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(3.) A sphere includes two or more spheres which exclude each other and fill it.

(4.) Two spheres include each a part of the other.

(5.) Two spheres lie in a third, but do not fill it.

This last case applies to all concepts whose spheres have nothing immediately in common, for there is always a third sphere, often a much wider one, which includes both.

To these cases all combinations of concepts may be referred, and from them the entire doctrine of the judgment, its conversion, contraposition, equipollence, disjunction (this according to the third figure) may be deduced. [pg 057]From these also may be derived the properties of the judgment, upon which Kant based his pretended categories of the understanding, with the exception however of the hypothetical form, which is not a combination of concepts, but of judgments. A full account is given in the Appendix of “Modality,” and indeed of every property of judgments on which the categories are founded.

With regard to the possible combinations of concepts which we have given, it has only further to be remarked that they may also be combined with each other in many ways. For example, the fourth figure with the second. Only if one sphere, which partly or wholly contains another, is itself contained in a third sphere, do these together exemplify the syllogism in the first figure, i.e., that combination of judgments, by means of which it is known that a concept which is partly or wholly contained in another concept, is also contained in a third concept, which again contains the first: and also, conversely, the negation; the pictorial representation of which can, of course, only be two connected spheres which do not lie within a third sphere. If many spheres are brought together in this way we get a long train of syllogisms. This schematism of concepts, which has already been fairly well explained in more than one textbook, may be used as the foundation of the doctrine of the judgment, and indeed of the whole syllogistic theory, and in this way the treatment of both becomes very easy and simple. Because, through it, all syllogistic rules may be seen in their origin, and may be deduced and explained. It is not necessary, however, to load the memory with these rules, as logic is never of practical use, but has only a theoretical interest for philosophy. For although it may be said that logic is related to rational thinking as thorough-bass is to music, or less exactly, as ethics is to virtue, or æsthetics to art; we must yet remember that no one ever became an artist by the study of æsthetics; that a noble character was never [pg 058]formed by the study of ethics; that long before Rameau, men composed correctly and beautifully, and that we do not need to know thorough-bass in order to detect discords: and just as little do we need to know logic in order to avoid being misled by fallacies. Yet it must be conceded that thorough-bass is of the greatest use in the practice of musical composition, although it may not be necessary for the understanding of it; and indeed æsthetics and even ethics, though in a much less degree, and for the most part negatively, may be of some use in practice, so that we cannot deny them all practical worth, but of logic even this much cannot be conceded. It is nothing more than the knowledge in the abstract of what every one knows in the concrete. Therefore we call in the aid of logical rules, just as little to enable us to construct a correct argument as to prevent us from consenting to a false one, and the most learned logician lays aside the rules of logic altogether in his actual thought. This may be explained in the following way. Every science is a system of general and therefore abstract truths, laws, and rules with reference to a special class of objects. The individual case coming under these laws is determined in accordance with this general knowledge, which is valid once for all; because such application of the general principle is far easier than the exhaustive investigation of the particular case; for the general abstract knowledge which has once been obtained is always more within our reach than the empirical investigation of the particular case. With logic, however, it is just the other way. It is the general knowledge of the mode of procedure of the reason expressed in the form of rules. It is reached by the introspection of reason, and by abstraction from all content. But this mode of procedure is necessary and essential to reason, so that it will never depart from it if left to itself. It is, therefore, easier and surer to let it proceed itself according to its nature in each particular case, than to [pg 059]present to it the knowledge abstracted from this procedure in the form of a foreign and externally given law. It is easier, because, while in the case of all other sciences, the general rule is more within our reach than the investigation of the particular case taken by itself; with the use of reason, on the contrary, its necessary procedure in a given case is always more within our reach than the general rule abstracted from it; for that which thinks in us is reason itself. It is surer, because a mistake may more easily occur in such abstract knowledge, or in its application, than that a process of reason should take place which would run contrary to its essence and nature. Hence arises the remarkable fact, that while in other sciences the particular case is always proved by the rule, in logic, on the contrary, the rule must always be proved from the particular case; and even the most practised logician, if he remark that in some particular case he concludes otherwise than the rule prescribes, will always expect to find a mistake in the rule rather than in his own conclusion. To desire to make practical use of logic means, therefore, to desire to derive with unspeakable trouble, from general rules, that which is immediately known with the greatest certainty in the particular case. It is just as if a man were to consult mechanics as to the motion of his body, and physiology as to his digestion; and whoever has learnt logic for practical purposes is like him who would teach a beaver to make its own dam. Logic is, therefore, without practical utility; but it must nevertheless be retained, because it has philosophical interest as the special knowledge of the organisation and action of reason. It is rightly regarded as a definite, self-subsisting, self-contained, complete, and thoroughly safe discipline; to be treated scientifically for itself alone and independently of everything else, and therefore to be studied at the universities. But it has its real value, in relation to philosophy as a whole, in the inquiry into the nature of knowledge, and indeed of [pg 060]rational and abstract knowledge. Therefore the exposition of logic should not have so much the form of a practical science, should not contain merely naked arbitrary rules for the correct formation of the judgment, the syllogism, &c., but should rather be directed to the knowledge of the nature of reason and the concept, and to the detailed investigation of the principle of sufficient reason of knowing. For logic is only a paraphrase of this principle, and, more exactly, only of that exemplification of it in which the ground that gives truth to the judgment is neither empirical nor metaphysical, but logical or metalogical. Besides the principle of sufficient reason of knowing, it is necessary to take account of the three remaining fundamental laws of thought, or judgments of metalogical truth, so nearly related to it; and out of these the whole science of reason grows. The nature of thought proper, that is to say, of the judgment and the syllogism, must be exhibited in the combination of the spheres of concepts, according to the analogy of the special schema, in the way shown above; and from all this the rules of the judgment and the syllogism are to be deduced by construction. The only practical use we can make of logic is in a debate, when we can convict our antagonist of his intentional fallacies, rather than of his actual mistakes, by giving them their technical names. By thus throwing into the background the practical aim of logic, and bringing out its connection with the whole scheme of philosophy as one of its chapters, we do not think that we shall make the study of it less prevalent than it is just now. For at the present day every one who does not wish to remain uncultured, and to be numbered with the ignorant and incompetent multitude, must study speculative philosophy. For the nineteenth century is a philosophical age, though by this we do not mean either that it has philosophy, or that philosophy governs it, but rather that it is ripe for philosophy, and, therefore, stands in need of it. This is a sign of a high [pg 061]degree of civilisation, and indeed, is a definite stage in the culture of the ages.¹⁴

