What is the source of Kant's analytical knowledge? Reward score: 0- answer time: August 2006-13-12: 20 Questioner: ahsix- trainee magician's second best answer. Gadamer, a famous contemporary interpreter, put it well on Kant's philosophy: "Spiritual science can't be described by the concept of progress" and "the great achievements of spiritual science research will almost never be out of date".
When talking about the so-called "bankruptcy of German idealism", Heidegger once wrote indignantly: "It is not that German idealism went bankrupt, but that the times no longer have the strength to bear the greatness, vastness and primitiveness of this spiritual world." Heidegger himself studied the existing problems, always exploring the source of rivers, peeling bananas to the heart, and returning to Greek thought with the help of language analysis.
In his view, modern people forget existence; The revival of ancient Greek thought is the only way to remember existence again. Only when people really exist can there be a real life. In this sense, it can be said that the spirit of the ancient Greeks is always alive, while the modern westerners died of mental weakness.
Heidegger is a new course, but if we really want to study and master Heidegger's philosophy, we should not leave Plato, Aristotle, Kant and Hegel behind. Kant's philosophy, in particular, not only made a great synthesis for the modern west to get out of post-medieval empiricism and rationalism, but also opened a big precedent for German idealism and a big source for modern western philosophy.
No matter phenomenology, hermeneutics or philosophy of science, they all seek inspiration from Kant, refine problems and build a foundation for the further development of thinking. Mr. Zheng Xin said: "Beyond Kant, there may be new philosophy, while beyond Kant, there can only be bad philosophy."
Mr Zheng Xin's words are not only applicable to western philosophers, but also to China's traditional theory of justice. If we want to make creative transformation, we must also pass Kant's philosophy. Fortunately, Mr Mou Zongsan, who lives in Hong Kong and Taiwan, has mastered and interpreted Kant's philosophy and "connected" it with China's traditional theory of justice (especially the Confucian theory of inner saints).
Mou Zongsan not only mastered and explained Kant's philosophy, but also developed and enriched it. Based on the Confucian theory of inner sage and Mahayana Buddhism's theory of "opening with one heart and two minds", he fully affirmed and confirmed Kant's universal knowledge and insight in transcendental decomposition, and constructed a philosophical system with "two-layer ontology" as the basic theoretical backbone, integrating ontology, epistemology and ethics, thus making China's philosophy, which has always lacked systematic phase, directly related to western philosophy.
It can be said that "Shengde is great!" Kang Youwei was probably one of the first people who came into contact with Kant's theory in China. Long before he was appointed as an imperial envoy, he wrote a book "Zhu Tian's Theory", which poured out all the astronomical knowledge he got from western miscellaneous books, including Kant's "Xing Yun Theory", and he also attached China's traditional theory of gas shape.
In fact, the Introduction to the Development of the Universe described by Kant in his Nebula is only a "small work" and has little to do with the whole system of Kant's philosophy. Another famous but often misinterpreted argument of Kant is the so-called "agnosticism".
Mr. Nanhai described it like this in "On Heaven": "However, things in the world are unfathomable, we are insignificant and our knowledge is limited. How can we do everything in the world with what we have seen and heard? " This is often said that life has a limit, knowledge has a limit, and finite cannot be infinite. Being called Kant is an unwarranted and arbitrary imposition. Yan Fu also gave full play to the "agnosticism" in his mind, and attributed it to Kant: "Western physics is developing day by day, and people of insight argue about the poverty and subtlety of things, so as to warn people who believe in the past and have the courage to be confident.
As far away as Polney in Greece, as close as Locke, Hume and Kant, it has been repeatedly explained. "Hume and Kant's two agnosticism have different meanings and argumentation methods. It is extremely different to drag them together.
This problem continues to the current college philosophy textbooks. Yan Houguan switched to Buddhism, and Gekant I said, "Speaking of the extreme, it is an incredible place.
It's not ridiculous, but it's hard to know why. This is the so-called incredible Buddhist book. "This is a bit interesting.
