1. Knowledge The source of knowledge
Kant’s analysis What is the source of knowledge? Reward points: 0 - Solution time: 2006-8-13 12:20 Asked by: ahsix - Apprentice Magician Level 2 best answer Evaluation of Kant's philosophy Gadamer, a famous contemporary hermeneutic, said it well: "Spiritual science cannot use progress like this. "The great achievements of spiritual scientific research almost never become obsolete."
Talking about the so-called "bankruptcy of German idealism", Heidegger once wrote with indignation: "It is not that German idealism is bankrupt, but that the times no longer have the strength to withstand this spiritual world. of greatness, breadth and originality”. When Heidegger himself studies existential issues, he always explores the source of the problem, peels off the banana to the core, and returns to the thoughts of the Greeks with the help of linguistic analysis.
In his view, modern people have forgotten existence; the return to ancient Greek thought is the only way to remember existence again. Only when people exist authentically can they have real life. In this sense, it can be said that the spirit of the ancient Greeks is always alive, while modern Westerners have died due to mental weakness.
Heidegger is a new course, but if we really want to seriously study and master Heidegger’s philosophy, we should not put Plato, Aristotle, Kant, and Hegel aside. Behind the head. Kant's philosophy, in particular, not only provided a synthesis of the two philosophies of empiricism and rationalism after the Middle Ages in the modern West, but also provided a starting point for German idealism and a source of modern Western philosophy.
Whether phenomenology, hermeneutics, or scientific philosophy, they all seek inspiration from Kant, refine questions, and build a base for further development of thinking. Mr. Zheng Xin said: "If you surpass Kant, you can have new philosophy; if you surpass Kant, you can only have bad philosophy."
Mr. Zheng Xin's words are not only true for Western philosophy, but also for Chinese tradition. As far as the theory of ethics is concerned, if it wants to undergo creative transformation and form a life-like knowledge with a modern form, it must also pass the level of Kant's philosophy. Fortunately, the "high degree of spiritual effort" in mastering and interpreting Kant's philosophy and "opening up" it with traditional Chinese philosophy (especially the Confucian theory of inner sage) has been accomplished by Mr. Mou Zongsan, who has taken refuge in Hong Kong and Taiwan. Done.
Mou Zongsan not only mastered and interpreted Kant's philosophy, but also developed and enriched Kant's philosophy. He took the Confucian theory of inner sage as his foundation and the Mahayana Buddhist philosophy of "one mind that opens two doors" as his outline. He gave full stability and confirmation to the general knowledge and insights that shone in Kant's "transcendental decomposition" , constructing a philosophical system with "two-level ontology" as the basic theoretical backbone and integrating ontology, epistemology, and ethics, thus enabling Chinese philosophy, which has always lacked a system, to be able to directly dialogue with Western philosophy. type.
It can be said that "the great cause of virtue has come to an end!" Kang Youwei was probably one of the first Chinese people to come into contact with Kant's theory. Long before he was appointed emperor's master, he wrote a book called "Talks on the Heavens", which contained all the astronomical knowledge he had gained from the Western Books. Among them was Kant's "Nebula Theory". He also used the traditional Chinese theory of astronomy Comparison with the theory of form and energy.
In fact, Kant's "Introduction to the History of the Development of the Universe" containing his nebula theory is only a "little work" and has little connection with the entire system of Kant's philosophy. Another famous but often misinterpreted argument of Kant's is the so-called "agnosticism".
Mr. Nanhai stated the following in "Teachings about All Heavens": "However, things in the world are extremely unpredictable, we are extremely insignificant, and our knowledge is limited. How can we understand the affairs of the world with what we see and hear with the physical body? "Huh?" This is a common saying that life has a limit, knowledge has no limit, and it cannot be infinite because of the limit. It is really an unreasonable and arbitrary imposition to call it Kant. Yan Fu also used his own ideas to develop the "agnosticism" and attributed it to Kant: "Physics in the West is developing day by day, and teaching disasters are disappearing day by day. People with deep knowledge are unable to discern the subtleties of things, and they clearly reveal the theory that the way of heaven must be unknowable. It reminds the world of those who believe in the past and have the courage to be confident.