Though logic is of so little practical use, it cannot be denied that it was invented for practical purposes. It appears to me to have originated in the following way:—As the love of debating developed among the Eleatics, the Megarics, and the Sophists, and by degrees became almost a passion, the confusion in which nearly every debate ended must have made them feel the necessity of a method of procedure as a guide; and for this a scientific dialectic had to be sought. The first thing which would have to be observed would be that both the disputing parties should always be agreed on some one proposition, to which the disputed points might be referred. The beginning of the methodical procedure consisted in this, that the propositions admitted on both sides were formally stated to be so, and placed at the head of the inquiry. But these propositions were at first concerned only with the material of the inquiry. It was soon observed that in the process of going back to the truth admitted on both sides, and of deducing their assertions from it, each party followed certain forms and laws about which, without any express agreement, there was no difference of opinion. And from this it became evident that these must constitute the peculiar and natural procedure of reason itself, the form of investigation. Although this was not exposed to any doubt or difference of opinion, some pedantically systematic philosopher hit upon the idea that it would look well, and be the completion of the method of dialectic, if this formal part of all discussion, this regular procedure of reason itself, were to be expressed in abstract propositions, just like the substantial propositions admitted on both sides, and placed at the beginning of every investigation, as the fixed canon of debate to which reference and appeal must always be made. In this [pg 062]way what had formerly been followed only by tacit agreement, and instinctively, would be consciously recognised and formally expressed. By degrees, more or less perfect expressions were found for the fundamental principles of logic, such as the principles of contradiction, sufficient reason, excluded middle, the dictum de omni et nullo, as well as the special rules of the syllogism, as for example, ex meris particularibus aut negativis nihil sequitur, a rationato ad rationem non valet consequentia, and so on. That all this was only brought about slowly, and with great pains, and up till the time of Aristotle remained very incomplete, is evident from the awkward and tedious way in which logical truths are brought out in many of the Platonic dialogues, and still more from what Sextus Empiricus tells us of the controversies of the Megarics, about the easiest and simplest logical rules, and the laborious way in which they were brought into a definite form (Sext. Emp. adv. Math. l. 8, p. 112). But Aristotle collected, arranged, and corrected all that had been discovered before his time, and brought it to an incomparably greater state of perfection. If we thus observe how the course of Greek culture had prepared the way for, and led up to the work of Aristotle, we shall be little inclined to believe the assertion of the Persian author, quoted by Sir William Jones with much approval, that Kallisthenes found a complete system of logic among the Indians, and sent it to his uncle Aristotle (Asiatic Researches, vol. iv. p. 163). It is easy to understand that in the dreary middle ages the Aristotelian logic would be very acceptable to the controversial spirit of the schoolmen, which, in the absence of all real knowledge, spent its energy upon mere formulas and words, and that it would be eagerly adopted even in its mutilated Arabian form, and presently established as the centre of all knowledge. Though its authority has since declined, yet up to our own time logic has retained the credit of a self-contained, practical, and highly important [pg 063]science. Indeed, in our own day, the Kantian philosophy, the foundation-stone of which is taken from logic, has excited a new interest in it; which, in this respect, at any rate, that is, as the means of the knowledge of the nature of reason, it deserves.