As the Buddhist said, "the reality is one phase, that is, there is no phase, that is, it is similar." This is incredible and far from it. Your heart is dead, your words are broken, and you are not in the realm of knowledge Kant's old translation of "things are in themselves" is quite meaningful.
Kant's Philosophy and Yin and Yang Studies Kant wrote three important books: Critique of Pure Reason is about how people know the world-truth. Critique of Practical Reason is about what human ethical rules are-goodness.
The object of the former is the phenomenal world, while the object of the latter is the ontological world. There is an insurmountable gap between phenomenon and ontology, and a bridge is built on the gap to make the phenomenon transition to ontology.
This bridge is the purpose of nature. It includes aesthetic feeling-beauty.
It means that nature transits to its purpose through people's subjective aesthetic feeling, that is, the ontology of objective view. This includes the natural purpose of aesthetic feeling, which is the main content of judgment and criticism in the third book.
Since Newton put forward the three laws of physics, Kant affirmed the reliability of mathematical physics and the impossibility of metaphysics from a philosophical point of view. Transcendental perceptual aesthetics affirms that it is possible for mathematics to pass through the spatio-temporal model.
Transcendental Logic transzendentale Logik's tranzendentale Analytik Tik affirms that physics is possible through the truth of intellectuals. Transcendental Dialectics of Transcendental Logic tranzendentale Dialektik reine Vernunft: 1. The world is finite and infinite, 2. The soul is free, 3. God is omnipotent.
Collectively known as transcendental concept. Kant's transcendental dialectics teaches us that transcendental concept is only an illusion Schein, and metaphysics is impossible.
Because these problems belong to ontology. Although metaphysics is impossible, pure reason points out the goal of our ontological world.
These goals can be achieved through practical rationality. Now we use pure rational criticism to define Yin-Yang studies, and Kant's second Phenomenology to practice rational criticism.
First, practical rationality praktische Vernunft has practical principles Grundsaetzen.
2. Sources of knowledge
What is the source of Kant's analytical knowledge? Reward score: 0- answer time: August 2006-13-12: 20 Questioner: ahsix- trainee magician's second best answer. Gadamer, a famous contemporary interpreter, put it well on Kant's philosophy: "Spiritual science can't be described by the concept of progress" and "the great achievements of spiritual science research will almost never be out of date".
When talking about the so-called "bankruptcy of German idealism", Heidegger once wrote indignantly: "It is not that German idealism went bankrupt, but that the times no longer have the strength to bear the greatness, vastness and primitiveness of this spiritual world." Heidegger himself studied the existing problems, always exploring the source of rivers, peeling bananas to the heart, and returning to Greek thought with the help of language analysis.
In his view, modern people forget existence; The revival of ancient Greek thought is the only way to remember existence again. Only when people really exist can there be a real life. In this sense, it can be said that the spirit of the ancient Greeks is always alive, while the modern westerners died of mental weakness.
Heidegger is a new course, but if we really want to study and master Heidegger's philosophy, we should not leave Plato, Aristotle, Kant and Hegel behind. Kant's philosophy, in particular, not only made a great synthesis for the modern west to get out of post-medieval empiricism and rationalism, but also opened a big precedent for German idealism and a big source for modern western philosophy.
No matter phenomenology, hermeneutics or philosophy of science, they all seek inspiration from Kant, refine problems and build a foundation for the further development of thinking. Mr. Zheng Xin said: "Beyond Kant, there may be new philosophy, while beyond Kant, there can only be bad philosophy."
Mr Zheng Xin's words are not only applicable to western philosophers, but also to China's traditional theory of justice. If we want to make creative transformation, we must also pass Kant's philosophy. Fortunately, Mr Mou Zongsan, who lives in Hong Kong and Taiwan, has mastered and interpreted Kant's philosophy and "connected" it with China's traditional theory of justice (especially the Confucian theory of inner saints).
