The World as Will and Idea (Vol. 1 of 3)

This quality of concepts by which they resemble the stones of a mosaic, and on account of which perception always remains their asymptote, is also the reason why nothing good is produced in art by their means. If the singer or the virtuoso attempts to guide his execution by reflection he remains silent. And this is equally true of the composer, the painter, and the poet. The concept always remains unfruitful in art; it can only direct the technical part of it, its sphere is science. We shall consider more fully in the third book, why all true art proceeds from sensuous knowledge, never from the concept. Indeed, with regard to behaviour also, and personal agreeableness in society, the concept has only a negative value in restraining the grosser manifestations of egotism and brutality; so that a polished manner is its commendable production. But all that is attractive, gracious, charming in behaviour, all affectionateness and friendliness, must not proceed from the concepts, for if it does, “we feel intention, and are put out of tune.” All dissimulation is the work of reflection; but it cannot be maintained constantly and without interruption: “nemopotest personam diu ferre fictum,” says Seneca in his book de clementia; and so it is generally found out and loses its effect. Reason is needed in the full stress of life, where quick conclusions, bold action, rapid and sure comprehension are required, but it may easily spoil all if it gains the upper hand, and by perplexing hinders the intuitive, direct discovery, and grasp of the right by simple understanding, and thus induces irresolution.

Lastly, virtue and holiness do not proceed from reflection, but from the inner depths of the will, and its relation to knowledge. The exposition of this belongs to another part of our work; this, however, I may remark here, that the dogmas relating to ethics may be the same in the reason of whole nations, but the action of every individual different; and the converse also holds good; action, we say, is guided by feelings, – that is, simply not by concepts, but as a matter of fact by the ethical character. Dogmas occupy the idle reason; but action in the end pursues its own course independently of them, generally not according to abstract rules, but according to unspoken maxims, the expression of which is the whole man himself. Therefore, however different the religious dogmas of nations may be, yet in the case of all of them, a good action is accompanied by unspeakable satisfaction, and a bad action by endless remorse. No mockery can shake the former; no priest's absolution can deliver from the latter. Notwithstanding this, we must allow, that for the pursuit of a virtuous life, the application of reason is needful; only it is not its source, but has the subordinate function of preserving resolutions which have been made, of providing maxims to withstand the weakness of the moment, and give consistency to action. It plays the same part ultimately in art also, where it has just as little to do with the essential matter, but assists in carrying it out, for genius is not always at call, and yet the work must be completed in all its parts and rounded off to a whole.[17 - Cf. Ch. 7 of the Supplement.]

§ 13. All these discussions of the advantages and disadvantages of the application of reason are intended to show, that although abstract rational knowledge is the reflex of ideas of perception, and is founded on them, it is by no means in such entire congruity with them that it could everywhere take their place: indeed it never corresponds to them quite accurately. And thus, as we have seen, many human actions can only be performed by the help of reason and deliberation, and yet there are some which are better performed without its assistance. This very incongruity of sensuous and abstract knowledge, on account of which the latter always merely approximates to the former, as mosaic approximates to painting, is the cause of a very remarkable phenomenon which, like reason itself, is peculiar to human nature, and of which the explanations that have ever anew been attempted, are insufficient: I mean laughter. On account of the source of this phenomenon, we cannot avoid giving the explanation of it here, though it again interrupts the course of our work to do so. The cause of laughter in every case is simply the sudden perception of the incongruity between a concept and the real objects which have been thought through it in some relation, and laughter itself is just the expression of this incongruity. It often occurs in this way: two or more real objects are thought through one concept, and the identity of the concept is transferred to the objects; it then becomes strikingly apparent from the entire difference of the objects in other respects, that the concept was only applicable to them from a one-sided point of view. It occurs just as often, however, that the incongruity between a single real object and the concept under which, from one point of view, it has rightly been subsumed, is suddenly felt. Now the more correct the subsumption of such objects under a concept may be from one point of view, and the greater and more glaring their incongruity with it, from another point of view, the greater is the ludicrous effect which is produced by this contrast. All laughter then is occasioned by a paradox, and therefore by unexpected subsumption, whether this is expressed in words or in actions. This, briefly stated, is the true explanation of the ludicrous.