Correct and accurate conclusions may be arrived at if we carefully observe the relation of the spheres of concepts, and only conclude that one sphere is contained in a third sphere, when we have clearly seen that this first sphere is contained in a second, which in its turn is contained in the third. On the other hand, the art of sophistry lies in casting only a superficial glance at the relations of the spheres of the concepts, and then manipulating these relations to suit our purposes, generally in the following way:—When the sphere of an observed concept lies partly within that of another concept, and partly within a third altogether different sphere, we treat it as if it lay entirely within the one or the other, as may suit our purpose. For example, in speaking of passion, we may subsume it under the concept of the greatest force, the mightiest agency in the world, or under the concept of the irrational, and this again under the concept of impotency or weakness. We may then repeat the process, and start anew with each concept to which the argument leads us. A concept has almost always several others, which partially come under it, and each of these contains part of the sphere of the first, but also includes in its own sphere something more, which is not in the first. But we draw attention only to that one of these latter concepts, under which we wish to subsume the first, and let the others remain unobserved, or keep them concealed. On the possession of this skill depends the whole art of sophistry and all finer fallacies; for logical fallacies such as mentiens, velatus, cornatus, &c., are clearly too clumsy for actual use. I am not aware that hitherto any one has traced the nature of all sophistry and persuasion back to this last [pg 064]possible ground of its existence, and referred it to the peculiar character of concepts, i.e., to the procedure of reason itself. Therefore, as my exposition has led me to it, though it is very easily understood, I will illustrate it in the following table by means of a schema. This table is intended to show how the spheres of concepts overlap each other at many points, and so leave room for a passage from each concept to whichever one we please of several other concepts. I hope, however, that no one will be led by this table to attach more importance to this little explanation, which I have merely given in passing, than ought to belong to it, from the nature of the subject. I have chosen as an illustration the concept of travelling. Its sphere partially includes four others, to any of which the sophist may pass at will; these again partly include other spheres, several of them two or more at once, and through these the sophist takes whichever way he chooses, always as if it were the only way, till at last he reaches, in good or evil, whatever end he may have in view. In passing from one sphere to another, it is only necessary always to follow the direction from the centre (the given chief concept) to the circumference, and never to reverse this process. Such a piece of sophistry may be either an unbroken speech, or it may assume the strict syllogistic form, according to what is the weak side of the hearer. Most scientific arguments, and especially philosophical demonstrations, are at bottom not much more than this, for how else would it be possible, that so much, in different ages, has not only been falsely apprehended (for error itself has a different source), but demonstrated and proved, and has yet afterwards been found to be fundamentally wrong, for example, the Leibnitz-Wolfian Philosophy, Ptolemaic Astronomy, Stahl's Chemistry, Newton's Theory of Colours, &c. &c.¹⁵

§ 10. Through all this, the question presses ever more upon us, how certainty is to be attained, how judgments [pg 065]are to be established, what constitutes rational knowledge, (wissen), andscience, which we rank with language and deliberate action as the third great benefit conferred by reason.

