The World as Will and Idea (Vol. 1-3). Arthur Schopenhauer

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 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 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 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 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 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