During the holiday, I read a book "Mathematics and Philosophy", which was a gift from Academician Zhang Jingzhong to math lovers. The main contents of this book include? What is it? Which geometry is real and changeable, the disintegration and regeneration of views? Infinitely small? The ghost of quantity, the number of natural numbers, the uproar caused by Russell's paradox, what is a number, which is true but cannot be proved, and so on. Because there are so many concrete mathematical problems, mathematicians are often immersed in solving mathematical problems all day and have no time to pay attention to what appears in the development of mathematics? Contradiction? . But the history of mathematics tells us that it happens to be? Contradiction? Only by solving it repeatedly can the development of mathematics leap and deepen.
Zhang Jingzhong's "Mathematics and Philosophy" tells these important historical events in the development of mathematics, and shows in a popular way the content and situation of the debate at that time, the solutions and the rapid development of mathematics. For example, about numbers, are only natural numbers and rational numbers generated by them enough? So what? What is 2? This led to the emergence of irrational numbers. In Euclidean geometry, many people tried to prove the fifth postulate, but they all failed. This leads to the appearance of non-Euclidean geometry; The application and definition of infinitesimal leads to the establishment of strict real limit theory; Comparison of infinite sets; Definition of set and Godel theorem. After each of these major historical events, mathematical thought has made a leap, thus making mathematics have a qualitative development and leap. Open the history of western mathematics or philosophy, people will find an interesting and important phenomenon: western mathematics and philosophy are inextricably linked.
This connection is not only endless, but also continues to this day. Looking back, mathematics and philosophy have been inextricably linked since the birth of western philosophy. Thales, the first philosopher in the West, was a mathematician. Pythagoras, a famous mathematician, came to a conclusion in his in-depth study of mathematics. What is it? A famous philosophical proposition; Plato, a great philosopher, thinks that number is a unique objective existence, which leads to mathematics? Platonism? In the 20th century, the three schools around the basic research of mathematics pushed their relationship to a peak. In these two thousand years, philosophy and mathematics have influenced and promoted each other, and at the same time, many problems have arisen between them. For example: how to understand the truth of mathematics? What are numbers? How to understand the concepts of infinity and continuity? Wait a minute. The research and discussion of this series of problems has contributed to the establishment of a branch of mathematical philosophy-mathematical philosophy analysis. However, due to its complexity, wide coverage and many differences, most people can only flinch, and it is difficult to have an overview of the study of mathematical philosophy. In the book, questions about the philosophy of mathematics and the relationship between mathematics and philosophy can be explained in easy-to-understand words, giving a very clear explanation.
In order to make the profound truth easier to be understood by ordinary people, the author also adds very appropriate metaphors from time to time. For example, when discussing the truth of mathematics, it is pointed out that the problem for mathematicians today is not whether the mathematical conclusion is truth, but to choose an appropriate structure. So is this choice completely arbitrary and there is no standard? No. Information about which structures should be added and which structures should be modified still comes from scientific practice. How can we make such an important truth clear? There is a metaphor in the book:? When customers go to a tailor's shop to order clothes, they can accuse them of wrong size, wrong color, wrong cloth and so on.
Once fashion design is not aimed at a specific group of people, there is no right or wrong problem, only a choice problem. Here are all kinds of clothes, please try them on. The kind of clothes that don't fit you may be liked by another customer! If the tailor does whatever he wants for this reason, does not investigate the body shape, does not study the psychology, and does not conform to the trend, then he can only close down. Mathematicians study structure, which is like no longer processing clothes for regular customers. They face the general demand and occupy a vast market. ? (Quoted from Mathematics and Philosophy 1 17) The profound viewpoints of mathematical philosophy become very easy to understand through common sense in life. Many novel ideas are also put forward in the book. If you use it? Fuzzy Philosophy and Precise Mathematics: A Human Perspective
Mirrors and microscopes Describe the respective characteristics of mathematics and philosophy; Think? The field of mathematics is expanding. The territory of philosophy is shrinking? Wait a minute. It is worth noting that the author also made a novel philosophical analysis of some of his own mathematical research work.
