Chapter 14 Part I The World as Representation §14

Therefore, on the one hand, there is a rational way of knowing, knowing, and concepts; The distinction and relationship between the two cognitions have been laid out very clearly.We have also had these two episodes of explanations about feelings and laughter, and this is what we will inevitably touch upon when discussing the special relationship between the two cognitions.Now I will turn back from these studies to talk about science, and language, the science of deliberate action as the third great advantage of human beings.It is our duty here to make a general survey of science. As for the problems to be touched, partly the form of science, partly the basis of its judgment, and finally its inner substance.

We have seen that the source of all [knowledge or] knowledge, apart from a purely logical basis, is not at all in reason itself; A way of knowing, an abstract way of knowing.This is the root of knowledge.All knowledge, that is, cognition that has risen to abstract consciousness, has the same relationship with science as the relationship between fragments and the whole.Anyone can acquire knowledge about certain things through experience, through the observation of ready-made things, but to obtain a complete understanding of a certain class of things in the abstract, [that is different,] and only those who make it their task are working hard for science.It is only through concepts that he can separate such things, so that at the beginning of every science there is always a concept.By virtue of this conception this [separate] part can be thought apart from the totality of all things, from which this science can hope for a complete cognition in the abstract; for example the notion of spatial relations, the interaction of inorganic bodies. concept, the concept of the properties of animals and plants, the concept of the continuous change of the earth's crust, the concept of the change of the whole species of human beings, the concept of language structure and so on.If science, in order to gain knowledge about its subject matter, takes the method of studying the things included in a general concept individually in order to gradually know all things, then, on the one hand, human memory is too limited, and on the other hand, it cannot guarantee the integrity of this knowledge.Science, therefore, makes use of the characteristic of the circles of meaning of the above-mentioned concepts, and makes them mutually encompassing; and the main thing is to pay attention to the larger circles of meaning that are originally in the general concept of this science.In determining the mutual relations of these circles of meaning, everything that is thought of in these circles of meaning is generally determined accordingly.And it is also possible to make more detailed regulations step by step by distinguishing narrower circles of meaning.A science thus completely encompasses its object.This approach to knowledge, from the general to the particular, is what distinguishes science from general knowledge.The systematic form is therefore an essential and peculiar mark of science.In any science, linking the most general circle of conceptual meanings, that is, knowing some of its highest principled propositions is an unavoidable condition for learning a science.As for how far to go deeper into more subtle special propositions, it is up to everyone; and going deeper does not add to the thorough understanding of this science, but only expands the scope of profound knowledge.All other propositions are subordinate to those of the superlative.The number of supreme propositions is very inconsistent in the sciences, so that in some sciences there are more subordinations; in others there are more parallels.In this respect, affiliation requires a little more judgment.Parallel relationships require more memory.The scholastics already knew that a conclusion requires two premises, so no science can start from a single, unextensible supreme proposition, but requires several, at least two propositions.The sciences which are really classified, such as zoology, botany, and if all inorganic interactions can also be reduced to a few fundamental forces of nature, then physics and chemistry; these are the sciences with the most subordinate relations.History, on the other hand, has no subordination at all; for in history the general exists only as an overview of the main historical stages, from which individual events cannot be deduced, but are subordinated only temporally and conceptually to them. Still parallel to these stages.Strictly speaking, therefore, history is not a science, although it is a kind of knowledge.In mathematics, according to Euclid's approach, only axioms are the highest propositions that cannot be proved, and all provable [propositions] are strictly graded and subordinate to axioms.However, this method is not the main one. In fact, each theorem initiates a new spatial structure, independent of the previous theorems and completely independent of the previous theorems. To be known for its own sake.In this intuition, any complex spatial structure is straightforward and self-evident, just like axioms.These are explained in detail below.What I want to say here is that every mathematical axiom is always a general truth, valid for countless individual matters, and in mathematics, the method of developing from simple propositions to complex propositions, and the latter can be reduced to the former is still the main method. of.So, in every respect, mathematics is a science.The reason why science is the perfection of science is that in terms of form, there are as many subordination relationships among propositions as possible and as few parallel relationships as possible.Genius in science, therefore, in general, is the faculty of subordinating the spheres of meaning of concepts according to different definitions, with which what constitutes science, as Plato repeatedly asserts, is not merely a general general concept, not endless. Diversity is immediately juxtaposed under the universal; but cognition descends from the universal to the particular through intermediary concepts, through various distinctions based on the criterion of successively detailed regulations.In Kant's words, this is called equal satisfaction of the law of homogeneity and "transformation".But just as this constitutes the true perfection of science, it can also be seen that the aim of science is not a higher certainty, as any separate and separate cognition can have; The simplification of knowledge lies in the possibility of obtaining complete knowledge.Therefore, it is wrong to say that the scientific nature of cognition lies in a high degree of certainty, although it is popular.From this arose the assertion that mathematics and logic are the only true sciences, and that, because of their complete a priori character, knowledge of all unshakable certainties lies only in these two sciences. Of.This view is also wrong.This superiority of logic and mathematics is indisputable, but this superiority does not give 108 the privilege of being exclusively "scientific". The requirement of "scientificity" does not lie in certainty, but in knowing all the systematic forms based on the descending from the general to the particular.This unique way of cognition of science, from general to special way, has resulted in the fact that many things in science are deduced from