Reason is feminine in nature; it can only give after it has received. Of itself it has nothing but the empty forms of its operation. There is no absolutely pure rational knowledge except the four principles to which I have attributed metalogical truth; the principles of identity, contradiction, excluded middle, and sufficient reason of knowledge. For even the rest of logic is not absolutely pure rational knowledge. It presupposes the relations and the combinations of the spheres of concepts. But concepts in general only exist after experience of ideas of perception, and as their whole nature consists in their relation to these, it is clear that they presuppose them. No special content, however, is presupposed, but merely the existence of a content generally, and so logic as a whole may fairly pass for pure rational science. In all other sciences reason has received its content from ideas of perception; in mathematics from the relations of space and time, presented in intuition or perception prior to all experience; in pure natural science, that is, in what we know of the course of nature prior to any experience, the content of the science proceeds from the pure understanding, i.e., from the a priori knowledge of the law of causality and its connection with those pure intuitions or perceptions of space and time. In all other sciences everything that is not derived from the sources we have just referred to belongs to experience. Speaking generally, to know rationally (wissen) means to have in the power of the mind, and capable of being reproduced at will, such judgments as have their sufficient ground of knowledge in something outside themselves, i.e., are true. Thus only abstract cognition isrational knowledge (wissen), which is therefore the result of reason, so that we cannot accurately say of the lower animals that they rationally [pg 066]know (wissen) anything, although they have apprehension of what is presented in perception, and memory of this, and consequently imagination, which is further proved by the circumstance that they dream. We attribute consciousness to them, and therefore although the word (bewusstsein) is derived from the verb to know rationally (wissen), the conception of consciousness corresponds generally with that of idea of whatever kind it may be. Thus we attribute life to plants, but not consciousness. Rational knowledge (wissen) is therefore abstract consciousness, the permanent possession in concepts of the reason, of what has become known in another way.

§ 11. In this regard the direct opposite of rational knowledge is feeling, and therefore we must insert the explanation of feeling here. The concept which the word feeling denotes has merely a negative content, which is this, that something which is present in consciousness, is not a concept, is not abstract rational knowledge. Except this, whatever it may be, it comes under the concept of feeling. Thus the immeasurably wide sphere of the concept of feeling includes the most different kinds of objects, and no one can ever understand how they come together until he has recognised that they all agree in this negative respect, that they are not abstract concepts. For the most diverse and even antagonistic elements lie quietly side by side in this concept; for example, religious feeling, feeling of sensual pleasure, moral feeling, bodily feeling, as touch, pain, sense of colour, of sounds and their harmonies and discords, feeling of hate, of disgust, of self-satisfaction, of honour, of disgrace, of right, of wrong, sense of truth, æsthetic feeling, feeling of power, weakness, health, friendship, love, &c. &c. There is absolutely nothing in common among them except the negative quality that they are not abstract rational knowledge. But this diversity becomes more striking when the apprehension of space relations presented a priori in perception, and also the [pg 067]knowledge of the pure understanding is brought under this concept, and when we say of all knowledge and all truth, of which we are first conscious only intuitively, and have not yet formulated in abstract concepts, we feel it. I should like, for the sake of illustration, to give some examples of this taken from recent books, as they are striking proofs of my theory. I remember reading in the introduction to a German translation of Euclid, that we ought to make beginners in geometry draw the figures before proceeding to demonstrate, for in this way they would already feel geometrical truth before the demonstration brought them complete knowledge. In the same way Schleiermacher speaks in his “Critique of Ethics” of logical and mathematical feeling (p. 339), and also of the feeling of the sameness or difference of two formulas (p. 342). Again Tennemann in his “History of Philosophy” (vol. I., p. 361) says, “One felt that the fallacies were not right, but could not point out the mistakes.” Now, so long as we do not regard this concept “feeling” from the right point of view, and do not recognise that one negative characteristic which alone is essential to it, it must constantly give occasion for misunderstanding and controversy, on account of the excessive wideness of its sphere, and its entirely negative and very limited content which is determined in a purely one-sided manner. Since then we have in German the nearly synonymous word empfindung(sensation), it would be convenient to make use of it for bodily feeling, as a sub-species. This concept “feeling,” which is quite out of proportion to all others, doubtless originated in the following manner. All concepts, and concepts alone, are denoted by words; they exist only for the reason, and proceed from it. With concepts, therefore, we are already at a one-sided point of view; but from such a point of view what is near appears distinct and is set down as positive, what is farther off becomes mixed up and is soon regarded as merely [pg 068]negative. Thus each nation calls all others foreign: to the Greek all others are barbarians; to the Englishman all that is not England or English is continent or continental; to the believer all others are heretics, or heathens; to the noble all others are roturiers; to the student all others are Philistines, and so forth. Now, reason itself, strange as it may seem, is guilty of the same one-sidedness, indeed one might say of the same crude ignorance arising from vanity, for it classes under the one concept, “feeling,” every modification of consciousness which does not immediately belong to its own mode of apprehension, that is to say, which is not an abstract concept. It has had to pay the penalty of this hitherto in misunderstanding and confusion in its own province, because its own procedure had not become clear to it through thorough self-knowledge, for a special faculty of feeling has been set up, and new theories of it are constructed.