I shall not pause here to relate anecdotes as examples to illustrate my theory; for it is so simple and comprehensible that it does not require them, and everything ludicrous which the reader may remember is equally valuable as a proof of it. But the theory is confirmed and illustrated by distinguishing two species into which the ludicrous is divided, and which result from the theory. Either, we have previously known two or more very different real objects, ideas of sense-perception, and have intentionally identified them through the unity of a concept which comprehends them both; this species of the ludicrous is called wit. Or, conversely, the concept is first present in knowledge, and we pass from it to reality, and to operation upon it, to action: objects which in other respects are fundamentally different, but which are all thought in that one concept, are now regarded and treated in the same way, till, to the surprise and astonishment of the person acting, the great difference of their other aspects appears: this species of the ludicrous is called folly. Therefore everything ludicrous is either a flash of wit or a foolish action, according as the procedure has been from the discrepancy of the objects to the identity of the concept, or the converse; the former always intentional, the latter always unintentional, and from without. To seem to reverse the starting-point, and to conceal wit with the mask of folly, is the art of the jester and the clown. Being quite aware of the diversity of the objects, the jester unites them, with secret wit, under one concept, and then starting from this concept he receives from the subsequently discovered diversity of the objects the surprise which he himself prepared. It follows from this short but sufficient theory of the ludicrous, that, if we set aside the last case, that of the jester, wit must always show itself in words, folly generally in actions, though also in words, when it only expresses an intention and does not actually carry it out, or when it shows itself merely in judgments and opinions.

Pedantry is a form of folly. It arises in this way: a man lacks confidence in his own understanding, and, therefore, does not wish to trust to it, to recognise what is right directly in the particular case. He, therefore, puts it entirely under the control of the reason, and seeks to be guided by reason in everything; that is to say, he tries always to proceed from general concepts, rules, and maxims, and to confine himself strictly to them in life, in art, and even in moral conduct. Hence that clinging to the form, to the manner, to the expression and word which is characteristic of pedantry, and which with it takes the place of the real nature of the matter. The incongruity then between the concept and reality soon shows itself here, and it becomes evident that the former never condescends to the particular case, and that with its generality and rigid definiteness it can never accurately apply to the fine distinctions of difference and innumerable modifications of the actual. Therefore, the pedant, with his general maxims, almost always misses the mark in life, shows himself to be foolish, awkward, useless. In art, in which the concept is unfruitful, he produces lifeless, stiff, abortive mannerisms. Even with regard to ethics, the purpose to act rightly or nobly cannot always be carried out in accordance with abstract maxims; for in many cases the excessively nice distinctions in the nature of the circumstances necessitate a choice of the right proceeding directly from the character; for the application of mere abstract maxims sometimes gives false results, because the maxims only half apply; and sometimes cannot be carried out, because they are foreign to the individual character of the actor, and this never allows itself to be entirely discovered; therefore, inconsistencies arise. Since then Kant makes it a condition of the moral worth of an action, that it shall proceed from pure rational abstract maxims, without any inclination or momentary emotion, we cannot entirely absolve him from the reproach of encouraging moral pedantry. This reproach is the significance of Schiller's epigram, entitled “Scruples of Conscience.” When we speak, especially in connection with politics, of doctrinaires, theorists, savants, and so forth, we mean pedants, that is, persons who know the things well in the abstract, but not in the concrete. Abstraction consists in thinking away the less general predicates; but it is precisely upon these that so much depends in practice.

To complete our theory it remains for us to mention a spurious kind of wit, the play upon words, the calembourg, the pun, to which may be added the equivocation, the double entendre, the chief use of which is the expression of what is obscene. Just as the witticism brings two very different real objects under one concept, the pun brings two different concepts, by the assistance of accident, under one word. The same contrast appears, only familiar and more superficial, because it does not spring from the nature of things, but merely from the accident of nomenclature. In the case of the witticism the identity is in the concept, the difference in the reality, but in the case of the pun the difference is in the concepts and the identity in the reality, for the terminology is here the reality. It would only be a somewhat far-fetched comparison if we were to say that the pun is related to the witticism as the parabola (sic) of the upper inverted cone to that of the lower. The misunderstanding of the word or the quid pro quo is the unintentional pun, and is related to it exactly as folly is to wit. Thus the deaf man often affords occasion for laughter, just as much as the fool, and inferior writers of comedy often use the former for the latter to raise a laugh.

I have treated laughter here only from the psychical side; with regard to the physical side, I refer to what is said on the subject in the “Parerga,” vol. II. ch. vi., § 98.[18 - Cf. Ch. 8 of Supplement.]

§ 14. By means of these various discussions it is hoped that both the difference and the relation between the process of knowledge that belongs to the reason, rational knowledge, the concept on the one hand, and the direct knowledge in purely sensuous, mathematical intuition or perception, and apprehension by the understanding on the other hand, has been clearly brought out. This remarkable relation of our kinds of knowledge led us almost inevitably to give, in passing, explanations of feeling and of laughter, but from all this we now turn back to the further consideration of science as the third great benefit which reason confers on man, the other two being speech and deliberate action. The general discussion of science which now devolves upon us, will be concerned partly with its form, partly with the foundation of its judgments, and lastly with its content.