It is as far away as the Greek Borne, and as close as Locke, Hume, and Kant, who have repeatedly deduced the two "agnosticisms" of Hume and Kant. ", the meanings and methods of argumentation are different, so to put them together and compare them is to say that they are extremely different.
This problem continues to exist in university philosophy textbooks today. Yan Houguan then used Buddhist language to express Kant's meaning: "When you talk about the truth and reach the extreme, you will reach the unbelievable state.
It is neither absurd, but the truth is difficult to understand. This is what the true Buddhist scriptures say It’s incredible. “This time it’s a little more interesting.
According to Buddhism, "Reality has one phase, which means it is without phase, that is, it is like phase." This cannot be imagined, nor can it be talked about. The realm of practice. The old translation of Kant's "thing in itself" is "thing like", which is quite subtle.
Kant’s Philosophy and Yin-Yang Theory Kant wrote three important books: The Critique of Pure Reason talks about how people understand the world—truth. The Critique of Practical Reason talks about how people’s ethical rules are—good.
The object of the former is the phenomenal world, while the object of the latter is the ontological world. There is an unsurpassable gap between phenomenon and ontology. A bridge is built across the gap to make the transition from phenomenon to ontology.
This bridge is the purpose of nature. It includes the sense of beauty—beauty.
It means that nature transitions to its purpose, that is, objective ontology, through people's subjective sense of beauty. This includes the natural purpose of beauty, which is the main content of the third book Critique of Judgment.
Since Newton proposed 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 transzendentale Aesthetik It is possible to affirm mathematics through time and space patterns.
Transcendental Logic transzendentale Logik Transcendental Analysis tranzendentale Analytik Borrowing the Category of Intellectual Verstand Kategorie affirms that physics is possible. Transcendental Logic Transcendental Dialectical Transcendental Dialektik Study of Pure Reason Reine Vernunft Its contents: 1. The finite and infinite world, 2. The freedom of the soul, 3. The omnipotence of God.
Collectively called transcendental ideas tranzendentale Idee. Kant's transcendental dialectic teaches us that transcendental ideas are just illusions and metaphysics is impossible.
Because these questions all belong to the ontological world Noumenon. Although metaphysically impossible, pure reason points to our ontological goal.
And these goals can be accomplished by practical reason. Now we define yin-yang theory in terms of the Critique of Pure Reason and practice the Critique of Reason in the Phenomenal Realm, Kant's second book.
I. Practical reason praktische Vernunft has practical principle Grundsaetzen.
2. Knowledge The source of knowledge
Kant’s analysis What is the source of knowledge? Reward points: 0 - Solution time: 2006-8-13 12:20 Asked by: ahsix - Apprentice Magician Level 2 best answer Evaluation of Kant's philosophy Gadamer, a famous contemporary hermeneutic, said it well: "Spiritual science cannot use progress like this. "The great achievements of spiritual scientific research almost never become obsolete."
Talking about the so-called "bankruptcy of German idealism", Heidegger once wrote with indignation: "It is not that German idealism is bankrupt, but that the times no longer have the strength to withstand this spiritual world. of greatness, breadth and originality”. When Heidegger himself studies existential issues, he always explores the source of the problem, peels off the banana to the core, and returns to the thoughts of the Greeks with the help of linguistic analysis.
In his view, modern people have forgotten existence; the return to ancient Greek thought is the only way to remember existence again. Only when people exist authentically can they have real life. In this sense, it can be said that the spirit of the ancient Greeks is always alive, while modern Westerners have died due to mental weakness.
Heidegger is a new course, but if we really want to seriously study and master Heidegger’s philosophy, we should not put Plato, Aristotle, Kant, and Hegel aside. Behind the head. Kant's philosophy, in particular, not only provided a synthesis of the two philosophies of empiricism and rationalism after the Middle Ages in the modern West, but also provided a starting point for German idealism and a source of modern Western philosophy.
Regardless of phenomenology, hermeneutics, or scientific philosophy, they all seek inspiration from Kant, refine questions, and build a base for further development of thinking. Mr. Zheng Xin said: "If you surpass Kant, you can have new philosophy; if you surpass Kant, you can only have bad philosophy."