For example, he discussed the unity of deduction and induction from the research of proving geometric theorems with his own examples; Explain the * * * properties of real number system and natural number system with the principle of continuous induction. After reading this book, I also consulted Academician Zhang Jingzhong's views on mathematics teaching, which was very enlightening. For example, he thinks that if the textbook is simple, but the exam is still difficult, then the students will not really? Reduce the burden? . He advocates? Study more and take fewer exams? The textbook might as well go deeper: if the depth of study is not enough, it is difficult for students to appreciate the interest of mathematics; If the exam is simpler, children can find the fun of mathematics in a relaxed way. In addition, we should strengthen the study of geometry in the curriculum of primary and junior high schools, instead of emphasizing mathematical operations as we do now. The United States is the country that spends the most energy on mathematics education, but even Americans themselves admit that their mathematics education has little effect.
He believes that one of the important reasons is that they have cut too much geometry in the compilation of textbooks since the 1960s. Graphics are not boring and easy to understand. In the early stage of learning mathematics, children may not understand many wonderful things of mathematics, so they should attract their interest through the movement changes of graphics. With the deepening of learning, children are gradually guided to solve geometric problems with algebra, operation and calculus. Similarly, teachers can also play a vital role in cultivating children's interest in mathematics. In his view, the worst teaching is to let students do dozens of similar problems after learning a formula. Mathematics teaching reform should not only focus on what to say, what not to say, what to say first, and what to say later. Teachers should make great efforts to study whether there are different and better expressions outside textbooks.
Reflections on the second part of The Story of Philosophy Once I accidentally saw a report introducing Liu, a math teacher in keshan town Middle School, Luo Zhuang, Linyi City. He teaches philosophy in math class, even foreign philosophers. What's more, he watched the World Cup football match with his students on the eve of his graduation class without any homework. What was the result? His junior two students took the unified examination in Linyi City, and their scores were better than those in junior three. In the Olympic competition, his class won half of the prizes in Linyi. Liu said that math teachers should be philosophers. Because many philosophers study mathematics, Socrates is a mathematician, and Marx loves mathematics. As soon as he studied calculus, he felt relaxed.
It's a pity that a math teacher in a rural junior high school thinks so deeply. I am also a math teacher. From his stories, I have a yearning for philosophy. With my ignorance of philosophy and shallowness of mathematics, Academician Zhang's book is very suitable for me and I can't put it down. The author can explain the philosophical problems of mathematics and the relationship between mathematics and philosophy in a simple way and make a very clear explanation. In order to make the profound truth easier to be understood by ordinary people, the author also adds very appropriate metaphors from time to time.
For example, when discussing the truth of mathematics, the author points out that the problem for mathematicians today is not whether the mathematical conclusion is truth, but to choose an appropriate structure. So is this choice completely arbitrary and there is no standard? No. In the author's opinion, which structures should be added and which structures should be modified still come from scientific practice. How can we make such an important truth clear? The author made a metaphor:? When customers go to a tailor's shop to order clothes, they can accuse them of wrong size, wrong color, wrong cloth and so on. Once fashion design is not aimed at a specific group of people, there is no right or wrong problem, only a choice problem. Here are all kinds of clothes, please try them on. The kind of clothes that don't fit you may be liked by another customer! If the tailor does whatever he wants for this reason, does not investigate the body shape, does not study the psychology, and does not conform to the trend, then he can only close down. Mathematicians study structure, which is like no longer processing clothes for regular customers. They face the general demand and occupy a vast market. ? (Quoted from Mathematics and Philosophy 1 17) The profound viewpoints of mathematical philosophy become very easy to understand through common sense in life. This metaphor seems handy, but it needs the author's skills to be simple and clear.
After reading it three times, there are still many doubts, such as: What is law of excluded middle mentioned in the article? What is continuous induction of real numbers? Is the continuity in mathematics the same as that in human perceptual knowledge? My mathematical literacy has greatly influenced my understanding of the article. The author basically explains some philosophical problems from the perspective of mathematics. In other words, this is a book that analyzes philosophical problems from the perspective of mathematicians.