We have seen that, with the exception of the basis of pure logic, rational knowledge in general has not its source in the reason itself; but having been otherwise obtained as knowledge of perception, it is stored up in the reason, for through reason it has entirely changed its character, and has become abstract knowledge. All rational knowledge, that is, knowledge that has been raised to consciousness in the abstract, is related to science strictly so called, as a fragment to the whole. Every one has gained a rational knowledge of many different things through experience, through consideration of the individual objects presented to him, but only he who sets himself the task of acquiring a complete knowledge in the abstract of a particular class of objects, strives after science. This class can only be marked off by means of a concept; therefore, at the beginning of every science there stands a concept, and by means of it the class of objects concerning which this science promises a complete knowledge in the abstract, is separated in thought from the whole world of things. For example, the concept of space-relations, or of the action of unorganised bodies upon each other, or of the nature of plants, or of animals, or of the successive changes of the surface of the globe, or of the changes of the human race as a whole, or of the construction of a language, and so forth. If science sought to obtain the knowledge of its object, by investigating each individual thing that is thought through the concept, till by degrees it had learned the whole, no human memory would be equal to the task, and no certainty of completeness would be obtainable. Therefore, it makes use of that property of concept-spheres explained above, that they include each other, and it concerns itself mainly with the wider spheres which lie within the concept of its object in general. When the relations of these spheres to each other have been determined, all that is thought in them is also generally determined, and can now be more and more accurately determined by the separation of smaller and smaller concept-spheres. In this way it is possible for a science to comprehend its object completely. This path which it follows to knowledge, the path from the general to the particular, distinguishes it from ordinary rational knowledge; therefore, systematic form is an essential and characteristic feature of science. The combination of the most general concept-spheres of every science, that is, the knowledge of its first principles, is the indispensable condition of mastering it; how far we advance from these to the more special propositions is a matter of choice, and does not increase the thoroughness but only the extent of our knowledge of the science. The number of the first principles to which all the rest are subordinated, varies greatly in the different sciences, so that in some there is more subordination, in others more co-ordination; and in this respect, the former make greater claims upon the judgment, the latter upon the memory. It was known to the schoolmen,[19 - Suarez, Disput. Metaphysicæ, disp. iii. sect. 3, tit. 3.] that, as the syllogism requires two premises, no science can proceed from a single first principle which cannot be the subject of further deduction, but must have several, at least two. The specially classifying sciences: Zoology, Botany, and also Physics and Chemistry, inasmuch as they refer all inorganic action to a few fundamental forces, have most subordination; history, on the other hand, has really none at all; for the general in it consists merely in the survey of the principal periods, from which, however, the particular events cannot be deduced, and are only subordinated to them according to time, but according to the concept are co-ordinate with them. Therefore, history, strictly speaking, is certainly rational knowledge, but is not science. In mathematics, according to Euclid's treatment, the axioms alone are indemonstrable first principles, and all demonstrations are in gradation strictly subordinated to them. But this method of treatment is not essential to mathematics, and in fact each proposition introduces quite a new space construction, which in itself is independent of those which precede it, and indeed can be completely comprehended from itself, quite independently of them, in the pure intuition or perception of space, in which the most complicated construction is just as directly evident as the axiom; but of this more fully hereafter. Meanwhile every mathematical proposition remains always a universal truth, which is valid for innumerable particular cases; and a graduated process from the simple to the complicated propositions which are to be deduced from them, is also essential to mathematics; therefore, in every respect mathematics is a science. The completeness of a science as such, that is, in respect of form, consists in there being as much subordination and as little co-ordination of the principles as possible. Scientific talent in general is, therefore, the faculty of subordinating the concept-spheres according to their different determinations, so that, as Plato repeatedly counsels, a science shall not be constituted by a general concept and an indefinite multiplicity immediately under it, but that knowledge shall descend by degrees from the general to the particular, through intermediate concepts and divisions, according to closer and closer definitions. In Kantian language this is called satisfying equally the law of homogeneity and that of specification. It arises from this peculiar nature of scientific completeness, that the aim of science is not greater certainty – for certainty may be possessed in just as high a degree by the most disconnected particular knowledge – but its aim is rather the facilitating of rational knowledge by means of its form, and the possibility of the completeness of rational knowledge which this form affords. It is therefore a very prevalent but perverted opinion that the scientific character of knowledge consists in its greater certainty, and just as false is the conclusion following from this, that, strictly speaking, the only sciences are mathematics and logic, because only in them, on account of their purely a priori character, is there unassailable certainty of knowledge. This advantage cannot be denied them, but it gives them no special claim to be regarded as sciences; for the special characteristic of science does not lie in certainty but in the systematic form of knowledge, based on the gradual descent from the general to the particular. The process of knowledge from the general to the particular, which is peculiar to the sciences, involves the necessity that in the sciences much should be established by deduction from preceding propositions, that is to say, by demonstration; and this has given rise to the old mistake that only what has been demonstrated is absolutely true, and that every truth requires a demonstration; whereas, on the contrary, every demonstration requires an undemonstrated truth, which ultimately supports it, or it may be, its own demonstration. Therefore a directly established truth is as much to be preferred to a truth established by demonstration as water from the spring is to water from the aqueduct. Perception, partly pure a priori, as it forms the basis of mathematics, partly empirical a posteriori, as it forms the basis of all the other sciences, is the source of all truth and the foundation of all science. (Logic alone is to be excepted, which is not founded upon perception but yet upon direct knowledge by the reason of its own laws.) Not the demonstrated judgments nor their demonstrations, but judgments which are created directly out of perception, and founded upon it rather than on any demonstrations, are to science what the sun is to the world; for all light proceeds from them, and lighted by their light the others give light also. To establish the truth of such primary judgments directly from perception, to raise such strongholds of science from the innumerable multitude of real objects, that is the work of the faculty of judgment, which consists in the power of rightly and accurately carrying over into abstract consciousness what is known in perception, and judgment is consequently the mediator between understanding and reason. Only extraordinary and exceptional strength of judgment in the individual can actually advance science; but every one who is possessed of a healthy reason is able to deduce propositions from propositions, to demonstrate, to draw conclusions. To lay down and make permanent for reflection, in suitable concepts, what is known through perception, so that, on the one hand, what is common to many real objects is thought through one concept, and, on the other hand, their points of difference are each thought through one concept, so that the different shall be known and thought as different in spite of a partial agreement, and the identical shall be known and thought as identical in spite of a partial difference, all in accordance with the end and intention which in each case is in view; all this is done by the faculty of judgment. Deficiency in judgment is silliness. The silly man fails to grasp, now the partial or relative difference of concepts which in one aspect are identical, now the identity of concepts which are relatively or partially different. To this explanation of the faculty of judgment, moreover, Kant's division of it into reflecting and subsuming judgment may be applied, according as it passes from the perceived objects to the concepts, or from the latter to the former; in both cases always mediating between empirical knowledge of the understanding and the reflective knowledge of the reason. There can be no truth which could be brought out by means of syllogisms alone; and the necessity of establishing truth by means of syllogisms is merely relative, indeed subjective. Since all demonstration is syllogistic, in the case of a new truth we must first seek, not for a demonstration, but for direct evidence, and only in the absence of such evidence is a demonstration to be temporarily made use of. No science is susceptible of demonstration throughout any more than a building can stand in the air; all its demonstrations must ultimately rest upon what is perceived, and consequently cannot be demonstrated, for the whole world of reflection rests upon and is rooted in the world of perception. All primal, that is, original, evidence is a perception, as the word itself indicates. Therefore it is either empirical or founded upon the perception a priori of the conditions of possible experience. In both cases it affords only immanent, not transcendent knowledge. Every concept has its worth and its existence only in its relation, sometimes very indirect, to an idea of perception; what is true of the concepts is also true of the judgments constructed out of them, and of all science. Therefore it must in some way be possible to know directly without demonstrations or syllogisms every truth that is arrived at through syllogisms and communicated by demonstrations. This is most difficult in the case of certain complicated mathematical propositions at which we only arrive by chains of syllogisms; for example, the calculation of the chords and tangents to all arcs by deduction from the proposition of Pythagoras. But even such a truth as this cannot essentially and solely rest upon abstract principles, and the space-relations which lie at its foundation also must be capable of being so presented a priori in pure intuition or perception that the truth of their abstract expression is directly established. But of mathematical demonstration we shall speak more fully shortly.