Mou Zongsan not only mastered and explained Kant's philosophy, but also developed and enriched it. Based on the Confucian theory of inner sage and Mahayana Buddhism's theory of "opening with one heart and two minds", he fully affirmed and confirmed Kant's universal knowledge and insight in transcendental decomposition, and constructed a philosophical system with "two-layer ontology" as the basic theoretical backbone, integrating ontology, epistemology and ethics, thus making China's philosophy, which has always lacked systematic phase, directly related to western philosophy.
It can be said that "Shengde is great!" Kang Youwei was probably one of the first people who came into contact with Kant's theory in China. Long before he was appointed as an imperial envoy, he wrote a book "Zhu Tian's Theory", which poured out all the astronomical knowledge he got from western miscellaneous books, including Kant's "Xing Yun Theory", and he also attached China's traditional theory of gas shape.
In fact, the Introduction to the Development of the Universe described by Kant in his Nebula is only a "small work" and has little to do with the whole system of Kant's philosophy. Another famous but often misinterpreted argument of Kant is the so-called "agnosticism".
Mr. Nanhai described it like this in "On Heaven": "However, things in the world are unfathomable, we are insignificant and our knowledge is limited. How can we do everything in the world with what we have seen and heard? " This is often said that life has a limit, knowledge has a limit, and finite cannot be infinite. Being called Kant is an unwarranted and arbitrary imposition. Yan Fu also gave full play to the "agnosticism" in his mind, and attributed it to Kant: "Western physics is developing day by day, and people of insight argue about the poverty and subtlety of things, so as to warn people who believe in the past and have the courage to be confident.
As far away as Polney in Greece, as close as Locke, Hume and Kant, it has been repeatedly explained. "Hume and Kant's two agnosticism have different meanings and argumentation methods. It is extremely different to drag them together.
This problem continues to the current college philosophy textbooks. Yan Houguan switched to Buddhism, and Gekant I said, "Speaking of the extreme, it is an incredible place.
It's not ridiculous, but it's hard to know why. This is the so-called incredible Buddhist book. "This is a bit interesting.
As the Buddhist said, "the reality is one phase, that is, there is no phase, that is, it is similar." This is incredible and far from it. Your heart is dead, your words are broken, and you are not in the realm of knowledge Kant's old translation of "things are in themselves" is quite meaningful.
Kant's Philosophy and Yin and Yang Studies Kant wrote three important books: Critique of Pure Reason is about how people know the world-truth. Critique of Practical Reason is about what human ethical rules are-goodness.
The object of the former is the phenomenal world, while the object of the latter is the ontological world. There is an insurmountable gap between phenomenon and ontology, and a bridge is built on the gap to make the phenomenon transition to ontology.
This bridge is the purpose of nature. It includes aesthetic feeling-beauty.
It means that nature transits to its purpose through people's subjective aesthetic feeling, that is, the ontology of objective view. This includes the natural purpose of aesthetic feeling, which is the main content of judgment and criticism in the third book.
Since Newton put forward the three laws of physics, Kant affirmed the reliability of mathematical physics and the impossibility of metaphysics from a philosophical point of view. Transcendental perceptual aesthetics affirms that it is possible for mathematics to pass through the spatio-temporal model.
Transcendental Logic transzendentale Logik's tranzendentale Analytik Tik affirms that physics is possible through the truth of intellectuals. Transcendental Dialectics of Transcendental Logic tranzendentale Dialektik reine Vernunft: 1. The world is finite and infinite, 2. The soul is free, 3. God is omnipotent.
Collectively known as transcendental concept. Kant's transcendental dialectics teaches us that transcendental concept is only an illusion Schein, and metaphysics is impossible.
Because these problems belong to ontology. Although metaphysics is impossible, pure reason points out the goal of our ontological world.
These goals can be achieved through practical rationality. Now we use pure rational criticism to define Yin-Yang studies, and Kant's second Phenomenology to practice rational criticism.