Mr. Zheng Xin's words are not only true for Western philosophy, but also for Chinese tradition. As far as the theory of ethics is concerned, if it wants to undergo creative transformation and form a life-like knowledge with a modern form, it must also pass the level of Kant's philosophy. Fortunately, the "high degree of spiritual effort" in mastering and interpreting Kant's philosophy and "opening up" it with traditional Chinese philosophy (especially the Confucian theory of inner sage) has been accomplished by Mr. Mou Zongsan, who has taken refuge in Hong Kong and Taiwan. Done.
Mou Zongsan not only mastered and interpreted Kant's philosophy, but also developed and enriched Kant's philosophy. He takes the Confucian theory of inner sage as his foundation and the Mahayana Buddhist philosophy of "one mind that opens two doors" as his outline. He fully consolidates and confirms the general knowledge and insights that shine in Kant's "transcendental decomposition". , constructing a philosophical system with "two-level ontology" as the basic theoretical backbone and integrating ontology, epistemology, and ethics, thus enabling Chinese philosophy, which has always lacked a system, to be able to directly dialogue with Western philosophy. type.
It can be said that "the great cause of virtue has come to an end!" Kang Youwei was probably one of the first Chinese people to come into contact with Kant's theory. Long before he was appointed emperor's master, he wrote a book called "Talks on the Heavens", which contained all the astronomical knowledge he had gained from the Western Books. Among them was Kant's "Nebula Theory". He also used the traditional Chinese theory Comparison with the theory of form and energy.
In fact, Kant's "Introduction to the History of the Development of the Universe" containing his nebula theory is only a "little work" and has little connection with the entire system of Kant's philosophy. Another famous but often misinterpreted argument of Kant's is the so-called "agnosticism".
Mr. Nanhai stated the following in "Teachings about All Heavens": "However, things in the world are extremely unpredictable, we are extremely insignificant, and our knowledge is limited. How can we understand the affairs of the world with what we see and hear with the physical body? "Huh?" This is a common saying that life has a limit, knowledge has no limit, and it cannot be infinite because of the limit. It is really an unreasonable and arbitrary imposition to call it Kant. Yan Fu also used his own ideas to develop the "agnosticism" and attributed it to Kant: "Physics in the West is developing day by day, and teaching disasters are disappearing day by day. People with deep knowledge are unable to discern the subtleties of things, and they clearly reveal the theory that the way of heaven must be unknowable. It reminds the world of people who believe in the past and have the courage to be confident.
It is as far as the Greek Borne, and as close as Locke, Hume, and Kant, they have repeatedly deduced the two "agnosticisms" of Hume and Kant. ", their meanings and methods of argumentation are different. To put them together and compare them is to say that they are extremely different.
This problem continues to exist in college philosophy textbooks today. Yan Houguan then used Buddhist language to express Kant's meaning: "When you talk about the truth and reach the extreme, you will reach the unbelievable state.
It is neither ridiculous, but the truth is difficult to understand. This is what the true Buddhist scriptures say It’s incredible. “This time it’s a little more interesting.
Buddhists say that "the reality is one phase, that is, it is without phase, that is, it is like phase." This cannot be imagined, nor can it be talked about. The realm of practice. The old translation of Kant's "thing in itself" is "thing like", which is quite subtle.
Kant’s Philosophy and Yin-Yang Theory Kant wrote three important books: The Critique of Pure Reason talks about how people understand the world—truth. The Critique of Practical Reason talks about how people’s ethical rules are—good.
The object of the former is the phenomenal world, while the object of the latter is the ontological world. There is an unsurpassable gap between phenomenon and ontology. A bridge is built across the gap to make the transition from phenomenon to ontology.
This bridge is the purpose of nature. It includes the sense of beauty—beauty.
It means that nature transitions to its purpose, that is, objective ontology, through people's subjective sense of beauty. This includes the natural purpose of beauty, which is the main content of the third book Critique of Judgment.
Since Newton proposed 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 transzendentale Aesthetik It is possible to affirm mathematics through time and space patterns.
Transcendental Logic transzendentale Logik Transcendental Analysis tranzendentale Analytik Borrowing the Category of Intellectual Verstand Kategorie affirms that physics is possible. Transcendental Logic Transcendental Dialectical Transcendental Dialektik Study of Pure Reason Reine Vernunft Its contents: 1. The finite and infinite world, 2. The freedom of the soul, 3. The omnipotence of God.