It is true we often hear men speak in a lofty strain of sciences which rest entirely upon correct conclusions drawn from sure premises, and which are consequently unassailable. But through pure logical reasoning, however true the premises may be, we shall never receive more than an articulate expression and exposition of what lies already complete in the premises; thus we shall only explicitly expound what was already implicitly understood. The esteemed sciences referred to are, however, specially the mathematical sciences, particularly astronomy. But the certainty of astronomy arises from the fact that it has for its basis the intuition or perception of space, which is given a priori, and is therefore infallible. All space-relations, however, follow from each other with a necessity (ground of being) which affords a priori certainty, and they can therefore be safely deduced from each other. To these mathematical properties we have only to add one force of nature, gravity, which acts precisely in relation to the masses and the square of the distance; and, lastly, the law of inertia, which follows from the law of causality and is therefore true a priori, and with it the empirical datum of the motion impressed, once for all, upon each of these masses. This is the whole material of astronomy, which both by its simplicity and its certainty leads to definite results, which are highly interesting on account of the vastness and importance of the objects. For example, if I know the mass of a planet and the distance of its satellite from it, I can tell with certainty the period of the revolution of the latter according to Kepler's second law. But the ground of this law is, that with this distance only this velocity will both chain the satellite to the planet and prevent it from falling into it. Thus it is only upon such a geometrical basis, that is, by means of an intuition or perception a priori, and also under the application of a law of nature, that much can be arrived at by means of syllogisms, for here they are merely like bridges from one sensuous apprehension to others; but it is not so with mere pure syllogistic reasoning in the exclusively logical method. The source of the first fundamental truths of astronomy is, however, properly induction, that is, the comprehension of what is given in many perceptions in one true and directly founded judgment. From this, hypotheses are afterwards constructed, and their confirmation by experience, as induction approaching to completeness, affords the proof of the first judgment. For example, the apparent motion of the planets is known empirically; after many false hypotheses with regard to the spacial connection of this motion (planetary course) the right one was at last found, then the laws which it obeyed (the laws of Kepler), and, lastly, the cause of these laws (universal gravitation), and the empirically known agreement of all observed cases with the whole of the hypotheses, and with their consequences, that is to say, induction, established them with complete certainty. The invention of the hypotheses was the work of the judgment, which rightly comprehended the given facts and expressed them accordingly; but induction, that is, a multitude of perceptions, confirmed their truth. But their truth could also be known directly, and by a single empirical perception, if we could pass freely through space and had telescopic eyes. Therefore, here also syllogisms are not the essential and only source of knowledge, but really only a makeshift.

