Chapter 12 Part I The World as Representation §12

I have explained above that the concept of sense and cognition [this concept] are exactly opposite symmetry, and cognition, as mentioned above, is abstract cognition, that is, rational cognition.But reason just puts what has been received from other sources before cognition, so it does not really expand our cognition, but only gives this cognition another form.That is to say, reason adds abstract and general knowledge to what is known intuitively and in the concrete.This, so to speak, is much more important than at first casual glance, since all secure preservation [in consciousness], all possibility of communication, and all proper and universal application of knowledge to practice depend on This knowing is a kind of knowing that depends on knowing that it has become abstract.Intuitive knowledge can always be useful only in individual cases, only to and finally to the nearest thing, because sensibility and reason can only grasp one object at any one time.Therefore, every continuous, combined, and planned action must start from principles, that is, from abstract knowledge, and proceed accordingly.For example, the understanding of cause and effect by the understanding is more complete, deeper, and more detailed than that obtained by thinking in the abstract. Only the understanding can directly and completely understand a lever, a set of pulleys, a gear, and the stability of a vault through intuition. Wait, what kind of effect does it have.However, as just mentioned, since the attribute of intuitive cognition can only reach all things at present, understanding alone is not enough to construct machines and buildings; here also needs reason to step in and act with abstract concepts instead of intuition standard.If these abstractions are correct, the expected consequences must also arise.Similarly, we can fully understand the nature and regularity of parabolas, hyperbolas, and spirals in intuition; but to apply this understanding to reality, this understanding must first become abstract knowledge.In this transformation, what is lost is the intuitive imagery, but what is gained is the validity and accuracy of abstract knowledge.All differential calculations, therefore, do not enlarge our knowledge of curves, do not add to that which is covered by simple intuition; but the kind of cognition is changed, and intuitive cognition becomes abstract cognition.This shift has the greatest effect on the application of knowledge.But there is another peculiarity of our faculty of cognition to be mentioned here.Nor can one pay attention to this property until one has made clear the difference between intuitive and abstract knowledge.That is, those relationships in space cannot be transferred directly to abstract cognition just as spatial relationships.To turn to abstract cognition, only the quantity in time, that is, number, is suitable.Only numbers, not spatial quantities, can be represented in abstract concepts that correspond exactly to them.The concept of a thousand differs from that of ten in the same way that these two quantities of time differ in perception; we think of a thousand as a definite multiple of tens, and thus we can decompose the thousand in time for the perception into any number of tens. , which is countable.But between the two abstract concepts of a mile and a foot, if there is no intuitive representation of the two sides, without the help of counting, there is simply no accurate quantitative difference that corresponds to the two sides.In both concepts, one thinks at all only of quantities in space; and to make a sufficient distinction between the two, one must either resort to the intuition of space, that is, leave the field of abstract cognition; Think about the difference.Therefore, if people want to obtain abstract knowledge from spatial relations, the spatial relations must first be transformed into time relations, that is, first transformed into numbers.Arithmetic alone, therefore, and not geometry, is the universal doctrine of quantity.If geometry is to have the possibility of communication, precise prescriptiveness, and possibility of practical application, it must first be translated into arithmetic.Of course, a spatial relationship can also be considered as a spatial relationship, for example, the lower chord increases with the increase of the angle; but to indicate the magnitude of this relationship, it must be expressed by numbers.When people require an abstract understanding of spatial relationships (that is, knowledge rather than simple intuition), it is necessary to translate the three-dimensional space into one-dimensional time.What makes mathematics so difficult is this necessity.This is easy to understand, we only need to compare the intuition of a curve with the analytical formula of this curve, or compare the logarithmic table applied to the triangle with the changing relationship between the various parts of the triangle shown in this table; Here it is fully and most accurately understood at a glance in the intuition, for example, how the cosine decreases with the increase of the sine, for example, the cosine of one angle is the sine of the other angle, for example, the two angles increase for one and decrease for one, and decrease for one. The inverse relationship of increase and so on.But in order to express these intuitively recognized things abstractly, it requires a huge digital network and difficult calculations.One can say that the time of the first direction is to copy the space of the third direction, how hard it is for oneself!But for the needs of the application, it is necessary to precipitate the spatial relationship into an abstract concept.Spatial relations cannot be transferred directly to abstract concepts, but only through the quantity of pure time, through the medium of numbers, because only numbers directly correspond to abstract cognition.It is also worth noting that space is suitable for intuition because of its three directions, and even complex relationships can be seen at a glance, which is impossible for abstract cognition.On the contrary, although time is easy to enter into abstract concepts, it can rarely be given intuition.Among the unique factors of numbers, in pure time, without involving space, our intuitive perception of numbers can hardly reach ten; above ten, we can only have abstract concepts, and no longer intuitive cognition of numbers.On the other hand, we can connect precisely defined abstractions with numbers and all the algebraic symbols.

Incidentally, it must be pointed out that there are some people whose minds are completely satisfied only in intuitively perceived [things].To express in images the grounds and consequences of existence in space is what these people seek.Neither Euclid's proofs, nor the arithmetical solutions to space problems appealed to them.Yet other human minds demand the only available abstractions in application and communication.They have patience and memory for abstract theorems, formulas, proofs in long series of inferences, and for calculations with symbols representing the most complex abstractions [things].One seeks accuracy, one seeks imagery.This difference is an expression of a difference in [person's] characteristics.