§ 12. Rational knowledge (wissen) is then all abstract knowledge,—that is, the knowledge which is peculiar to the reason as distinguished from the understanding. Its contradictory opposite has just been explained to be the concept “feeling.” Now, as reason only reproduces, for knowledge, what has been received in another way, it does not actually extend our knowledge, but only gives it another form. It enables us to know in the abstract and generally, what first became known in sense-perception, in the concrete. But this is much more important than it appears at first sight when so expressed. For it depends entirely upon the fact that knowledge has become rational or abstract knowledge (wissen), that it can be safely preserved, that it is communicable and susceptible of certain and wide-reaching application to practice. Knowledge in the form of sense-perception is valid only of the particular case, extends only to what is nearest, and ends with it, for sensibility and understanding can only comprehend one object at a time. Every [pg 069]enduring, arranged, and planned activity must therefore proceed from principles,—that is, from abstract knowledge, and it must be conducted in accordance with them. Thus, for example, the knowledge of the relation of cause and effect arrived at by the understanding, is in itself far completer, deeper and more exhaustive than anything that can be thought about it in the abstract; the understanding alone knows in perception directly and completely the nature of the effect of a lever, of a pulley, or a cog-wheel, the stability of an arch, and so forth. But on account of the peculiarity of the knowledge of perception just referred to, that it only extends to what is immediately present, the mere understanding can never enable us to construct machines and buildings. Here reason must come in; it must substitute abstract concepts for ideas of perception, and take them as the guide of action; and if they are right, the anticipated result will happen. In the same way we have perfect knowledge in pure perception of the nature and constitution of the parabola, hyperbola, and spiral; but if we are to make trustworthy application of this knowledge to the real, it must first become abstract knowledge, and by this it certainly loses its character of intuition or perception, but on the other hand it gains the certainty and preciseness of abstract knowledge. The differential calculus does not really extend our knowledge of the curve, it contains nothing that was not already in the mere pure perception of the curve; but it alters the kind of knowledge, it changes the intuitive into an abstract knowledge, which is so valuable for application. But here we must refer to another peculiarity of our faculty of knowledge, which could not be observed until the distinction between the knowledge of the senses and understanding and abstract knowledge had been made quite clear. It is this, that relations of space cannot as such be directly translated into abstract knowledge, but only temporal quantities,—that is, numbers, are suitable for this. [pg 070]Numbers alone can be expressed in abstract concepts which accurately correspond to them, not spacial quantities. The concept “thousand”is just as different from the concept “ten,” as both these temporal quantities are in perception. We think of a thousand as a distinct multiple of ten, into which we can resolve it at pleasure for perception in time,—that is to say, we can count it. But between the abstract concept of a mile and that of a foot, apart from any concrete perception of either, and without the help of number, there is no accurate distinction corresponding to the quantities themselves. In both we only think of a spacial quantity in general, and if they must be completely distinguished we are compelled either to call in the assistance of intuition or perception in space, which would be a departure from abstract knowledge, or we must think the difference in numbers. If then we wish to have abstract knowledge of space-relations we must first translate them into time-relations,—that is, into numbers; therefore only arithmetic, and not geometry, is the universal science of quantity, and geometry must be translated into arithmetic if it is to be communicable, accurately precise and applicable in practice. It is true that a space-relation as such may also be thought in the abstract; for example, “the sine increases as the angle,” but if the quantity of this relation is to be given, it requires number for its expression. This necessity, that if we wish to have abstract knowledge of space-relations (i.e., rational knowledge, not mere intuition or perception), space with its three dimensions must be translated into time which has only one dimension, this necessity it is, which makes mathematics so difficult. This becomes very clear if we compare the perception of curves with their analytical calculation, or the table of logarithms of the trigonometrical functions with the perception of the changing relations of the parts of a triangle, which are expressed by them. What vast mazes of figures, what laborious calculations [pg 071]it would require to express in the abstract what perception here apprehends at a glance completely and with perfect accuracy, namely, how the co-sine diminishes as the sine increases, how the co-sine of one angle is the sine of another, the inverse relation of the increase and decrease of the two angles, and so forth. How time, we might say, must complain, that with its one dimension it should be compelled to express the three dimensions of space! Yet this is necessary if we wish to possess, for application, an expression, in abstract concepts, of space-relations. They could not be translated directly into abstract concepts, but only through the medium of the pure temporal quantity, number, which alone is directly related to abstract knowledge. Yet it is worthy of remark, that as space adapts itself so well to perception, and by means of its three dimensions, even its complicated relations are easily apprehended, while it eludes the grasp of abstract knowledge; time, on the contrary, passes easily into abstract knowledge, but gives very little to perception. Our perceptions of numbers in their proper element, mere time, without the help of space, scarcely extends as far as ten, and beyond that we have only abstract concepts of numbers, no knowledge of them which can be presented in perception. On the other hand, we connect with every numeral, and with all algebraical symbols, accurately defined abstract concepts.