As a third example taken from a different sphere we may mention that the so-called metaphysical truths, that is, such truths as those to which Kant assigns the position of the metaphysical first principles of natural science, do not owe their evidence to demonstration. What is a priori certain we know directly; as the form of all knowledge, it is known to us with the most complete necessity. For example, that matter is permanent, that is, can neither come into being nor pass away, we know directly as negative truth; for our pure intuition or perception of space and time gives the possibility of motion; in the law of causality the understanding affords us the possibility of change of form and quality, but we lack powers of the imagination for conceiving the coming into being or passing away of matter. Therefore that truth has at all times been evident to all men everywhere, nor has it ever been seriously doubted; and this could not be the case if it had no other ground of knowledge than the abstruse and exceedingly subtle proof of Kant. But besides this, I have found Kant's proof to be false (as is explained in the Appendix), and have shown above that the permanence of matter is to be deduced, not from the share which time has in the possibility of experience, but from the share which belongs to space. The true foundation of all truths which in this sense are called metaphysical, that is, abstract expressions of the necessary and universal forms of knowledge, cannot itself lie in abstract principles; but only in the immediate consciousness of the forms of the idea communicating itself in apodictic assertions a priori, and fearing no refutation. But if we yet desire to give a proof of them, it can only consist in showing that what is to be proved is contained in some truth about which there is no doubt, either as a part of it or as a presupposition. Thus, for example, I have shown that all empirical perception implies the application of the law of causality, the knowledge of which is hence a condition of all experience, and therefore cannot be first given and conditioned through experience as Hume thought. Demonstrations in general are not so much for those who wish to learn as for those who wish to dispute. Such persons stubbornly deny directly established insight; now only the truth can be consistent in all directions, and therefore we must show such persons that they admit under one form and indirectly, what they deny under another form and directly; that is, the logically necessary connection between what is denied and what is admitted.

