What is Perception?

Perception is the primary source of all evidence.

Only direct or indirect connection with it is absolute truth.

The shortest way to this is always the surest, as every interposition of concepts means exposure to many deceptions;

We apply this conviction to mathematics, as established as a science by Euclid, and has remained as a whole to our own day, we cannot help regarding the method it adopts, as strange and indeed perverted. We ask that every logical proof shall be traced back to an origin in perception; but mathematics, on the contrary, is at great pains deliberately to throw away the evidence of perception which is peculiar to it, and always at hand, that it may substitute for it a logical demonstration.

This must seem to us like the action of a man who cuts off his legs in order to [091] go on crutches, or like that of the prince in the “Triumph der Empfindsamkeit” who flees from the beautiful reality of nature, to delight in a stage scene that imitates it. I must here refer to what I have said in the sixth chapter of the essay on the principle of sufficient reason, and take for granted that it is fresh and present in the memory of the reader; so that I may link my observations on to it without explaining again the difference between the mere ground of knowledge of a mathematical truth, which can be given logically, and the ground of being, which is the immediate connection of the parts of space and time, known only in perception. It is only insight into the ground of being that secures satisfaction and thorough knowledge. The mere ground of knowledge must always remain superficial; it can afford us indeed rational knowledge that a thing is as it is, but it cannot tell why it is so. Euclid chose the latter way to the obvious detriment of the science. For just at the beginning, for example, when he ought to show once for all how in a triangle the angles and sides reciprocally determine each other, and stand to each other in the relation of reason and consequent, in accordance with the form which the principle of sufficient reason has in pure space, and which there, as in every other sphere, always affords the necessity that a thing is as it is, because something quite different from it, is as it is; instead of in this way giving a thorough insight into the nature of the triangle, he sets up certain disconnected arbitrarily chosen propositions concerning the triangle, and gives a logical ground of knowledge of them, through a laborious logical demonstration, based upon the principle of contradiction. Instead of an exhaustive knowledge of these space-relations we therefore receive merely certain results of them, imparted to us at pleasure, and in fact we are very much in the position of a man to whom the different effects of an ingenious machine are[092] shown, but from whom its inner connection and construction are withheld. We are compelled by the principle of contradiction to admit that what Euclid demonstrates is true, but we do not comprehend why it is so. We have therefore almost the same uncomfortable feeling that we experience after a juggling trick, and, in fact, most of Euclid’s demonstrations are remarkably like such feats. The truth almost always enters by the back door, for it manifests itself per accidens through some contingent circumstance. Often a reductio ad absurdum shuts all the doors one after another, until only one is left through which we are therefore compelled to enter. Often, as in the proposition of Pythagoras, lines are drawn, we don’t know why, and it afterwards appears that they were traps which close unexpectedly and take prisoner the assent of the astonished learner, who must now admit what remains wholly inconceivable in its inner connection, so much so, that he may study the whole of Euclid through and through without gaining a real insight into the laws of space- relations, but instead of them he only learns by heart certain results which follow from them. This specially empirical and unscientific knowledge is like that of the doctor who knows both the disease and the cure for it, but does not know the connection between them. But all this is the necessary consequence if we capriciously reject the special kind of proof and evidence of one species of knowledge, and forcibly introduce in its stead a kind which is quite foreign to its nature. However, in other respects the manner in which this has been accomplished by Euclid deserves all the praise which has been bestowed on him through so many centuries, and which has been carried so far that his method of treating mathematics has been set up as the pattern of all scientific exposition. Men tried indeed to model all the sciences after it, but later they gave up the attempt without quite knowing why.