Collectively called transcendental ideas tranzendentale Idee. Kant's transcendental dialectic teaches us that transcendental ideas are just illusions and metaphysics is impossible.
Because these questions all belong to the ontological world Noumenon. Although metaphysically impossible, pure reason points to our ontological goal.
And these goals can be accomplished by practical reason. Now we define yin-yang theory in terms of the Critique of Pure Reason and practice the Critique of Reason in the Phenomenal Realm, Kant's second book.
I. Practical reason praktische Vernunft has practical principle Gru.
3. What is the origin of Ling in common sense of words?
Mao Xianshu, a native of the Qing Dynasty, changed words within fifty-eight characters into Xiao Ling, which is a later generation practice.
In fact, although most of the poems are based on contemporary ditties, some are also based on larger tunes. For example, "Brahman Order" comes from "Brahman", "Ganzhou Order" comes from Daqu "Ganzhou", and so on.
Many of the lingci of Daqu have many long characters, which are different from ordinary lings. For example, Liu Yong's "Ganzhou Order" has 78 characters, "Brahman Order" has 86 characters, Ouyang Xiu's "Liangzhou Order" has 105 characters, "Liu Mo Order" has 94 characters, and "Plucking Lotus Order" has 91 characters. Words, etc.
In terms of number of words, almost all of these edicts can be classified as long tones. But they are still poems rather than slow songs, because of their cheerful rhythm.
Of course, some poems also have slow songs with the same name, such as Liu Yong's "Lang Tao Sha Ling" and "Lang Tao Sha Slow", etc. Compared with the slow songs of the same name, these songs obviously have fewer words and shorter tunes. However, there are exceptions. For example, compared with "Xiantian Shou Ling" in "Xiantian Shou Ling" recorded in the "History of Goryeo? Music Records", the poems are longer than the slow songs. song.
4. The origin of the word "knowledge"
Knowledge is the understanding, judgment or skill acquired through learning, practice or exploration
Knowledge is also The achievements of human beings in understanding the objective world (including human beings themselves) in practice. It includes descriptions of facts, information, or skills acquired in education and practice. It can be about theory or it can be about practice. In philosophy, the study of knowledge is called epistemology. The acquisition of knowledge involves many complex processes: sensing, communication, reasoning.
Knowledge can also be regarded as the most fundamental factor that constitutes human wisdom.
From Han Liu Xiang's "Biography of Women: Qi Guan Concubine": "People have spoken to you, don't you know the evil?" "Book of Wei·Biography of Eunuchs·Jia Can": "At the end of Emperor Shizong's reign , Gradually, he became a servant." Tang Xue Yongruo's "Ji Yi Ji·Wang Feng" said: "Each side has seven nests of Zhu Ji, and the writing is like a wrong seal script, but it is twisted and connected, so it cannot be understood." Volume 27 of "Patching Cases and Surprises": "The master of the courtyard has great respect for me, and seeing that he has a lot of knowledge, all matters in the courtyard, big or small, are based on his opinions." Lu Xun's "Sanxian Ji·An Overview of Today's New Literature": "In Literature The same goes for the world, we know too little, and there are too few materials to help us know. ”
5. The meaning of knowledge
What exactly knowledge is is still controversial. . Our country's definition of knowledge is generally made from a philosophical perspective. For example, the "knowledge" entry in "Encyclopedia of China·Education" states: "The so-called knowledge, in terms of the content it reflects, is the attribute of objective things. The reflection of the objective world in the human brain is the subjective image of the objective world in the human brain. In terms of its form of reflection activity, it sometimes appears as the subject's perceptual perception or representation of things, which is perceptual knowledge, and sometimes it appears as concepts or concepts about things. Laws belong 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 external world, so knowledge is objective; but knowledge itself is not objective reality, but the reflection of the characteristics and connections of things in the human brain. It is a subjective representation of objective things. Knowledge is the interaction between subject and object. Based on the reflection activities of the human brain. Knowledge is the only source that produces the love and principles of human freedom.
The above definition provides a philosophical basis for our discussion of the connotation of knowledge. However, the understanding of the macroscopic philosophical reflection theory still needs to be concreted from the perspective of individual cognition, so that it can be effectively used to guide specific teaching in schools.