It is also a consequence of the scientific form, the subordination of everything particular under a general, and so on always to what is more general, that the truth of many propositions is only logically proved, – that is, through their dependence upon other propositions, through syllogisms, which at the same time appear as proofs. But we must never forget that this whole form of science is merely a means of rendering knowledge more easy, not a means to greater certainty. It is easier to discover the nature of an animal, by means of the species to which it belongs, and so on through the genus, family, order, and class, than to examine on every occasion the animal presented to us: but the truth of all propositions arrived at syllogistically is always conditioned by and ultimately dependent upon some truth which rests not upon reasoning but upon perception. If this perception were always as much within our reach as a deduction through syllogisms, then it would be in every respect preferable. For every deduction from concepts is exposed to great danger of error, on account of the fact we have considered above, that so many spheres lie partly within each other, and that their content is often vague or uncertain. This is illustrated by a multitude of demonstrations of false doctrines and sophisms of every kind. Syllogisms are indeed perfectly certain as regards form, but they are very uncertain on account of their matter, the concepts. For, on the one hand, the spheres of these are not sufficiently sharply defined, and, on the other hand, they intersect each other in so many ways that one sphere is in part contained in many others, and we may pass at will from it to one or another of these, and from this sphere again to others, as we have already shown. Or, in other words, the minor term and also the middle can always be subordinated to different concepts, from which we may choose at will the major and the middle, and the nature of the conclusion depends on this choice. Consequently immediate evidence is always much to be preferred to reasoned truth, and the latter is only to be accepted when the former is too remote, and not when it is as near or indeed nearer than the latter. Accordingly we saw above that, as a matter of fact, in the case of logic, in which the immediate knowledge in each individual case lies nearer to hand than deduced scientific knowledge, we always conduct our thought according to our immediate knowledge of the laws of thought, and leave logic unused.[20 - Cf. Ch. 12 of Supplement.]

§ 15. If now with our conviction that perception is the primary source of all evidence, and that only direct or indirect connection with it is absolute truth; and further, that the shortest way to this is always the surest, as every interposition of concepts means exposure to many deceptions; if, I say, we now turn with this conviction to mathematics, as it was 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 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 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, φαινομενον,[21 - The reader must not think here of Kant's misuse of these Greek terms, which is condemned in the Appendix.] and what is thought, νουμενον, 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 (φαινομενον), but all the rest he based upon reasoning (νουμενον). 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 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 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 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: “Ακριβεστερα δ᾽ επιστημη επιστημης και προτερα, ἡτε του ὁτι και του διοτι ἡ αυτη, αλλα μη χωρις του ὁτι, της του διοτι” (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 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 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 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 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 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 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](r^b) so that we do not perform them, but merely symbolise them.

We might establish truth in geometry also, through pure 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 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 - 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.]

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, 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 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 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 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 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 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 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 three following examples, which may be taken as types or representatives of the three 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 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 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 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 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, 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 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 only added as a confirmation of their truth. This problem itself can only become quite clear in being solved.[23 - Cf. Ch. 17 of Supplement.]

§ 16. After this full consideration of reason as a special faculty of knowledge belonging to man alone, and the results and phenomena peculiar to human nature brought about by it, it still remains for me to speak of reason, so far as it is the guide of human action, and in this respect may be called practical. But what there is to say upon this point has found its place elsewhere in the appendix to this work, where I controvert the existence of the so-called practical reason of Kant, which he (certainly very conveniently) explained as the immediate source of virtue, and as the seat of an absolute (i. e., fallen from heaven) imperative. The detailed and thorough refutation of this Kantian principle of morality I have given later in the “Fundamental Problems of Ethics.” There remains, therefore, but little for me to say here about the actual influence of reason, in the true sense of the word, upon action. At the commencement of our treatment of reason we remarked, in general terms, how much the action and behaviour of men differs from that of brutes, and that this difference is to be regarded as entirely due to the presence of abstract concepts in consciousness. The influence of these upon our whole existence is so penetrating and significant that, on account of them, we are related to the lower animals very much as those animals that see are related to those that have no eyes (certain larvae, worms, and zoophytes). Animals without eyes know only by touch what is immediately present to them in space, what comes into contact with them; those which see, on the contrary, know a wide circle of near and distant objects. In the same way the absence of reason confines the lower animals to the ideas of perception, i. e., the real objects which are immediately present to them in time; we, on the contrary, on account of knowledge in the abstract, comprehend not only the narrow actual present, but also the whole past and future, and the wide sphere of the possible; we view life freely on all its sides, and go far beyond the present and the actual. Thus what the eye is in space and for sensuous knowledge, reason is, to a certain extent, in time and for inner knowledge. But as the visibility of objects has its worth and meaning only in the fact that it informs us of their tangibility, so the whole worth of abstract knowledge always consists in its relation to what is perceived. Therefore men naturally attach far more worth to immediate and perceived knowledge than to abstract concepts, to that which is merely thought; they place empirical knowledge before logical. But this is not the opinion of men who live more in words than in deeds, who have seen more on paper and in books than in actual life, and who in their greatest degeneracy become pedants and lovers of the mere letter. Thus only is it conceivable that Leibnitz and Wolf and all their successors could go so far astray as to explain knowledge of perception, after the example of Duns Scotus, as merely confused abstract knowledge! To the honour of Spinoza, I must mention that his truer sense led him, on the contrary, to explain all general concepts as having arisen from the confusion of that which was known in perception (Eth. II., prop. 40, Schol. 1). It is also a result of perverted opinion that in mathematics the evidence proper to it was rejected, and logical evidence alone accepted; that everything in general which was not abstract knowledge was comprehended under the wide name of feeling, and consequently was little valued; and lastly that the Kantian ethics regarded the good will which immediately asserts itself upon knowledge of the circumstances, and guides to right and good action as mere feeling and emotion, and consequently as worthless and without merit, and would only recognise actions which proceed from abstract maxims as having moral worth.