We may further remark here that some minds only find full satisfaction in what is known through perception. What they seek is the reason and consequent of being in space, sensuously expressed; a demonstration after the manner of Euclid, or an arithmetical solution of spacial problems, does not please them. Other minds, on the contrary, seek merely the abstract concepts which are needful for applying and communicating knowledge. They have patience and memory for abstract principles, formulas, demonstrations in long trains of reasoning, and calculations, in which the symbols represent the most [pg 072]complicated abstractions. The latter seek preciseness, the former sensible perception. The difference is characteristic.

The greatest value of rational or abstract knowledge is that it can be communicated and permanently retained. It is principally on this account that it is so inestimably important for practice. Any one may have a direct perceptive knowledge through the understanding alone, of the causal connection, of the changes and motions of natural bodies, and he may find entire satisfaction in it; but he cannot communicate this knowledge to others until it has been made permanent for thought in concepts. Knowledge of the first kind is even sufficient for practice, if a man puts his knowledge into practice himself, in an action which can be accomplished while the perception is still vivid; but it is not sufficient if the help of others is required, or even if the action is his own but must be carried out at different times, and therefore requires a pre-conceived plan. Thus, for example, a practised billiard-player may have a perfect knowledge of the laws of the impact of elastic bodies upon each other, merely in the understanding, merely for direct perception; and for him it is quite sufficient; but on the other hand it is only the man who has studied the science of mechanics, who has, properly speaking, a rational knowledge of these laws, that is, a knowledge of them in the abstract. Such knowledge of the understanding in perception is sufficient even for the construction of machines, when the inventor of the machine executes the work himself; as we often see in the case of talented workmen, who have no scientific knowledge. But whenever a number of men, and their united action taking place at different times, is required for the completion of a mechanical work, of a machine, or a building, then he who conducts it must have thought out the plan in the abstract, and such co-operative activity is only possible through the assistance of reason. It is, however, remarkable that in [pg 073]the first kind of activity, in which we have supposed that one man alone, in an uninterrupted course of action, accomplishes something, abstract knowledge, the application of reason or reflection, may often be a hindrance to him; for example, in the case of billiard-playing, of fighting, of tuning an instrument, or in the case of singing. Here perceptive knowledge must directly guide action; its passage through reflection makes it uncertain, for it divides the attention and confuses the man. Thus savages and untaught men, who are little accustomed to think, perform certain physical exercises, fight with beasts, shoot with bows and arrows and the like, with a certainty and rapidity which the reflecting European never attains to, just because his deliberation makes him hesitate and delay. For he tries, for example, to hit the right position or the right point of time, by finding out the mean between two false extremes; while the savage hits it directly without thinking of the false courses open to him. In the same way it is of no use to me to know in the abstract the exact angle, in degrees and minutes, at which I must apply a razor, if I do not know it intuitively, that is, if I have not got it in my touch. The knowledge of physiognomy also, is interfered with by the application of reason. This knowledge must be gained directly through the understanding. We say that the expression, the meaning of the features, can only be felt, that is, it cannot be put into abstract concepts. Every man has his direct intuitive method of physiognomy and pathognomy, yet one man understands more clearly than another these signatura rerum. But an abstract science of physiognomy to be taught and learned is not possible; for the distinctions of difference are here so fine that concepts cannot reach them; therefore abstract knowledge is related to them as a mosaic is to a painting by a Van der Werft or a Denner. In mosaics, however fine they may be, the limits of the stones are always there, and therefore no continuous passage from [pg 074]one colour to another is possible, and this is also the case with regard to concepts, with their rigidity and sharp delineation; however finely we may divide them by exact definition, they are still incapable of reaching the finer modifications of the perceptible, and this is just what happens in the example we have taken, knowledge of physiognomy.¹⁶