Yet in our eyes this method of Euclid in mathematics can appear only as a very brilliant piece of perversity. But when a great error in life or in science has been intentionally and methodically carried out with universal applause, it is always possible to discover its source in the philosophy which prevailed at the time. The Eleatics first brought out the difference, and indeed often the conflict, that exists between what is perceived, ∆±πΩøºμΩøΩ,21 and what is thought, Ωø≈ºμΩøΩ, and used it in many ways in their philosophical epigrams, and also in sophisms. They were followed later by the Megarics, the Dialecticians, the Sophists, the New-Academy, and the Sceptics; these drew attention to the illusion, that is to say, to the deception of the senses, or rather of the understanding which transforms the data of the senses into perception, and which often causes us to see things to which the reason unhesitatingly denies reality; for example, a stick broken in water, and such like. It came to be known that sense-perception was not to be trusted unconditionally, and it was therefore hastily concluded that only rational, logical thought could establish truth; although Plato (in the Parmenides), the Megarics, Pyrrho, and the New-Academy, showed by examples (in the manner which was afterwards adopted by Sextus Empiricus) how syllogisms and concepts were also sometimes misleading, and indeed produced paralogisms and sophisms which arise much more easily and are far harder to explain than the illusion of sense-perception. However, this rationalism, which arose in opposition to empiricism, kept the upper hand, and Euclid constructed the science of mathematics in accordance with it. He was compelled by necessity to found the axioms upon evidence of perception (∆±πΩøºμΩøΩ), but all the rest he based upon reasoning (Ωø≈ºμΩøΩ). His method reigned supreme through all the succeeding centuries, and it could not but do so as long as pure intuition or perception, a priori, was not [094] distinguished from empirical perception. Certain passages from the works of Proclus, the commentator of Euclid, which Kepler

translated into Latin in his book, “De Harmonia Mundi,” seem to show that he fully recognised this distinction.

But Proclus did not attach enough importance to the matter; he merely mentioned it by the way, so that he remained unnoticed and accomplished nothing. Therefore, not till two thousand years later will the doctrine of Kant, which is destined to make such great changes in all the knowledge, thought, and action of European nations, produce this change in mathematics also. For it is only after we have learned from this great man that the intuitions or perceptions of space and time are quite different from empirical perceptions, entirely independent of any impression of the senses, conditioning it, not conditioned by it, i.e., are a priori, and therefore are not exposed to the illusions of sense; only after we have learned this, I say, can we comprehend that Euclid’s logical method of treating mathematics is a useless precaution, a crutch for sound legs, that it is like a wanderer who during the night mistakes a bright, firm road for water, and carefully avoiding it, toils over the broken ground beside it, content to keep from point to point along the edge of the supposed water. Only now can we affirm with certainty that what presents itself to us as necessary in the perception of a figure, does not come from the figure on the paper, which is perhaps very defectively drawn, nor from the abstract concept under which we think it, but immediately from the form of all knowledge of which we are conscious a priori. This is always the principle of sufficient reason; here as the form of perception, i.e., space, it is the principle of the ground of being, the evidence and validity of which is, however, just as great and as immediate as that of the principle of the ground of knowing, i.e., logical certainty. Thus we need not and ought not to leave the peculiar province of mathematics in order to put our trust[095] only in logical proof, and seek to authenticate mathematics in a sphere which is quite foreign to it, that of concepts. If we confine ourselves to the ground peculiar to mathematics, we gain the great advantage that in it the rational knowledge that something 113 is, is one with the knowledge why it is so, whereas the method of Euclid entirely separates these two, and lets us know only the first, not the second. Aristotle says admirably in the Analyt., post. i. 27: “ë∫¡π≤μ√ƒμ¡± ¥Ω μ¿π√ƒ∑º∑ μ¿π√ƒ∑º∑¬ ∫±π ¿¡øƒμ¡±, !ƒμ ƒø≈ Aƒπ ∫±π ƒø≈ ¥πøƒπ ! ±≈ƒ∑, ±ªª± º∑ «…¡π¬ ƒø≈ Aƒπ, ƒ∑¬ ƒø≈ ¥πøƒπ” (Subtilior autem et praestantior ea est scientia, quâ QUOD aliquid sit, et CUR sit una simulque intelligimus non separatim QUOD, et CUR sit). In physics we are only satisfied when the knowledge that a thing is as it is is combined with the knowledge why it is so. To know that the mercury in the Torricellian tube stands thirty inches high is not really rational knowledge if we do not know that it is sustained at this height by the counterbalancing weight of the atmosphere. Shall we then be satisfied in mathematics with the qualitas occulta of the circle that the segments of any two intersecting chords always contain equal rectangles? That it is so Euclid certainly demonstrates in the 35th Prop. of the Third Book; why it is so remains doubtful. In the same way the proposition of Pythagoras teaches us a qualitas occulta of the right-angled triangle; the stilted and indeed fallacious demonstration of Euclid forsakes us at the why, and a simple figure, which we already know, and which is present to us, gives at a glance far more insight into the matter, and firm inner conviction of that necessity, and of the dependence of that quality upon the right angle:—