antecedent propositions and established by proofs.This contributes to the age-old fallacy that only what is proven is completely true, and that every truth needs a proof.In fact, on the contrary, every proof requires an unproved truth; this truth ultimately supports the proof or some proofs of the proof.Hence an immediately established truth is preferable to that established by demonstration, as water from a spring is preferable to water from a pipe.Intuition is the source of all truth and the basis of all science; its pure, a priori part is the basis of mathematics, and its a posteriori part the basis of all other sciences. (The only exception is logic. Logic is not based on intuitive knowledge. It is based on reason's direct knowledge of its own laws.) Just as the sun is in the universe, all light comes from here, and here the light shines. Underneath, everything else shines; and it is not proven judgments, not proofs of judgments, that have this place in science, but judgments that are directly derived from intuition, and are based on intuitions and not on proofs.It is the task of judgment to establish the truth of these primitive judgments directly from intuition, and to build up the fortress of science from the vast sea of ​​actual things.Since the [function] of judgment exists in the ability to correctly and accurately transfer [things] intuitively recognized to abstract consciousness, it is of course the "mediator" between understanding and reason.Only when personal judgment has a particularly outstanding strength beyond the average level can science really advance; as for deriving propositions from propositions, making proofs, and drawing conclusions, everyone can do it, as long as he has sound reason.On the contrary, for the purpose of introspective thinking, the intuitively recognized things are deposited and fixed in corresponding concepts. On the one hand, the common features of many real objects can be thought with one concept. On the other hand, the differences between these objects There are as many points of difference as there are concepts to think; therefore, although there are partial similarities between objects, the differences are still recognized as differences, and when thinking, everything is guided by the purpose and consideration each time. All this is judgment. power to do.Lack of judgment is called simple minded.Simple-minded people sometimes fail to see that concepts that are the same on the one hand have partial or relative differences, and sometimes they do not see that relative or partial differences have the same [side].In addition, Kant distinguishes two kinds of judgments: reflective thinking and generalizing. This distinction can also be applied to the explanation here, that is, it is respectively applicable to the transition from the intuitive object to the concept, or from the latter to the former.In both cases the power of judgment is always intermediate between the intuitive knowledge of the understanding and that of the rational reflective mind.There cannot be any truth that is absolutely only derived from inference, and the necessity of establishing truth from inference alone is relative; yes, even subjective.Since all proofs are three-stage inferences, for a new truth, the first thing to do is not to find a proof, but to find a direct basis; only when no direct basis can be found, the proof is temporarily presented.No science can be proved thoroughly, just like a building cannot be suspended in the air.All scientific proofs must be reduced to an intuitive, that is, something that can no longer be proved.It turns out that the entire world of reflective thinking is based on and rooted in this intuitive world.All final, i.e. original, grounds are an intuitively self-evident ground.The word itself tells the story.Accordingly, it is either an empirical ground, or is based on [one's] a priori intuition of the conditions of possible experience: in both cases the ground furnishes only the immanent rather than the knowledge.Any concept has its value only in its relationship with an intuitive representation, and it actually reveals and draws out what is already present in the premise, and can no longer gain anything else.One is merely manifesting what is implicitly and implicitly understood in the premises.In the case of those sciences which are so highly celebrated, they mean especially the physical sciences, that is to say astronomy.But the truth of astronomy comes from this: it is based on the intuition of space which is given a priori and therefore can never be mistaken, but all spatial relations are based on a necessity (ground of existence)—this Necessity provides certainty a priori—and one is derived from the other, so that spatial relations can be properly inferred from each other.In addition to these mathematical regulations, there is only one natural force to be added here, that is, gravitation; and gravitation works exactly according to the relationship between mass and distance multiplied by the square.Finally there are added the laws of inertia arising from causality and thus valid a priori, together with empirical data representing the motion of each mass once and for all.That's all the stuff of astronomy.The simplicity and propriety of the material lead to definite results; and the size and importance of the objects lead to very interesting results.For example, if I already know the mass of a planet, its satellites and its distance, I can accurately calculate the time for the satellite to go around a circle according to Kepler's second law.But this law is based on the fact that at a certain distance only a certain velocity can sustain a satellite without sinking into a planet.So it is only necessary to apply a natural law on the basis of this geometry, that is, by means of a priori intuition, and it can be used to obtain good results by inference.It turns out that the inference here is really just a bridge from one intuitive experience to another intuitive experience; but it is not the case if a simple inference is made on the logical path.But the source of the highest fundamental truths in astronomy is induction.Induction is to sum up many things already in intuition into a correct and directly grounded judgment, and then form some hypotheses from this judgment, which are confirmed by experience; , found a proof for that judgment.For example, the visible planetary motions are known empirically: after making many wrong assumptions about the spatial relations of this motion (planetary orbits), the correct assumption is finally found, that is, the laws to which these motions obey (Gr. Buller's law), and finally found the cause of this motion (gravity).And this [thing] known by experience is, on the one hand, all the circumstances that have arisen, and on the other hand, all the hypotheses and the conclusions that follow from them. , bringing complete certainty.The establishment of hypotheses is a matter of judgment, which correctly perceives the facts at hand and expresses them accordingly, and the action of induction, that is, repeated intuitions, confirms these hypotheses.If we could one day travel freely through space, if we had telescope-like glasses, we would even be able to justify these hypotheses directly, through an empirical intuition.Therefore, even in astronomy, the mode of inference is not the main and only source of this knowledge, and in fact is always only an emergency expedient.