The many-sided view of life as a whole which man, as distinguished from the lower animals, possesses through reason, may be compared to a geometrical, colourless, abstract, reduced plan of his actual life. He, therefore, stands to the lower animals as the navigator who, by means of chart, compass, and quadrant, knows accurately his course and his position at any time upon the sea, stands to the uneducated sailors who see only the waves and the heavens. Thus it is worth noticing, and indeed wonderful, how, besides his life in the concrete, man always lives another life in the abstract. In the former he is given as a prey to all the storms of actual life, and to the influence of the present; he must struggle, suffer, and die like the brute. But his life in the abstract, as it lies before his rational consciousness, is the still reflection of the former, and of the world in which he lives; it is just that reduced chart or plan to which we have referred. Here in the sphere of quiet deliberation, what completely possessed him and moved him intensely before, appears to him cold, colourless, and for the moment external to him; he is merely the spectator, the observer. In respect of this withdrawal into reflection he may be compared to an actor who has played his part in one scene, and who takes his place among the audience till it is time for him to go upon the stage again, and quietly looks on at whatever may happen, even though it be the preparation for his own death (in the piece), but afterwards he again goes on the stage and acts and suffers as he must. From this double life proceeds that quietness peculiar to human beings, so very different from the thoughtlessness of the brutes, and with which, in accordance with previous reflection, or a formed determination, or a recognised necessity, a man suffers or accomplishes in cold blood, what is of the utmost and often terrible importance to him; suicide, execution, the duel, enterprises of every kind fraught with danger to life, and, in general, things against which his whole animal nature rebels. Under such circumstances we see to what an extent reason has mastered the animal nature, and we say to the strong: σιδηρειον νυ τοι ἡτορ! (ferreum certe tibi cor), Il. 24, 521. Here we can say truly that reason manifests itself practically, and thus wherever action is guided by reason, where the motives are abstract concepts, wherever we are not determined by particular ideas of perception, nor by the impression of the moment which guides the brutes, there practical reason shows itself. But I have fully explained in the Appendix, and illustrated by examples, that this is entirely different from and unrelated to the ethical worth of actions; that rational action and virtuous action are two entirely different things; that reason may just as well find itself in connection with great evil as with great good, and by its assistance may give great power to the one as well as to the other; that it is equally ready and valuable for the methodical and consistent carrying out of the noble and of the bad intention, of the wise as of the foolish maxim; which all results from the constitution of its nature, which is feminine, receptive, retentive, and not spontaneous; all this I have shown in detail in the Appendix, and illustrated by examples. What is said there would have been placed here, but on account of my polemic against Kant's pretended practical reason I have been obliged to relegate it to the Appendix, to which I therefore refer.