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: “nemo [pg 075]potest 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

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§ 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 [pg 077]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 [pg 078]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 [pg 079]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 [pg 080]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

§ 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 [pg 081]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, [pg 082]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 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 [pg 083]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 [pg 084]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 oneconcept, 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 [pg 085]is in view; all this is done by thefaculty 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 [pg 086]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 [pg 087]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 [pg 088]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 [pg 089]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 [pg 090]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

§ 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 [pg 091]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 [pg 092]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 areductio 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 [pg 093]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, öáéíïìåíïí,²¹ and what is thought, íïõìåíïí, 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 (öáéíïìåíïí), but all the rest he based upon reasoning (íïõìåíïí). 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, [pg 094]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[pg 095]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: “Áêñéâåóôåñá ä᾽ åðéóôçìç åðéóôçìçò êáé ðñïôåñá, ἡôå ôïõ ὁôé êáé ôïõ äéïôé ἡ áõôç, áëëá ìç ÷ùñéò ôïõ ὁôé, ôçò ôïõ äéïôé” (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:—

[pg 096]

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 [pg 097]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 [pg 098]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. [pg 099]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 [pg 100]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

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, [pg 101]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 [pg 102]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 [pg 103]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, [pg 104]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 [pg 105]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 [pg 106]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 [pg 107]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 [pg 108]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. [pg 109]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, [pg 110]but is only added as a confirmation of their truth. This problem itself can only become quite clear in being solved.²³

§ 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 [pg 111]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 [pg 112]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 [pg 113]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: óéäçñåéïí íõ ôïé ἡôïñ! (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 [pg 114]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: ôåëïò ôï åõäáé ìïíåéí (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 (áôáñáîéá), 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, [pg 115]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: Äåé êôáóèáé íïõí, ç âñï÷ïí (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. Ïõ ðåíéá ëõðçí åñãáæåôáé, áëëá åðéèõìéá (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 [pg 116]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 Therefore Chrysippus says: äåé æῃí êáô᾽ åìðåéñéáí ôùí öõóåé óõìâáéíïíôùí (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 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 áôáñáîéá.

In accordance with this spirit and aim of the Stoa, Epictetus began and ended with the doctrine as the kernel [pg 117]of his philosophy, that we should consider well and distinguish what depends upon us and what does not, and therefore entirely avoid counting upon the latter, whereby we shall certainly remain free from all pain, sorrow, and anxiety. But that which alone is dependent upon us is the will; and here a transition gradually takes place to a doctrine of virtue, for it is observed that as the outer world, which is independent of us, determines good and bad fortune, so inner contentment with ourselves, or the absence of it, proceeds from the will. But it was then asked whether we ought to apply the words bonum and malum to the two former or to the two latter? This was indeed arbitrary and a matter of choice, and did not make any real difference, but yet the Stoics disputed everlastingly with the Peripatetics and Epicureans about it, and amused themselves with the inadmissible comparison of two entirely incommensurable quantities, and the antithetical, paradoxical judgments which proceeded from them, and which they flung at each other. The Paradoxa of Cicero afford us an interesting collection of these from the Stoical side.

Zeno, the founder, seems originally to have followed a somewhat different path. The starting-point with him was that for the attainment of the highest good, i.e., blessedness and spiritual peace, one must live in harmony with oneself (ὁìïëïãïõìåíïõò îῃí; ä᾽ åóôé êáè᾽ ἑíá ëïãïí êáé óõìöùíïí îῃí.—Consonanter vivere: hoc est secundum unam rationem et concordem sibi vivere. Stob. Ecl. eth. L. ii., c. 7, p. 132. Also: Áñåôçí äéáèåóéí åéíáé øõ÷çò óõìöùíïí ἑáõôῃ ðåñé ὁëïí ôïí âéïí. Virtutem esse animi affectiomem secum per totam vitam consentientem,ibid., p. 104.) Now this was only possible for a man if he determined himself entirely rationally, according to concepts, not according to changing impressions and moods; since, however, only the maxims of our conduct, not the consequences nor the outward circumstances, are in our power, in order to be always consistent we must set [pg 118]before us as our aim only the maxims and not the consequences and circumstances, and thus again a doctrine of virtue is introduced.

