whe ther they agreed with the former or not In other words, it would seem that it were possible to fur nish 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 know ledge 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 cor rect 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 whe ther they agreed with the presupposed laws or not. If they did not, we should be sure either that the J presupposed laws were wrong, or the discovered laws, or, which is most probable, both. It is, there fore, not allowable to draw such a conclusion in a circle. We merely conclude from the harmony of the presupposed and the discovered laws of reflec tion that the system is correct. This, to be sure, is only a negative proof, which gives simply proba- INTRODUCTION. 55 INTRODUCTION. 55 bHity. If the presupposed and the discovered laws do not agree, then the system is surely false. If they do agree, it may be correct. Bat 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 lite conchtsions arc 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 calcu lating; 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 5x9=36. It is thus with the science of know ledge. 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 cor rectly 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 prov en, but only accepted as probable; namely, that this unity has not been the result of chance, or of in correct conclusions. Various means may be devised 56 INTRODUCTION.
to heighten this probability; the series of proposi tions 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 reflec tion, 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 sys tem 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 vicn erred, the fault lay not in the necessary, but in the freedom of re flection, which substituted one law for another. And if our science of knowledge is a correct representa tion of this system, it is absolutely certain and in fallible as that system; but the very question is,