The greatest value of cognition or abstract cognition lies in its possibility of communication and possibility of being fixed and preserved.Therefore, it is actually of such inestimable importance.It is true that anyone can intuitively recognize the causal relationship between changes and movements of natural objects in a simple comprehension, and can be very proud of it; but in order to convey it to others, the intuitive knowledge must first be fixed as a concept before it can be used.Intuitive knowledge is enough in practice if a person is only carrying out an activity alone, especially if intuitive knowledge is still vivid in the performance of the activity; To do it, but it takes a while to proceed, so when a plan is needed, it is not enough.For example, a person who is good at billiards has a complete knowledge of pure intellect about the laws of the collision of elastic objects; although this is only an intuitive understanding for the moment, it is more than enough for his game.The difference is that only a learned mechanics can really know these laws, that is to say, only he has abstract knowledge.Even in the manufacture of a machine, if the inventor works alone, simple intuitive understanding is enough to apply; this is what we often see among craftsmen who are talented and have no scientific knowledge.On the contrary, if it is to complete a mechanical project, a machine, or a building, some people are needed, and these people are required to coordinate activities carried out at different times, then the leader of this activity is A plan must first be drawn up in the abstract, and such concerted activity is possible only with the aid of reason.It is worth noting, but also somewhat special, that in the former kind of activities, that is, when a person wants to accomplish something in uninterrupted activities alone, knowledge, rational application, and thinking may often be an obstacle; In the game of billiards, in fencing, in orchestral tuning, in singing, for example.On these occasions, intuition must directly guide the activities; they would be rendered inappropriate if reflections were mixed in, because reflections would distract and confuse.Therefore, just because they have no habit of thinking, savages and old men are able to complete some physical activities steadily and quickly, such as fighting with beasts and hitting arrows; all these are beyond the reach of Europeans who are accustomed to thinking.For example [archery], the European, no matter in space or time, he has to measure up and down, left and right, successively, etc., and then find the equidistant midpoint between these two poles, [how can this be done like this? ] A natural person can't think in distance at all, but can he hit it directly?In the same way, although I can tell in the abstract the angle at which the razor should be used, if I do not know it intuitively, that is, without sensitivity in my fingers, abstract knowledge is still of no use to me.Likewise, the application of reason to physiognomy can interfere with the understanding of human physiognomy.This kind of understanding must also be through the understanding, because what the human figure expresses, the ups and downs of the lines of the face, etc. can only be felt; people say that this is what cannot enter into abstract concepts.Everyone has his own direct and intuitive [set] of physiognomy and pathological symptoms, but some people know the signs of these things better than others.But it is also impossible to write a teachable physiognomy in the abstract; because the differences and changes in human appearance are too subtle for concepts to do anything about it. [Using a metaphor,] abstract knowledge is related to these slight differences.As a mosaic of polychrome fragments is to a painting by Weffert or Tenle.The concept is like the craftsmanship of mosaic, no matter how detailed it is, there must always be boundaries between the mosaic pieces, so it is impossible to transition from one color to another color without trace.This is exactly the case with concepts, because of its rigid rules and precise boundaries, no matter how finely people use more detailed rules to divide a concept, they can never achieve the fine division in intuition; and here Physiognomy as an example depends precisely on this delicate division.

It is this very nature of the concept which makes it approximate to the fragments of a mosaic, and because of this, intuition is always the limit of its accessibility.This is also the reason why concepts cannot be used to get good grades in art.If a singer or musician directs his performance with rumination, it is fatal.The same is true of composers, painters, and even poets.Concepts are always fruitless when used in art.Concepts can only guide the technical part of art, which belongs to the academic field.In the third part, we will further explore why all real art can only start from intuitive knowledge, but never from concepts.Even in the manners of men, in good manners in society, concepts have only a negative use, and can only prevent the outbreak of gross selfishness and bestiality;But the personable, pompous, admirable manners: affectionate, friendly touches could not have come from conception, otherwise "people feel [your] intentions, people get discouraged." They are all products of thinking, but they cannot last long without revealing their flaws. "No one can continue to pretend", this is what Sinaiga said in the book "On Mercy". Most of the disguise is to be seen through and become invalid.In the critical juncture of life, when it is necessary to act decisively, act boldly, and deal with accidents quickly and firmly, although rationality is also necessary, if the theory prevails, it will hinder the direct and direct action of the party with confusion. , purely savvy insights and correct grasp of countermeasures, thereby causing indecision, it will easily mess up the overall situation.

And finally, the sanctity of virtue does not come from reflection, but from the inner depths of the will and its relation to knowledge.To illustrate the point which ought to have been taken up elsewhere in this book, I will simply point out here that the dogmas concerning ethics may be the same in the reason of a whole, a whole people, and yet act differently from one individual to another: and vice versa. [Behavior is the same, but the beliefs about ethics are different]: People often say that behavior is based on feelings, that is, not based on concepts, that is, not based on ethical implications.Dogma keeps busy reason only at its leisure, and conduct in the end stands outside of dogma and has its own course; The whole person himself.Therefore, although the religious dogmas of different peoples are different, yet in all peoples, good deeds are accompanied by indescribable pleasure, and evil deeds are accompanied by infinite misery.The former cannot be swayed by cynicism, nor the latter by a priestly absolution.Having said that, we cannot deny that it is still necessary to apply reason to realize virtue and conduct, but reason is not the source of virtue.The function of rationality is secondary, which is to help people stick to their existing resolutions, and often put norms on the right side of people's seats, so as to resist temporary weakness of will and implement behavior from beginning to end.Finally, reason has the same function in art: in the main respects it is impotent, but it can support the progress of artistic work; It is necessary to complete part by part to complete the whole project satisfactorily.