Praktische Vernunft has practical principles, Gru.
3. What is the origin of order in word common sense?
Mao in A Qing's time composed a poem with the tunes of words within 58 words, which belongs to later generations.
In fact, although most of the lyrics are out of tune, some of them are Daqu. For example, the Brahman Order comes from Brahman, the Ganzhou Order comes from Ganzhou, and so on.
Because the lyrics of Daqu have many long words, which are different from ordinary poems. For example, Liu Yong's Ganzhou Order is 78 words, Brahman Order is 86 words, Ouyang Xiu's Liangzhou Order is 105 words, Liu Yaoling is 94 words, and Lotus Picking Order is 9 1 words, and so on.
As far as the number of words is concerned, almost all these words can be summed up in a long tune. But it still rhymes, not slow songs, because the rhythm is cheerful.
Of course, there are also some other slow songs of the same name, such as Liu Yong's "Sand Washing Order in the Waves" and "Sand Washing in Slow Waves". Compared with slow songs of the same name, these songs are obviously shorter and shorter, but there are exceptions, such as "Korean history?" Compared with the preface of offering longevity, the poem "Dedicating Longevity to Longevity" in Lezhi is longer than the slow song.
4. The origin of the word "knowledge"
Knowledge is knowledge, judgment or skill acquired through study, practice or exploration.
Knowledge is also the result of human's understanding of the objective world (including human itself) in practice. It includes facts, descriptions of information or skills acquired in education and practice. It can be either theory or practice. In philosophy, the study of knowledge is called epistemology. The acquisition of knowledge involves many complicated processes: feeling, communication and reasoning. Knowledge can also be regarded as the most fundamental factor that constitutes human wisdom.
From Liu Xiang's Biography of Han Women: "People have words for you, but you don't know evil?" Biography of Shu Wei Yan Guan Jia: "In the last years of Sejong, he gradually learned and became a servant." Tang Xueyong used Feng Wang's Weak Collection: "There are seven absurd bamboo slips of Zhu Ji and Wen Ruo on each side, but they are intertwined and unknown." Volume 27 of Surprise at the First Moment: "The owner of the hospital is very respectful, and everything in the hospital is decided by him." Lu Xun's Three Leisure Collections: An Overview of Modern New Literature: "In the literary world, the same is true. We don't know much, and there are too few materials to help us with our knowledge."
5. The meaning of knowledge
What exactly is knowledge is still controversial. China's definition of knowledge is generally from a philosophical point of view. For example, the entry of "knowledge" in "China Encyclopedia of Education" states: "As far as its content is concerned, the so-called knowledge is the reflection of the attributes and connections of objective things and the subjective image of the objective world in the human brain. As far as the form of activity is concerned, sometimes it is manifested as subjective perception or representation of things, which belongs to perceptual knowledge, and sometimes it is manifested as the concept or law of things, which belongs to rational knowledge. " From this definition, we can see that knowledge is the product of the unity of subject and object. It comes from the outside world, so knowledge is objective; However, knowledge itself is not an objective reality, but a reflection of the characteristics and connections of things in the human brain and a subjective representation of objective things. Knowledge is produced on the basis of the interaction between subject and object through the reflective activities of the human brain. Knowledge is the only source of human free love and principles.
The above definition provides a philosophical basis for us to discuss the connotation of knowledge. The macroscopic understanding of philosophical reflection theory needs to be concretized from the perspective of individual cognition, so that it can be effectively used to guide the specific teaching of schools.
Different from philosophy, cognitive psychology studies knowledge from the perspectives of the source of knowledge, the generation process and manifestation of individual knowledge. For example, Piaget believes that experience (that is, knowledge) comes from the interaction between individuals and the environment. This kind of experience can be divided into two categories: one is physical experience, which comes from the outside world and is the understanding of objective things and their connections obtained by individuals acting on objects; The other is logic-mathematical experience, which comes from the actions of the subject and is the result of the individual's understanding of the coordination between actions. For example, children gain experience about quantity conservation by fiddling with objects, and students gain knowledge about mathematical principles through mathematical reasoning. Piaget's definition of knowledge is expressed from the generation process of individual knowledge. In the classification of educational objectives, Bloom thinks that knowledge is "the memory of specific things and universal principles, the memory of methods and processes, or the memory of models, structures or frameworks", which is a description of phenomena from the perspective of the contents contained in knowledge.