But the ethical principle of Zeno—to live in harmony with oneself—appeared even to his immediate successors to be too formal and empty. They therefore gave it material content by the addition—“to live in harmony with nature” (ὁìïëïãïõìåíùò ôῃ öõóåé æῃí), which, as Stobæus mentions in another place, was first added by Kleanthes, and extended the matter very much on account of the wide sphere of the concept and the vagueness of the expression. For Kleanthes meant the whole of nature in general, while Chrysippus meant human nature in particular (Diog. Laert., 7, 89). It followed that what alone was adapted to the latter was virtue, just as the satisfaction of animal desires was adapted to animal natures; and thus ethics had again to be forcibly united to a doctrine of virtue, and in some way or other established through physics. For the Stoics always aimed at unity of principle, as for them God and the world were not dissevered.

The ethical system of Stoicism, regarded as a whole, is in fact a very valuable and estimable attempt to use the great prerogative of man, reason, for an important and salutary end; to raise him above the suffering and pain to which all life is exposed, by means of a maxim—

“Qua ratione queas traducere leniter œvum:

Ne te semper inops agitet vexetque cupido,

Ne pavor et rerum mediocriter utilium spes,”

and thus to make him partake, in the highest degree, of the dignity which belongs to him as a rational being, as distinguished from the brutes; a dignity of which, in this sense at any rate, we can speak, though not in any other. It is a consequence of my view of the ethical system of Stoicism that it must be explained at the part of my work at which I consider what [pg 119]reason is and what it can do. But although it may to a certain extent be possible to attain that end through the application of reason, and through a purely rational system of ethics, and although experience shows that the happiest men are those purely rational characters commonly called practical philosophers,—and rightly so, because just as the true, that is, the theoretical philosopher carries life into the concept, they carry the concept into life,—yet it is far from the case that perfection can be attained in this way, and that the reason, rightly used, can really free us from the burden and sorrow of life, and lead us to happiness. Rather, there lies an absolute contradiction in wishing to live without suffering, and this contradiction is also implied in the commonly used expression, “blessed life.” This will become perfectly clear to whoever comprehends the whole of the following exposition. In this purely rational system of ethics the contradiction reveals itself thus, the Stoic is obliged in his doctrine of the way to the blessed life (for that is what his ethical system always remains) to insert a recommendation of suicide (as among the magnificent ornaments and apparel of Eastern despots there is always a costly vial of poison) for the case in which the sufferings of the body, which cannot be philosophised away by any principles or syllogistic reasonings, are paramount and incurable; thus its one aim, blessedness, is rendered vain, and nothing remains as a mode of escape from suffering except death; in such a case then death must be voluntarily accepted, just as we would take any other medicine. Here then a marked antagonism is brought out between the ethical system of Stoicism and all those systems referred to above which make virtue in itself directly, and accompanied by the most grievous sorrows, their aim, and will not allow a man to end his life in order to escape from suffering. Not one of them, however, was able to give the true reason for the rejection of suicide, but they laboriously collected illusory explanations from all sides: the true [pg 120]reason will appear in the Fourth Book in the course of the development of our system. But the antagonism referred to reveals and establishes the essential difference in fundamental principle between Stoicism, which is just a special form of endæmonism, and those doctrines we have mentioned, although both are often at one in their results, and are apparently related. And the inner contradiction referred to above, with which the ethical system of Stoicism is affected even in its fundamental thought, shows itself further in the circumstance that its ideal, the Stoic philosopher, as the system itself represents him, could never obtain life or inner poetic truth, but remains a wooden, stiff lay-figure of which nothing can be made. He cannot himself make use of his wisdom, and his perfect peace, contentment, and blessedness directly contradict the nature of man, and preclude us from forming any concrete idea of him. When compared with him, how entirely different appear the overcomers of the world, and voluntary hermits that Indian philosophy presents to us, and has actually produced; or indeed, the holy man of Christianity, that excellent form full of deep life, of the greatest poetic truth, and the highest significance, which stands before us in perfect virtue, holiness, and sublimity, yet in a state of supreme suffering.²⁶

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