Finally, for the sake of a third example of a different nature, let us point out that even those so-called metaphysical truths, such as those proposed by Kant in his Introduction to the Metaphysics of Natural Science, do not arise from the demonstration And has its basis.What is true a priori is what we know directly.As all forms of cognition, this is what we are conscious of with the greatest necessity.Matter, for example, is perpetual, that is to say neither born nor destroyed, which is a negative truth we know immediately; The possibility of changing shape and physical properties; but for the birth and death of matter, we have no such form that can be imagined.This truth, therefore, is self-evident to everyone at any time, anywhere, and has never been seriously doubted.It is of course impossible to say that this truth has no other basis for understanding except Kant's difficult proof of galloping on the tip of a needle.Also, I found (as discussed in the appendix) that Kant's proof was wrong.I also pointed out in the previous article that the immortality of matter is not derived from the share that time occupies in the possibility of experience, but from the share that space occupies in the possibility of experience.This means that so-called metaphysical truths are abstract representations of universally necessary forms of knowledge.The true grounds of these truths cannot again be found in abstract propositions, but only in [man's] immediate consciousness of the form in which representations take place, in the consciousness which expresses itself in a priori assertions which are decisive and careless of refutation.If one were to offer a proof for this, it could only be one in which one would have to show that in every undoubted truth there is already something to be proved, either as [a constituent] part, or As a premise, I have pointed out, for example, that all empirical intuitions involve the application of the law of causality, and therefore the knowledge of the law of causality is the condition of all experience: so it cannot be said that the law of causality is produced by experience, as Hume maintains, and presupposes experience. of. —Actually, proofs are not so much for those who want to learn, as they are for those who want to argue.These men stubbornly deny insights that are directly grounded.But truth alone is consistent in all respects, and we shall show these men that what they admit indirectly in one mode is what they directly deny in the other, that is, what they deny and what they deny. The admitted logical connection between the two.

Moreover, the form of science, that is, the subordination of the particular to the universal, in successive order, has the consequence that many propositions are true only by virtue of attachment to other propositions, that is, by Only some inferences that appear as proofs at the same time have a logical basis.But one must never forget that the whole dominant form is only a means of simplification of knowledge, not a means of attaining a higher degree of certainty.It is easier to identify the nature of an animal from the "species" to which it belongs, and proceed to the genus, family, class, and order than to study each animal encountered individually [this is a fact].But the truth of all propositions deriving from deduction is always ultimately determined and dependent on some truth which is not deduced but grounded in intuition.If intuition is often as convenient as inference, it is certainly preferable to intuition.For all derivations from concepts, owing to the intertwining of circles of meaning and the inconsistency of content indicated above, are not immune to error; various heresies and sophistry are examples of this.Formally speaking, the inference is perfectly correct; but because of its material, that is, because of the concept, the inference is very unreliable.On the one hand, the definition of the circle of meaning is not strict enough, and on the other hand, the circle of meaning overlaps in many ways, so that various parts of one circle of meaning can be contained in many other circles of meaning; Get to one or the other of the latter, then do the same and keep going.In other words, both the small word and the middle word can belong to different concepts at will, and people choose the big word and the middle word arbitrarily among these concepts, so the conclusions are also different.Wherefore, the truth by demonstration is far from being equal to the immediate self-evident grounds; the former is adopted only when the latter is far from timely; not when both are equally near, or the latter is more near. , also adopt the former.We have therefore seen before that, logically, in every particular case, if immediate knowledge is more convenient to us than deductive scientific knowledge, we in fact always rely on our immediate knowledge of the laws of thought To guide thinking and put logic aside.