The ideal explained in the Stoical philosophy is the most complete development of practical reason in the true and genuine sense of the word; it is the highest summit to which man can attain by the mere use of his reason, and in it his difference from the brutes shows itself most distinctly. For the ethics of Stoicism are originally and essentially, not a doctrine of virtue, but merely a guide to a rational life, the end and aim of which is happiness through peace of mind. Virtuous conduct appears in it as it were merely by accident, as the means, not as the end. Therefore the ethical theory of Stoicism is in its whole nature and point of view fundamentally different from the ethical systems which lay stress directly upon virtue, such as the doctrines of the Vedas, of Plato, of Christianity, and of Kant. The aim of Stoical ethics is happiness: τελος το ευδαι μονειν (virtutes omnes finem habere beatitudinem) it is called in the account of the Stoa by Stobæus (Ecl., L. ii. c. 7, p. 114, and also p. 138). Yet the ethics of Stoicism teach that happiness can only be attained with certainty through inward peace and quietness of spirit (αταραξια), and that this again can only be reached through virtue; this is the whole meaning of the saying that virtue is the highest good. But if indeed by degrees the end is lost sight of in the means, and virtue is inculcated in a way which discloses an interest entirely different from that of one's own happiness, for it contradicts this too distinctly; this is just one of those inconsistencies by means of which, in every system, the immediately known, or, as it is called, felt truth leads us back to the right way in defiance of syllogistic reasoning; as, for example, we see clearly in the ethical teaching of Spinoza, which deduces a pure doctrine of virtue from the egoistical suum utile quærere by means of palpable sophisms. According to this, as I conceive the spirit of the Stoical ethics, their source lies in the question whether the great prerogative of man, reason, which, by means of planned action and its results, relieves life and its burdens so much, might not also be capable of freeing him at once, directly, i. e., through mere knowledge, completely, or nearly so, of the sorrows and miseries of every kind of which his life is full. They held that it was not in keeping with the prerogative of reason that the nature given with it, which by means of it comprehends and contemplates an infinity of things and circumstances, should yet, through the present, and the accidents that can be contained in the few years of a life that is short, fleeting, and uncertain, be exposed to such intense pain, to such great anxiety and suffering, as arise from the tempestuous strain of the desires and the antipathies; and they believed that the due application of reason must raise men above them, and can make them invulnerable. Therefore Antisthenes says: Δει κτασθαι νουν, η βροχον (aut mentem parandam, aut laqueum. Plut. de stoic. repugn., c. 14), i. e., life is so full of troubles and vexations, that one must either rise above it by means of corrected thoughts, or leave it. It was seen that want and suffering did not directly and of necessity spring from not having, but from desiring to have and not having; that therefore this desire to have is the necessary condition under which alone it becomes a privation not to have and begets pain. Ου πενια λυπην εργαζεται, αλλα επιθυμια (non paupertas dolorem efficit, sed cupiditas), Epict., fragm. 25. Men learned also from experience that it is only the hope of what is claimed that begets and nourishes the wish; therefore neither the many unavoidable evils which are common to all, nor unattainable blessings, disquiet or trouble us, but only the trifling more or less of those things which we can avoid or attain; indeed, not only what is absolutely unavoidable or unattainable, but also what is merely relatively so, leaves us quite undisturbed; therefore the ills that have once become joined to our individuality, or the good things that must of necessity always be denied us, are treated with indifference, in accordance with the peculiarity of human nature that every wish soon dies and can no more beget pain if it is not nourished by hope. It followed from all this that happiness always depends upon the proportion between our claims and what we receive. It is all one whether the quantities thus related be great or small, and the proportion can be established just as well by diminishing the amount of the first as by increasing the amount of the second; and in the same way it also follows that all suffering proceeds from the want of proportion between what we demand and expect and what we get. Now this want of proportion obviously lies only in knowledge, and it could be entirely abolished through fuller insight.[24 - Omnes perturbationes judicio censent fieri et opinione. Cic. Tusc., 4, 6. Ταρασσει τους ανθρωπους ου τα πραγματα, αλλα τα περι των πραγματων δογματα (Perturbant homines non res ipsæ, sed de rebus opiniones). Epictet., c. v.] Therefore Chrysippus says: δει ζῃν κατ᾽ εμπειριαν των φυσει συμβαινοντων (Stob. Ecl., L. ii. c. 7, p. 134), that is, one ought to live with a due knowledge of the transitory nature of the things of the world. For as often as a man loses self-command, or is struck down by a misfortune, or grows angry, or becomes faint-hearted, he shows that he finds things different from what he expected, consequently that he was caught in error, and did not know the world and life, did not know that the will of the individual is crossed at every step by the chance of inanimate nature and the antagonism of aims and the wickedness of other individuals: he has therefore either not made use of his reason in order to arrive at a general knowledge of this characteristic of life, or he lacks judgment, in that he does not recognise in the particular what he knows in general, and is therefore surprised by it and loses his self-command.[25 - Τουτο γαρ εστι το αιτιον τοις ανθρωποις παντων των κακων, το τας προληψεις τας κοινας μη δυνασθαι εφαρμοξειν ταις επι μερους (Hæc est causa mortalibus omnium malorum, non posse communes notiones aptare singularibus). Epict. dissert., ii., 26.] Thus also every keen pleasure is an error and an illusion, for no attained wish can give lasting satisfaction; and, moreover, every possession and every happiness is but lent by chance for an uncertain time, and may therefore be demanded back the next hour. All pain rests on the passing away of such an illusion; thus both arise from defective knowledge; the wise man therefore holds himself equally aloof from joy and sorrow, and no event disturbs his αταραξια.