Different from philosophy, cognitive psychology studies knowledge from the perspective of the source of knowledge, the production process and representation form of individual knowledge. For example, Piaget believed that experience (i.e. knowledge) comes from the interaction between the individual and the environment. This kind of experience can be divided into two categories: one is physical experience, which comes from the external world and is the information obtained by the individual acting on the object. Knowledge of objective things and their connections; the other type is logical-mathematical experience, which comes from the actions of the subject and is the result of individual understanding of actions and the mutual coordination between actions. For example, children gain experience in conservation of quantity by playing with objects, and students gain knowledge of mathematical principles through mathematical reasoning. Piaget's definition of knowledge is expressed from the production process of individual knowledge. Bloom's "Taxonomy of Educational Objectives" believes that knowledge is "the recollection of specific things and general principles, the recollection of methods and processes, or the recollection of a pattern, structure, or framework", which is derived from what knowledge contains. From the perspective of content, it belongs to a kind of phenomenon description.
We believe that when understanding the meaning of knowledge, it is necessary to distinguish knowledge as the common wealth of human society from knowledge as the knowledge in the individual mind. Knowledge in human society exists objectively, but the knowledge in an 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 both feelings, perceptions, representations, etc. Concepts, propositions, and schemas respectively mark the different breadth and depth of an individual's response to objective things, which are formed through individual cognitive activities. Generally speaking, individual knowledge is stored in the brain in the form of a hierarchical network structure (cognitive structure) from concrete to abstract. Philosophy mainly studies the nature of collective knowledge in human society, while psychology mainly studies the nature of individual knowledge.
6. Where does all knowledge come from?
Knowledge comes from life, creation comes from life, inspiration comes from life, and knowledge also comes from life,
" "Everything you pay attention to will lead to learning", this seems to be a famous saying that has been passed down through the ages, but it is indeed the best way to gain knowledge and discovery from life.
Yes, how can there be knowledge in life? However, as long as you pay attention to life and observe life, you will also benefit a lot.
The famous scientist Newton was able to discover the gravity of the earth precisely because he paid attention to everything in life and observed carefully. As we all know, Newton discovered the earth's gravity because of a falling apple. However, there are countless apples falling from the tree every year. Why was only Newton able to notice it and discover the earth's gravity? This is because he is good at observation and diligent in thinking.
I believe everyone is familiar with the world-famous "Dujiangyan". However, when Li Bing built it, he had a story that was neither big nor small.
At that time, Li Bing was determined to turn the Minjiang River water hazard into water conservancy, so he built a weir. However, the method of building weirs has been tried many times, but all failed. One day, he saw some bamboo baskets in the mountain stream with clothes to be washed in them, so he got inspiration from them. He asked people to weave large bamboo baskets and put them in pebbles. Then he connected the bamboo baskets and placed them layer by layer in the river. He built a large weir in the river and reinforced it with big pebbles on both sides to create a strong water diversion. The weir was finally built.
This is the famous water conservancy project "Dujiangyan".
Li Bing was able to observe life carefully and use his life experience to find a way to build a water diversion weir and achieve success.
Watt, known as the "Father of the Steam Engine," was also a person who was good at discovering things from life.
At the age of eight, Watt was able to question the phenomenon of "why the kettle lid is pushed up when boiling water." It was this question that led Watt to start studying it and eventually invented the steam engine, which promoted the progress of human society.
There are many, many examples like this. The success of many great people mostly comes from life. The knowledge gained in life is the most unforgettable, and I have a deep understanding of this.
I remember that I was very young and an ignorant child at that time.
It seemed to be a day during summer vacation. I was playing and having fun in the garden. Suddenly, I was attracted by a strange phenomenon: in the corner, there was a large group of ants, walking neatly towards the tall mound of soil. There was a small hole in the mound, and the ants got in one by one.
My mother brought the kettle and wanted to scald them to death, but I refused and insisted on seeing what they were doing.
Curious, I kept squatting aside until they all "transferred" into the small holes, and I couldn't figure out why.
At this time, the sky was covered with dark clouds, the wind was blowing, and it was going to rain. My mother pulled me back into the house, and I stood blankly in front of the window, still thinking about that strange thing. Finally the weather cleared up, and I went to the corner again and found that the ants' original "home" had been flooded by rain, but the holes in the mound were intact, and a few ants were walking leisurely next to their new "home".