We believe that in understanding the meaning of knowledge, it is necessary to distinguish knowledge as the wealth of human society from knowledge as an individual's mind. The knowledge of human society exists objectively, but the knowledge in the individual's mind is not the objective reality itself, but a subjective representation of the individual, that is, the knowledge structure in the human brain, which includes not only feelings, perceptions and representations, but also concepts, propositions and schemas, respectively indicating the different breadth and depth of the individual's response to objective things, and is formed through the individual's cognitive activities. Generally speaking, individual knowledge is stored in the brain in the form of hierarchical network structure (cognitive structure) from concrete to abstract. Philosophy mainly studies the nature of common knowledge in human society, while psychology mainly studies the nature of individual knowledge.
Where did all the knowledge come from?
Knowledge comes from life, creation comes from life, inspiration comes from life and knowledge comes from life.
"Pay attention to everything and learn" seems to be a famous saying that has been passed down through the ages, but it is definitely the best way to acquire knowledge and discover from life.
Yes, how can there be knowledge in life? However, as long as you pay attention to life and observe it, you will also benefit a lot.
Newton, a famous scientist, discovered the gravity of the earth precisely because he paid attention to life everywhere and observed it carefully. As we all know, Newton discovered the gravity of the earth because of a falling apple. However, countless apples fall from trees every year. Why can only Newton notice it and discover the gravity of the earth? This is because he is good at observation and diligent in thinking.
I believe everyone is no stranger to the world-famous Dujiangyan. However, when Li Bing built it, he had a modest story.
At that time, Li Bing was determined to turn the Minjiang River flood into water conservancy, so he built a weir. But the method of building weir has been tried many times and failed. One day, he saw some bamboo baskets in the mountain stream, which contained clothes to be washed, so he was inspired. He told people to weave large bamboo baskets, put them into pebbles, and then connected them, put them into the river layer by layer, piled a big weir in the river, reinforced with pebbles on both sides, and finally built a strong diversion weir.
This is the famous water conservancy project "Dujiangyan". Li Bing was able to observe life carefully and use his own life experience to find a way to build a diversion weir, which succeeded.
Watt, known as the "father of the steam engine", is also a person who is good at discovering from life.
Eight-year-old Watt can question why the lid of the pot is pushed up when boiling water. It was this problem that led Watt to study it and eventually invented the steam engine, which promoted the progress of human society.
There are many examples like this, and the success of many great men mostly comes from life. The knowledge gained in life is the most unforgettable, and I have a deep understanding of it.
I remember that I was very young, and I was still an ignorant child.
It was like a day in summer vacation, and I was playing in the garden. Suddenly, I was attracted by a strange phenomenon: in the corner, there was a large group of ants, walking neatly to the high mound. There was a small hole in the mound, and ants got in one by one.
Mother brought the kettle to burn them, but I insisted on seeing what they were doing.
Curious, I squatted aside until they were all "transferred" to the small hole, and I couldn't see why.
At this time, the sky is overcast and windy, and it's going to rain. Mother pulled me back into the house, and I stood at the window, still thinking about that strange thing. It finally cleared up. I came to the corner again and found that the original "home" of ants had been flooded by rain, but the hole in the mound was intact, and several ants were taking a leisurely walk next to their new "home".
I suddenly understood that ants moved "home" to shelter from the rain. From then on, I knew that as long as I saw ants moving home, it would definitely rain.
"Pay attention to everything and learn." Life is rich and colorful, and it has infinite knowledge, waiting for us to observe, discover, practice and understand. I believe that one day, the knowledge in life will also benefit you a lot.