In the case of unequal catheti also, and indeed generally in the case of every possible geometrical truth, it is quite possible to obtain such a conviction based on perception, because these truths were always discovered by such an empirically known necessity, and their demonstration was only thought out afterwards in addition. Thus we only require an analysis of the process of thought in the first discovery of a geometrical truth in order to know its necessity empirically. It is the analytical method in general that I wish for the exposition of mathematics, instead of the synthetical method which Euclid made use of. Yet this would have very great, though not insuperable, difficulties in the case of complicated mathematical truths. Here and there in Germany men are beginning to alter the exposition of mathematics, and to proceed more in this analytical way. The greatest effort in this direction has been made by Herr Kosack, teacher of mathematics and physics in the Gymnasium at Nordhausen, who added a thorough attempt to teach geometry according to my principles to the programme of the school examination on the 6th of April 1852. In order to improve the method of mathematics, it is especially necessary to overcome the prejudice that demonstrated truth has any superiority over what is known through perception, or that logical truth founded upon the principle of contradiction has any superiority over metaphysical truth, which is immediately evident, and to which belongs the pure intuition or perception of space. That which is most certain, and yet always inexplicable, is what is involved in the principle of sufficient reason, for this principle, in its different aspects, expresses the universal form of all our ideas and knowledge. All explanation consists of reduction to it, exemplification in the particular case of the connection of ideas expressed generally through it. It is thus the principle of all explanation, and therefore it is neither susceptible of an explanation itself, nor does it stand in need of it; for every[097] explanation presupposes it, and only obtains meaning through it. Now, none of its forms are superior to the rest; it is equally certain and incapable of demonstration as the principle of the ground of being, or of change, or of action, or of knowing. The 115 relation of reason and consequent is a necessity in all its forms, and indeed it is, in general, the source of the concept of necessity, for necessity has no other meaning. If the reason is given there is no other necessity than that of the consequent, and there is no reason that does not involve the necessity of the consequent. Just as surely then as the consequent expressed in the conclusion follows from the ground of knowledge given in the premises, does the ground of being in space determine its consequent in space: if I know through perception the relation of these two, this certainty is just as great as any logical certainty. But every geometrical proposition is just as good an expression of such a relation as one of the twelve axioms; it is a metaphysical truth, and as such, just as certain as the principle of contradiction itself, which is a metalogical truth, and the common foundation of all logical demonstration. Whoever denies the necessity, exhibited for intuition or perception, of the space-relations expressed in any proposition, may just as well deny the axioms, or that the conclusion follows from the premises, or, indeed, he may as well deny the principle of contradiction itself, for all these relations are equally undemonstrable, immediately evident and known a priori. For any one to wish to derive the necessity of space-relations, known in intuition or perception, from the principle of contradiction by means of a logical demonstration is just the same as for the feudal superior of an estate to wish to hold it as the vassal of another. Yet this is what Euclid has done. His axioms only, he is compelled to leave resting upon immediate evidence; all the geometrical truths which follow are demonstrated logically, that is to say, from the agreement of [098] the assumptions made in the proposition with the axioms which are presupposed, or with some earlier proposition; or from the contradiction between the opposite of the proposition and the assumptions made in it, or the axioms, or earlier propositions, or even itself. But the axioms themselves have no more immediate evidence than any other geometrical problem, but only more 116 The World As Will And Idea (Vol. 1 of 3) simplicity on account of their smaller content. When a criminal is examined, a procès-verbal is made of his statement in order that we may judge of its truth from its consistency. But this is only a makeshift, and we are not satisfied with it if it is possible to investigate the truth of each of his answers for itself; especially as he might lie consistently from the beginning. But Euclid investigated space according to this first method. He set about it, indeed, under the correct assumption that nature must everywhere be consistent, and that therefore it must also be so in space, its fundamental form. Since then the parts of space stand to each other in a relation of reason and consequent, no single property of space can be different from what it is without being in contradiction with all the others. But this is a very troublesome, unsatisfactory, and roundabout way to follow. It prefers indirect knowledge to direct, which is just as certain, and it separates the knowledge that a thing is from the knowledge why it is, to the great disadvantage of the science; and lastly, it entirely withholds from the beginner insight into the laws of space, and indeed renders him unaccustomed to the special investigation of the ground and inner connection of things, inclining him to be satisfied with a mere historical knowledge that a thing is as it is. The exercise of acuteness which this method is unceasingly