I suddenly realized that the ants moved "home" to avoid the rain. From then on, I learned that whenever I see ants moving "home", it must be raining.
"Everything you pay attention to is learning." Life is colorful and 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 are the sources of blood lipids in the human body
The composition of blood lipids is more complex, including triacylglycerol, phospholipids, cholesterol and cholesterol esters, and free fatty acids, but usually we talk about The blood lipids mainly refer to triacylglycerol and cholesterol.
There are two sources of blood lipids. One is from the food we eat, that is, the lipids ingested from food enter the blood after digestion and absorption; the other is from synthesis in our body, mainly It is synthesized by the liver, fat cells and other tissues and released into the blood. Normally, triacylglycerol and cholesterol in human blood are mainly synthesized by themselves, and the influence of food cannot be ignored. After all, they are the raw materials needed for synthesis.
The blood lipid content in the human body fluctuates widely and is easily affected by many factors such as diet, age, gender, occupation, and metabolism. Triacylglycerol is the form in which the body stores energy. When the body consumes sugar, fat and other foods, it can synthesize fat and store it in adipose tissue to meet energy needs during fasting and hunger.
Usually Chinese people eat starch (such as rice, wheat, corn, etc.) as their staple food, so the main source of triacylglycerol is starch. In addition, fat meat, animal fats, and various fried foods also contain large amounts of triacylglycerol. Saturated fatty acids. The main synthesis sites of triacylglycerol in the body are in the liver, fat cells and small intestine. Among them, the liver has the strongest synthesis ability, but liver cells can synthesize fat, but cannot store fat. For example, triacylglycerol synthesized by liver cells can be reduced due to malnutrition. , poisoning, lack of essential fatty acids, choline or protein deficiency, when very low-density lipoprotein cannot be formed and secreted into the blood, it will accumulate in liver cells, forming "fatty liver"; fat cells can store large amounts of fat, which is the body's synthesis and storage Fat "warehouse".
The sources of cholesterol are also divided into two types: exogenous cholesterol and endogenous cholesterol. Exogenous cholesterol comes from daily meals. Generally, about 40% of the cholesterol in food can be absorbed by the small intestine. For normal adults, The daily intake of cholesterol should be between 500 and 800 mg. Almost all cholesterol in the diet comes from animal foods, among which meat, liver, offal, brain, egg yolk, etc. are the most abundant. Plant foods do not contain cholesterol. Most of the cholesterol needed by the human body is synthesized by the body itself. A normal adult can synthesize about 1 gram of cholesterol per day. Almost every tissue and cell in the human body can synthesize cholesterol. The liver is the most active place for cholesterol synthesis in the body. 70% to 80% of cholesterol in the body is synthesized by the liver and 10% by the small intestine.
Therefore, even if there is no cholesterol in food, the body can still synthesize it by itself without causing cholesterol deficiency.
8. The origin of mathematical knowledge
Mathematics, whose English is mathematics, is a plural noun, "Mathematics used to be four subjects: arithmetic, geometry, astronomy and music. A higher status than the three disciplines of grammar, rhetoric and dialectics. ”
Since ancient times, most people have regarded mathematics as a system of knowledge, a system formed through rigorous logical reasoning. It reflects people’s understanding of “the spatial forms and quantitative relationships of the real world (Engels)” and also reflects people’s understanding of “possible quantitative relationships and forms”.
Mathematics can come from direct abstraction from the real world, or it can come from the labor creation of the human mind.
Judging from the development history of human society, people’s understanding of the essential characteristics of mathematics is constantly changing and deepening. "The roots of mathematics lie in common common sense. The most obvious example is non-negative integers.
"Euclidean arithmetic originated from non-negative integers in common sense, and until the middle of the 19th century, the understanding of numbers Scientific inquiry remains at ordinary common sense," another example is the similarity in geometry, "geometry even precedes arithmetic in individual development," of which "one of the earliest symptoms is the knowledge of similarity," knowledge of similarity Being discovered so early, “it’s like a big baby. "Therefore, before the 19th century, people generally believed that mathematics was a natural science and an empirical science, because the connection between mathematics and reality at that time was very close. With the continuous deepening of mathematical research, from the middle of the 19th century, mathematics was The view of a deductive science gradually became dominant. This view was developed in the research of the Bourbaki school. They believed that mathematics is the science of studying structures. All mathematics is based on three types: algebraic structure, ordinal structure and topological structure. On top of the parent structure.