7. Where is the source of blood lipids in human common sense?
The composition of blood lipids is complex, including triacylglycerol, phospholipids, cholesterol and cholesterol esters, free fatty acids, etc. But usually we refer to blood lipids mainly as triacylglycerol and cholesterol.
The source of blood lipids is nothing more than two ways. First, it comes from the food we eat, that is, the lipids ingested from food are digested and absorbed into the blood; The second is the synthesis from our body, which is mainly synthesized by tissues such as liver and fat cells and released into the blood. Usually, triacylglycerol and cholesterol in human blood are mainly synthesized by themselves, and the influence of food can not be ignored. After all, it is the raw material needed for synthesis.
The blood lipid content in human body fluctuates greatly and is easily influenced by many factors such as diet, age, sex, occupation, metabolism and so on. Triacylglycerol is a form of energy storage in the body. When the body ingests food such as sugar and fat, it can synthesize fat and store it in adipose tissue for energy demand during fasting and hunger.
Usually people in China use starch (such as rice, wheat, corn, etc. ) is the staple food, so the main source of triacylglycerol is starch. In addition, fat, animal fat and various fried foods also contain a lot of saturated fatty acids. The main synthesis sites of triacylglycerol in the body are liver, fat cells and small intestine, among which the liver has the strongest synthesis ability, but liver cells can synthesize fat, but they cannot store fat. For example, when triacylglycerol synthesized by liver cells cannot form very low density lipoprotein due to malnutrition, poisoning, lack of essential fatty acids, and lack of choline or protein, it will gather in liver cells and form "fatty liver"; Fat cells can store a lot of fat, which is the "warehouse" for the body to synthesize and store fat.
The sources of cholesterol are also divided into exogenous cholesterol and endogenous cholesterol. Exogenous cholesterol comes from daily diet. Usually about 40% cholesterol in food can be absorbed by small intestine. Normal adults should consume 500 cholesterol every day. 800 mg, almost all the cholesterol in the diet comes from animal foods, among which meat, liver, viscera, brain and egg yolk are the most abundant, while plant foods do not contain cholesterol. Most of the cholesterol needed by the human body is synthesized by the body itself. Normal adults can synthesize about 1 g cholesterol every day, and almost all tissues and cells in the human body can synthesize cholesterol. Among them, the liver is the most abundant place for human body to synthesize cholesterol, and the cholesterol in the body accounts for 70%? 80% is synthesized by liver, and 10% is synthesized by small intestine.
Therefore, even if there is no cholesterol in food, the body can still synthesize itself without cholesterol deficiency.
8. The origin of mathematical knowledge
Mathematics, whose English is Mathematics, is a plural noun. "Mathematics used to be arithmetic, geometry, astronomy and music, which was higher than grammar, rhetoric and dialectics."
Since ancient times, most people regard mathematics as a kind of knowledge system, which is the systematic summation of theoretical knowledge formed through strict logical reasoning. It not only reflects people's understanding of "Engels' spatial form and quantitative relationship in the real world", but also reflects people's understanding of "possible quantitative relationship and form" Mathematics can not only come from the direct abstraction of the real world, but also from the labor creation of human thinking.
Judging from the development history of human society, people's understanding of the essential characteristics of mathematics is constantly changing and deepening. "The root of mathematics lies in common sense, and the most obvious example is non-negative integers.
"Euclid's arithmetic comes from non-negative integers in common sense. Until the middle of19th century, the scientific exploration of numbers remained in common sense." Another example is the similarity in geometry. "In individual development, geometry even precedes arithmetic", and its "one of the earliest signs is the understanding of similarity." Finding similar knowledge so early is "like being born." Therefore, before the19th century, it was generally believed that mathematics was a natural science and an empirical science, because mathematics was closely related to reality at that time. With the deepening of mathematical research, the view that mathematics is a deductive science gradually occupied a dominant position after the middle of19th century, which was developed in the research of Bourbaki school. They think that mathematics is a science of studying structure, and all mathematics is based on algebraic structure.