For example, from the standpoint of mathematicians, the author gives ingenious explanations on Zeno's paradox, the theory that white horses are not horses, and whether chickens lay eggs or eggs lay chickens. After reading the whole book, the deep relationship between mathematics and philosophy is still incomprehensible. But it has some influence on my work. Mathematics classroom teaching can concretize philosophical connotation, such as seeking knowledge and differences, seeking common ground while reserving differences, solving multiple problems in one problem, solving multiple problems in one way, solving multiple problems in one way, dealing with divergent problems and concentrating opinions. The connotation of personality wisdom also includes problem-solving consciousness, inquiry consciousness, reflection consciousness after problem-solving, inductive meaning after reflection, and principal contradiction consciousness when solving problems. It can reflect the understanding of the laws of cognition, understanding, induction and sublimation followed in the study of anything, so that students can understand that learning is not only to acquire knowledge and skills, but also to include the methods of acquiring skills and a good learning mentality without the best, so that students can master the viewpoint of being good at discussion and reflection.
About 13 or 4 years ago, I read Russell's Why I Live in an English magazine. He said that his irresistible curiosity for true knowledge and his irresistible sympathy and love for human suffering were the three major driving forces of his life? . At that time, I was young and easy to be full of these things? Calm passion? The words were deeply moved, so they were copied in the notebook.
Let's talk about Russell's three main motives in life. In fact, Russell's words are in the same spirit as the wisdom of the three sages of ancient Greece, the exploration of Columbus and the exploration of Americans going to the sea. This same spirit runs through the history of western thought ―― even in the dark Middle Ages (after all, universities and professors originated from the church, and there seems to be no lack of meticulous logic in scholasticism). In my opinion, the essence of western spirit is to explore the world-nature, society and human beings with sharp tools of speculation and logic.
People in China are different. The wise words of China's great philosophers (mostly great scholars after the Han Dynasty), regarded as heroic words of moral models, are all about the compromise between man and the world (nature, society, others and self) or the struggle between people, or are they made by the authorities? Promulgated? Yes, like, what? Harmony between man and nature? Like Su Shi's? If you are poor, you will be immune to it, and if you are rich, you will help the world? Lei Feng's? I will devote my limited life to serving the people indefinitely? How many people have improved their lives because of Lei Feng style? Service) and so on, moreover, the struggle between people is the essence and the main melody, and the compromise between people and the world is the ladder and excuse for the psychological relief of the losers in the struggle, and it is a sub-melody. So, what is the core of all these eastern wisdom? Man to man? -If you can't fight, just say so, okay? Unity? , is it? Picking chrysanthemums under the east fence, leisurely seeing Nanshan? ; The winner wanted to maintain the status of victory and let the enslaved people give up their resistance ideologically, so he entrusted fate and published the book of sages.
This is just to illustrate the value of "the happiness of thinking". Wang Xiaobo is a writer who I can't put down with a book. In my opinion, his works are like this: based on conscience, life-oriented, and logic-oriented, he constantly devoted himself to the real evil that lasted and deepened for more than half a century.
About conscience, think of Mark? Nothing is more useless than conscience. If conscience becomes a puppy, I will definitely drown it. It can be seen that conscience was originally given to everyone by creation, but the evil in reality forced people to destroy it bit by bit.
The happiness of reading thinking, or reading Wang Xiaobo's mature words, has three kinds of enjoyment: the interest of words, the debate of philosophical thinking and the detachment of reading all human feelings.
Almost every word he writes is simple. It seems that every word you use only needs to be read and written after primary school. But it seems difficult to find out that the second person can write like this by writing chapters in a string of sentences.
Perhaps it is the subtle influence of his father, who studies logic. Almost all his articles are logical deduction, which unfolds trivial matters in a way of children bickering, full of gossip and enthusiasm.
If you are lucky enough to be a happy prince in the palace, you don't know the danger of life; Or, you are suffering in the world, but you lament the unfairness of fate. I don't know if there are more people who live as hard or harder; What if? Adults? Like your father, you can erase a vicious and cold history, so that Kong Lung can't turn back. Then, you can look at Wang Xiaobo's prose, as well as this book "The Joy of Thinking". It is like a special history book, occasionally picking up and rambling about small events deposited in personal memory, and the erased era is presented with clear high pixels.
Wang Xiaobo's essays seem to be idle talk, but they are not nonsense at all. He thinks deeply because of people's difficulties, because of pain, and writes because of deep thinking.