Corresponding to this view, starting from Plato in ancient Greece, many people believe that mathematics is the study of patterns. The mathematician A. N. Whitehead (186----1947) ) said in "Mathematics and Goodness", "The essential characteristic of mathematics is: the study of patterns in the process of abstraction from patterned individuals." Mathematics is the most powerful for understanding patterns and analyzing the relationships between patterns. "Technology." In 1931, G?del's (1978) proof of the incompleteness theorem announced the shortcomings in the axiomatic logical deduction system. In this way, people thought of the view that mathematics is an empirical science. The famous mathematics The scientist von Neumann believed that mathematics has the characteristics of both deductive science and empirical science.
Regarding the above-mentioned views on the essential characteristics of mathematics, we should analyze it from a historical perspective. In fact, the understanding of the essential characteristics of mathematics has developed with the development of mathematics. Since mathematics originated from practices such as allocating goods, calculating time, measuring land and volume, the mathematical objects at this time (as the product of abstract thinking) are very close to objective reality, and people can easily find the realistic prototypes of mathematical concepts. In this way, people naturally think that mathematics is an empirical science; with the deepening of mathematical research, the emergence of non-Euclidean geometry, abstract algebra, and *** theory, especially the development of modern mathematics towards abstraction, multivariate, and high dimensions, people's As attention focused on these abstract objects, mathematics became increasingly distant from reality, and mathematical proof (as a form of deductive reasoning) assumed an important place in the study of mathematics, hence the emergence of the view that mathematics is the human mind Free creation is a science that studies the relationship between quantities, a theory that studies abstract structures, a knowledge of patterns, and so on.
These understandings not only reflect people's deepening understanding of mathematics, but also are the result of people's understanding of mathematics from different aspects. As someone said, "Engels's statement that mathematics is the study of quantitative relationships and spatial forms in the real world is not inconsistent with Bourbaki's structural views. The former reflects the origin of mathematics, and the latter reflects the development of modern mathematics. level, modern mathematics is an edifice built from a series of abstract structures.”
The statement that mathematics is the study of patterns is an analysis of the essential characteristics of mathematics from the perspective of the abstract process and abstract level of mathematics. In addition, from the perspective of ideological roots, the reason why people regard mathematics as a deductive science and a science that studies structures is based on human beings' innate belief in the inevitability and accuracy of mathematical reasoning. The epitome of confidence in the ability, origin and power of human reason, it is therefore believed that this method of developing mathematical theories, namely deductive reasoning starting from self-evident axioms, is absolutely reliable, that is, if the axioms are true , then the conclusions deduced from it must also be true. By applying these seemingly clear, correct, and perfect logics, the conclusions drawn by mathematicians are obviously unquestionable and irrefutable. In fact, the above-mentioned understanding of the essential characteristics of mathematics is based on the source, way of existence, level of abstraction, etc. of mathematics, and is mainly based on the results of mathematical research.
Obviously, the result (as a theoretical deduction system) does not reflect the whole picture of mathematics. Another very important aspect that makes up the whole of mathematics is the process of mathematical research, and generally speaking, mathematics is A dynamic process is an "experimental process of thinking" and an abstract generalization process of mathematical truth. Logical deduction systems are a natural outcome of this process.
In the process of mathematical research, the rich, vivid and changing side of mathematical objects can be fully displayed. G. Poliva (1888-1985) believed that "mathematics has two sides. It is a rigorous science like Euclidean, but it is also something else.
By Euclid The mathematics proposed by the German method seems to be a systematic deductive science, but the mathematics in the creative process looks like an experimental inductive science," Freidenthal said, "Mathematics is a kind of science. Quite a special activity, this view "is distinguished from mathematics as something printed in books and imprinted in the mind.
"
He believes that mathematicians or mathematics textbooks like to express mathematics as "a well-organized state," that is, the "mathematical form" is when mathematicians put the mathematics (activity) content through their own It is formed by organizations (activities); but for most people, they regard mathematics as a tool. They cannot live without mathematics because they need to apply mathematics, which is, for the public, to pass.