extolled as affording consists merely in this, that the pupil practises drawing conclusions, i.e., he practises applying the principle of contradiction, but specially he exerts his memory to retain all those data whose agreement is to be tested. Moreover, it is worth noticing that this method[099] of proof was applied only to geometry and not to arithmetic. In arithmetic the truth is really allowed to come home to us through perception alone, which in it consists simply in counting. As the perception of numbers is in time alone, and therefore cannot be represented by a sensuous schema like the geometrical figure, the suspicion that perception is merely empirical, and possibly illusive, disappeared in arithmetic, and the introduction of the 117 logical method of proof into geometry was entirely due to this suspicion. As time has only one dimension, counting is the only arithmetical operation, to which all others may be reduced; and yet counting is just intuition or perception a priori, to which there is no hesitation in appealing here, and through which alone everything else, every sum and every equation, is ultimately proved. We prove, for example, not that (7 + 9 × 8 - 2)/3 = 42; but we refer to the pure perception in time, counting thus makes each individual problem an axiom. Instead of the demonstrations that fill geometry, the whole content of arithmetic and algebra is thus simply a method of abbreviating counting. We mentioned above that our immediate perception of numbers in time extends only to about ten. Beyond this an abstract concept of the numbers, fixed by a word, must take the place of the perception; which does not therefore actually occur any longer, but is only indicated in a thoroughly definite manner. Yet even so, by the important assistance of the system of figures which enables us to represent all larger numbers by the same small ones, intuitive or perceptive evidence of every sum is made possible, even where we make such use of abstraction that not only the numbers, but indefinite quantities and whole operations are thought only in the abstract and indicated as so thought, as sqrt so that we do not perform them, but merely symbolise them. We might establish truth in geometry also, through pure [100] a priori perception, with the same right and certainty as in arithmetic. It is in fact always this necessity, known through perception in accordance with the principle of sufficient reason of being, which gives to geometry its principal evidence, and upon which in the consciousness of every one, the certainty of its propositions rests. The stilted logical demonstration is always foreign to the matter, and is generally soon forgotten, without weakening our conviction. It might indeed be dispensed with altogether without diminishing the evidence of geometry, for this is always quite independent of such demonstration, which 118 The World As Will And Idea (Vol. 1 of 3) never proves anything we are not convinced of already, through another kind of knowledge. So far then it is like a cowardly soldier, who adds a wound to an enemy slain by another, and then boasts that he slew him himself.22 After all this we hope there will be no doubt that the evidence of mathematics, which has become the pattern and symbol of all evidence, rests essentially not upon demonstration, but upon immediate perception, which is thus here, as everywhere else, the ultimate ground and source of truth. Yet the perception which lies at the basis of mathematics has a great advantage over all other perception, and therefore over empirical perception. It is a priori, and therefore independent of experience, which is always given only in successive parts; therefore everything is equally near to it, and we can start either from the reason or from the consequent, as we please. Now this makes it absolutely reliable, for in it the consequent is known from the reason,[101] and this is the only kind of knowledge that has necessity; for example, the equality of the sides is known as established by the equality of the angles. All empirical perception, on the other hand, and the greater part of experience, proceeds conversely from the consequent to the reason, and this kind of knowledge is not infallible, for necessity only attaches to the consequent on account of the reason being given, and no necessity attaches to the knowledge of the reason from the consequent, for the same 22 Spinoza, who always boasts that he proceeds more geometrico, has actually done so more than he himself was aware. For what he knew with certainty and decision from the immediate, perceptive apprehension of the nature of the world, he seeks to demonstrate logically without reference to this knowledge. He only arrives at the intended and predetermined result by starting from arbitrary concepts framed by himself (substantia causa sui, &c.), and in the demonstrations he allows himself all the freedom of choice for which the nature of the wide concept-spheres afford such convenient opportunity. That his doctrine is true and excellent is therefore in his case, as in that of geometry, quite independent of the demonstrations of it. Cf. ch. 13 of supplementary volume. 