Corresponding to this view, from Plato in ancient Greece, many people think that mathematics is the knowledge of research mode. Mathematician A.N. Whiiehead (186- 1947) said in Mathematics and Goodness, "The essential feature of mathematics is to study patterns in the process of abstracting from patterned individuals. 193 1 year, the proof of Godel's incompleteness theorem (k, G0de 1, 1978) declared the deficiency in the deductive system of axiomatic logic, so people thought that mathematics is an empirical science, and the famous mathematician von Neumann thought that mathematics has both deductive science and empirical science.
For the above viewpoints about the essential characteristics of mathematics, we should analyze them from a historical perspective. In fact, the understanding of logarithmic essential characteristics develops with the development of mathematics. Because mathematics comes from the practice of distributing goods, calculating time and measuring land and volume, the mathematical object at this time (as the product of abstract thinking) is very close to objective reality, and it is easy for people to find the realistic prototype of mathematical concepts, so people naturally think that mathematics is an empirical science; With the deepening of mathematical research, non-Euclidean geometry, abstract algebra and * * * theory have emerged, especially modern mathematics is developing towards abstraction, pluralism and high dimension. People's attention is focused on these abstract objects, and the distance between mathematics and reality is getting farther and farther. Moreover, mathematical proof (as deductive reasoning) plays an important role in mathematical research. Therefore, mathematics has emerged as the free creation of human thinking and the science of studying the relationship between quantity and quantity.
These understandings not only reflect the deepening of people's understanding of mathematics, but also are the result of people's understanding of mathematics from different aspects. As someone said, "Engels thought that mathematics is the study of quantitative relations and spatial forms in the real world, which is not contradictory to bourbaki's structural view. The former reflects the origin of mathematics, while the latter reflects the level of modern mathematics. It is a building built by a series of abstract structures. "
The statement that mathematics is the knowledge of research methods is an explanation of the essential characteristics of mathematics from the perspective of abstract process and abstract level of mathematics. In addition, from the ideological source, people regard mathematics as a science of deduction and research structure, which is based on human innate belief in the inevitability and accuracy of mathematical reasoning and a concentrated expression of self-confidence in their own rational ability, roots and strength. Therefore, people think that this method of developing mathematical theory, that is, deductive reasoning from axioms that are self-evident, is absolutely reliable, that is, if axioms are true, then the conclusions deduced from axioms must also be true. Applying these seemingly clear, correct and perfect logics, the conclusions drawn by mathematicians are obviously beyond doubt and irrefutable. In fact, the above-mentioned understanding of the essential characteristics of mathematics is carried out from the origin, existing mode and abstract level of mathematics, mainly from the achievements of mathematical research.
Obviously, the result (as a theoretical deduction system) cannot reflect the whole picture of mathematics. Another very important aspect that constitutes the whole of mathematics is the process of mathematical research. On the whole, mathematics is a dynamic process, an "experimental process of thinking" and an abstract generalization process of mathematical truth. Logical deduction system is the natural result of this process.
In the process of mathematical research, the rich, vivid and changeable side of mathematical objects can be fully displayed. Paulia (G. Poliva, 1888- 1985) believes that "mathematics has two sides, it is Euclid's strict science, but it is also something else.
Mathematics proposed by Euclid's method seems to be a systematic deductive science, but mathematics in the process of creation seems to be an experimental inductive science. Friedenthal said, "Mathematics is a very special activity, and this view" is different from what mathematics is printed in books and engraved in the mind. "
He believes that mathematicians or mathematics textbooks like to describe mathematics as "a well-organized state", that is, "the form of mathematics" is formed by mathematicians through their own organizations (activities); But for most people, they regard mathematics as a tool. They can't live without mathematics, because they need to apply mathematics, that is, for the public, they have to pass.