119 consequent may follow from different reasons. The latter kind of knowledge is simply induction, i.e., from many consequents which point to one reason, the reason is accepted as certain; but as the cases can never be all before us, the truth here is not unconditionally certain. But all knowledge through sense- perception, and the great bulk of experience, has only this kind of truth. The affection of one of the senses induces the understanding to infer a cause of the effect, but, as a conclusion from the consequent to the reason is never certain, illusion, which is deception of the senses, is possible, and indeed often occurs, as was pointed out above. Only when several of the senses, or it may be all the five, receive impressions which point to the same cause, the possibility of illusion is reduced to a minimum; but yet it still exists, for there are cases, for example, the case of counterfeit money, in which all the senses are deceived. All empirical knowledge, and consequently the whole of natural science, is in the same position, except only the pure, or as Kant calls it, metaphysical part of it. Here also the causes are known from the effects, consequently all natural philosophy rests upon hypotheses, which are often false, and must then gradually give place to more correct ones. Only in the case of purposely arranged experiments, knowledge proceeds from the cause to the effect, that is, it follows the method that affords certainty; but these experiments themselves are undertaken in consequence [102] of hypotheses. Therefore, no branch of natural science, such as physics, or astronomy, or physiology could be discovered all at once, as was the case with mathematics and logic, but required and requires the collected and compared experiences of many centuries. In the first place, repeated confirmation in experience brings the induction, upon which the hypothesis rests, so near completeness that in practice it takes the place of certainty, and is regarded as diminishing the value of the hypothesis, its source, just as little as the incommensurability of straight and curved lines diminishes the value of the application of geometry, or 120 The World As Will And Idea (Vol. 1 of 3) that perfect exactness of the logarithm, which is not attainable, diminishes the value of arithmetic. For as the logarithm, or the squaring of the circle, approaches infinitely near to correctness through infinite fractions, so, through manifold experience, the induction, i.e., the knowledge of the cause from the effects, approaches, not infinitely indeed, but yet so near mathematical evidence, i.e., knowledge of the effects from the cause, that the possibility of mistake is small enough to be neglected, but yet the possibility exists; for example, a conclusion from an indefinite number of cases to all cases, i.e., to the unknown ground on which all depend, is an induction. What conclusion of this kind seems more certain than that all men have the heart on the left side? Yet there are extremely rare and quite isolated exceptions of men who have the heart upon the right side. Sense-perception and empirical science have, therefore, the same kind of evidence. The advantage which mathematics, pure natural science, and logic have over them, as a priori knowledge, rests merely upon this, that the formal element in knowledge upon which all that is a priori is based, is given as a whole and at once, and therefore in it we can always proceed from the cause to the effect, while in the former kind of knowledge we are generally obliged to proceed from the effect to the cause. In other respects, the law of[103] causality, or the principle of sufficient reason of change, which guides empirical knowledge, is in itself just as certain as the other forms of the principle of sufficient reason which are followed by the a priori sciences referred to above. Logical demonstrations from concepts or syllogisms have the advantage of proceeding from the reason to the consequent, just as much as knowledge through perception a priori, and therefore in themselves, i.e., according to their form, they are infallible. This has greatly assisted to bring demonstration in general into such esteem. But this infallibility is merely relative; the demonstration merely subsumes under the first principles of the science, and it is these which contain the whole material truth of science, and they 121 must not themselves be demonstrated, but must be founded on perception. In the few a priori sciences we have named above, this perception is pure, but everywhere else it is empirical, and is only raised to universality through induction. If, then, in the empirical sciences also, the particular is proved from the general, yet the general, on the other hand, has received its truth from the particular; it is only a store of collected material, not a self-constituted foundation. So much for the foundation of truth. Of the source and possibility of error many explanations have been tried since Plato’s metaphorical solution of the dove-cot where the wrong pigeons are caught, &c. (Theætetus, p. 167, et seq.) Kant’s vague, indefinite explanation of the source of error by means of the diagram of diagonal motion, will be found in the “Critique of Pure Reason,” p. 294 of the first edition, and p. 350 of the fifth. As truth is the relation of a judgment to its ground of knowledge, it is always a problem how the person judging can believe that he has such a ground of knowledge and yet not have it; that is to say, how error, the deception of reason, is possible. I find this possibility quite analogous to that of illusion, or the deception of the understanding, which has been explained above. My [104] opinion is (and this is what gives this explanation its proper place here) that every error is an inference from the consequent to the reason, which indeed is valid when we know that the consequent has that reason and can have no other; but otherwise is not valid. The person who falls into error, either attributes to a consequent a reason which it cannot have, in which case he shows actual deficiency of understanding, i.e., deficiency in the capacity for immediate knowledge of the connection between the cause and the effect, or, as more frequently happens, he attributes to the effect a cause which is possible, but he adds to the major proposition of the syllogism, in which he infers the cause from the effect, that this effect always results only from this cause. Now he could only be assured of this by a complete induction, which, however, he assumes without having made it. This “always” is therefore too wide a concept, and instead of it he ought to have used “sometimes” or “generally.”

The conclusion would then be problematical, and therefore not erroneous. That the man who errs should proceed in this way is due either to haste, or to insufficient knowledge of what is possible, on account of which he does not know the necessity of the induction that ought to be made. Error then is quite analogous to illusion. Both are inferences from the effect to the cause; the illusion brought about always in accordance with the law of causality, and by the understanding alone, thus directly, in perception itself; the error in accordance with all the forms of the principle of sufficient reason, and by the reason, thus in thought itself; yet most commonly in accordance with the law of causality, as will appear from the 3 following examples which are representatives of the 3 kinds of error.

1. The illusion of the senses (deception of the understanding) induces error (deception of the reason)

For example, if one mistakes a painting for an alto-relief, and actually takes it for such; the error[105] results from a conclusion from the following major premise: “If dark grey passes regularly through all shades to white; the cause is always the light, which strikes differently upon projections and depressions, ergo—.”

2. “If there is no money in my safe, the cause is always that my servant has got a key for it: ergo—.” (3.) “If a ray of sunlight, broken through a prism, i.e., bent up or down, appears as a coloured band instead of round and white as before, the cause must always be that light consists of homogeneous rays, differently coloured and refrangible to different degrees, which, when forced asunder on account of the difference of their refrangibility, give an elongated and variously-coloured spectrum: ergo—bibamus!”—It must be possible to trace every error to such a conclusion, drawn from a major premise which is often only falsely generalised, hypothetical, and founded on the assumption that some particular cause is that of a certain effect.

Only certain mistakes in counting are to be excepted, and they are not really errors, but merely mistakes. The operation prescribed by the concepts of the numbers has not been carried out in pure intuition or perception, in counting, but some other operation instead of it.

As regards the content of the sciences generally, it is, in fact, always the relation of the phenomena of the world to each other, according to the principle of sufficient reason, under the guidance of the why, which has validity and meaning only through this principle. Explanation is the establishment of this relation. Therefore explanation can never go further than to show two ideas standing to each other in the relation peculiar to that form of the principle of sufficient reason which reigns in the class to which they belong. If this is done we cannot further be asked the question, why: for the relation proved is that one which absolutely cannot be imagined as other than it is, i.e., it is the form of all knowledge. Therefore we do not ask why 2 + 2 = 4; or why the equality of the angles of a triangle determines [106] the equality of the sides; or why its effect follows any given cause; or why the truth of the conclusion is evident from the truth of the premises. Every explanation which does not ultimately lead to a relation of which no “why” can further be demanded, stops at an accepted qualitas occulta; but this is the character of every original force of nature.

Every explanation in natural science must ultimately end with such a qualitas occulta, and thus with complete obscurity. It must leave the inner nature of a stone just as much unexplained as that of a human being; it can give as little account of the weight, the cohesion, the chemical qualities, &c., of the former, as of the knowing and acting of the latter. Thus, for example, weight is a qualitas occulta, for it can be thought away, and does not proceed as a necessity from the form of knowledge; which, on the contrary, is not the case with the law of inertia, for it follows from the law of causality, and is therefore sufficiently explained if it is referred to that law.

There are two things which are altogether inexplicable,—that is to say, do not ultimately lead to the relation which the principle of sufficient reason expresses. These are, first, the principle of sufficient reason itself in all its four forms, because it is the principle of all explanation, which has meaning only in relation to it; secondly, that to which this principle does not extend, but which is the original source of all phenomena; the thing-in-itself, the knowledge of which is not subject to the principle of sufficient reason. We must be content for the present not to understand this thing-in-itself, for it can only be made intelligible by means of the following book, in which we shall resume this consideration of the possible achievements of the sciences. But at the point at which natural science, and indeed every science, leaves things, because not only its explanation of them, but even the principle of this explanation, the principle of sufficient reason, does not extend beyond this point; there philosophy takes them up and[107] treats them after its own method, which is quite distinct from the method of science. In my essay on the principle of sufficient reason, § 51, I have shown how in the different sciences the chief guiding clue is one or other form of that principle; and, in fact, perhaps the most appropriate classification of the sciences might be based upon this circumstance. Every explanation arrived at by the help of this clue is, as we have said, merely relative; it explains things in relation to each other, but something which indeed is presupposed is always left unexplained. In mathematics, for example, this is space and time; in mechanics, physics, and chemistry it is matter, qualities, original forces and laws of nature; in botany and zoology it is the difference of species, and life itself; in history it is the human race with all its properties of thought and will: in all it is that form of the principle of sufficient reason which is respectively applicable. It is peculiar to philosophy that it presupposes nothing as known, but treats everything as equally external and a problem; not merely the relations of phenomena, but also the phenomena themselves, and even the principle of sufficient reason to which the other sciences are content to refer everything. In philosophy nothing would be gained by such a reference, as one member of the series is just as external to it as another; and, moreover, that kind of connection is just as much a problem for philosophy as what is joined together by it, and the latter again is just as much a problem after its combination has been explained as before it.

For, as we have said, just what the sciences presuppose and lay down as the basis and the limits of their explanation, is precisely and peculiarly the problem of philosophy, which may therefore be said to begin where science ends. It cannot be founded upon demonstrations, for they lead from known principles to unknown, but everything is equally unknown and external to philosophy. There can be no principle in consequence of which the world with all its phenomena first came into existence, and therefore [108] it is not possible to construct, as Spinoza wished, a philosophy which demonstrates ex firmis principiis. Philosophy is the most general rational knowledge, the first principles of which cannot therefore be derived from another principle still more general. The principle of contradiction establishes merely the agreement of concepts, but does not itself produce concepts. The principle of sufficient reason explains the connections of phenomena, but not the phenomena themselves; therefore philosophy cannot proceed upon these principles to seek a causa efficiens or a causa finalis of the whole world. My philosophy, at least, does not by any means seek to know whence or wherefore the world exists, but merely what the world is. But the why is here subordinated to the what, for it already belongs to the world, as it arises and has meaning and validity only through the form of its phenomena, the principle of sufficient reason. We might indeed say that every one knows what the world is without help, for he is himself that subject of knowledge of which the world is the idea; and so far this would be true. But that knowledge is empirical, is in the concrete; the task of philosophy is to reproduce this in the abstract to raise to permanent rational knowledge the successive changing perceptions, and in general, all that is contained under the wide concept of feeling and merely negatively defined as not abstract, distinct, rational knowledge. It must therefore consist of a statement in the abstract, of the nature of the whole world, of the whole, and of all the parts. In order then that it may not lose itself in the endless multitude of particular judgments, it must make use of abstraction and think everything individual in the universal, and its differences also in the universal. It must therefore partly separate and partly unite, in order to present to rational knowledge the whole manifold of the world generally, according to its nature, comprehended in a few abstract concepts. Through these concepts, in which it fixes the nature of the world,[109] the whole individual must be known as well as the universal, the knowledge of both therefore must be bound together to the minutest point. Therefore the capacity for philosophy consists just in that in which Plato placed it, the knowledge of the one in the many, and the many in the one. Philosophy will therefore be a sum-total of general judgments, whose ground of knowledge is immediately the world itself in its entirety, without excepting anything; thus all that is to be found in human consciousness; it will be a complete recapitulation, as it were, a reflection, of the world in abstract concepts, which is only possible by the union of the essentially identical in one concept and the relegation of the different to another. This task was already prescribed to philosophy by Bacon of Verulam when he said: ea demum vera est philosophia, quae mundi ipsius voces fidelissime reddit, et veluti dictante mundo conscripta est, et nihil aliud est, quam ejusdem SIMULACRUM ET REFLECTIO, neque addit quidquam de proprio, sed tantum iterat et resonat (De Augm. Scient., L. 2, c. 13). But we take this in a wider sense than Bacon could then conceive.

The agreement which all the sides and parts of the world have with each other, just because they belong to a whole, must also be 127 found in this abstract copy of it. Therefore the judgments in this sum-total could to a certain extent be deduced from each other, and indeed always reciprocally so deduced. Yet to make the first judgment possible, they must all be present, and thus implied as prior to it in the knowledge of the world in the concrete, especially as all direct proof is more certain than indirect proof; their harmony with each other by virtue of which they come together into the unity of one thought, and which arises from the harmony and unity of the world of perception itself, which is their common ground of knowledge, is not therefore to be made use of to establish them, as that which is prior to them, but is [110] only added as a confirmation of their truth. This problem itself can only become quite clear in being solved.