Gottfriend Wilhelm von Leibniz, the great philosopher and scientist.

Character

Gottfried Wilhelm von Leibniz (July 1, 1646 - November 14, 1716) was Germany's foremost natural scientist, mathematician, physicist, historian, and philosopher. He was a rare scientific genius in the world. He was also the founder of calculus with Newton (January 4, 1643 - March 31, 1727). He read widely, dabbled in encyclopedias, and made an indelible contribution to enriching the scientific knowledge of mankind.

Personal life and deeds

On July 1, 1646, Gottfried Wilhelm van Leibniz was born into a bookish family in Leipzig, eastern Germany. His father, Friedrich Leibniz, was a professor of moral philosophy at the University of Leipzig, and his mother, Catherina Schmalk, was born into a family of professors and was a devout Lutheran Protestant.

Leibniz's parents personally served as their children's initial teachers. His exposure made Leibniz very studious and highly talented since childhood. He had a strong interest in poetry and history when he was a child. Unfortunately, his father passed away when he was 6 years old, but he left him a rich library of books.

Leibniz's father died when he was only six years old, leaving him with a rich collection of books more valuable than money, and a well-informed mother who took care of his son's early education. As a result, Leibniz was widely exposed to ancient Greco-Roman culture, reading the works of many famous scholars, and thus gained a solid cultural foundation and clear academic goals.

At the age of 8, Leibniz entered the Nikolai School and studied Latin, Greek, lyrics, arithmetic, logic, music, the Bible, Lutheran doctrine, etc.

In 1661, at the age of 15, Leibniz entered the University of Leipzig to study law. As soon as he entered the school, he followed the standard humanities courses of the second year of the university, and he also took the time to study philosophy and science. In May 1663, he received his bachelor's degree in "On the Metaphysical Controversies on the Principles of the Individual." During this period, Leibniz also read widely the works of Bacon, Kepler, Galileo and others, and conducted in-depth thinking and evaluation of their writings. After listening to the course taught by the professor on Euclid's Elements of Geometry, Leibniz developed a keen interest in mathematics.

In January 1664, Leibniz completed his thesis "On the Difficulties of Legal Science" and obtained a master's degree in philosophy. On February 12 of that year, his mother passed away unfortunately. The 18-year-old Leibniz lived alone since then. He was deeply influenced by his mother in his thoughts, character and other aspects.

In 1665, Leibniz submitted his doctoral thesis "On Identity" to the University of Leipzig. In 1666, the review committee refused to grant him a doctorate in law on the grounds that he was too young (only 20 years old). Hegel believed that this may be because Leibniz has too many philosophical insights, and the professors who reviewed the paper were very unhappy when they saw that he was vigorously studying philosophy. He was very angry about this, so he resolutely left Leipzig and went to the University of Altdorf near Nuremberg. He immediately submitted the doctoral thesis that he had already prepared to the school. In February 1667, the University of Altdorf awarded him a doctorate in law. degree and hired him as a professor of law.

That year, Leibniz published his first mathematical paper,"On the Art of Combination." This is an article about mathematical logic. Its basic idea is to attribute the truth demonstration of a theory to a calculation result. Although this paper is not mature enough, it shines with innovative wisdom and mathematical talent. Later, a series of work made him the founder of mathematical logic.

In 1666, after receiving a doctorate in law, Leibniz joined a group of alchemists in Nuremberg. In 1667, he met the political figure John Christie Wen, Baron of Boynburg, and was recommended by the baron to the elector Mainz. From then on, Leibniz entered the political arena and joined the diplomatic world, working under the archbishop of Mainz, Schoenborn.

In the winter of 167l-1672, he was commissioned by the Elector of Mainz to prepare plans to stop the French attack on Germany. In 1672, Leibniz went to Paris as a diplomat to try to persuade King Louis XIV of France to give up the attack, but he was never able to meet the French king, let alone complete the task assigned to him by the elector. This diplomatic activity ended in failure, but during this time, he was deeply inspired by Huygens and determined to study higher mathematics. He studied the works of Descartes, Fermat, Pascal, and others, and began creative work.

In January 1673, in order to promote reconciliation between England and the Netherlands, he went to London to mediate unsuccessfully. However, he took the opportunity to establish contact with famous scholars in English academia. He met with the secretary of the Royal Society, the mathematician Odenberg, and the physicist Hooke and the chemist Boyle, who corresponded with him for three years. Leibniz returned to Paris in March 1673 and was recommended as a member of the Royal Society in April. During this period, his interests became increasingly apparent in mathematics and the natural sciences.

When the Elector of Mainz died in October 1672, Leibniz lost his position and salary, and was only a governess. At that time, he had tried many times to seek a formal position as a diplomat, or to obtain a position in the French Academy of Sciences. Unsuccessful, he had to accept the invitation of John Friedrich, Duke of Hanover, to go to Hanover.

On October 4, 1676, Leibniz left Paris with a brief stop in London. Then he went to the Netherlands and met Leeuwenhoek, the biologist who used a microscope to observe bacteria, protozoa and sperm for the first time, which had an impact on Leibniz's later philosophical thought. In The Hague, he met Spinoza. In January 1677, Leibniz arrived in Hanover as legal advisor and librarian of the Duke's House of Brunzwijk and historian of the Brunzwijk family, and was responsible for international communications and acted as technical advisor. Hanover became his permanent residence.

In his spare time, Leibniz extensively studied philosophy and various scientific and technical issues, and engaged in various academic, cultural, and social and political activities. Soon, he became a member of the court, became famous in society, and his life was prosperous. In 1682, Leibniz and Menke founded the influential Latin scientific journal "Academic Chronicle" (also known as "Teacher's Journal") in the history of modern science, and most of his mathematical and philosophical articles were published in this journal; at this time, his philosophical thought gradually matured.

In December 1679, John Friedrich, Duke of Brunswick, died suddenly, and his brother August succeeded him, while Leibniz retained his title. Sophie, the new Duchess, was an admirer of his philosophy, and the famous saying that "no two leaves are exactly the same in the world" came from his conversation with Sophie.

In order to realize his ambition to excel throughout Germany, August suggested that Leibniz conduct extensive historical research and investigation and write a book on the modern history of their family. He began this work in 1686. After studying valuable local archival materials, he requested an extensive tour of Europe.

Leibniz left Hanover in November 1687 and arrived in Vienna in the early summer of May 1688. In addition to searching archives, he spent a lot of time getting to know scholars and celebrities from all walks of life. In Vienna, he met with the Austrian Emperor Leopold I and formulated a series of economic and scientific plans for the emperor, which left a deep impression on the emperor. He tried to find a position in the Austrian court, but did not receive a positive answer until 1713, and his plan to ask ancient Austria to establish a "world library" never came true. He then traveled to Venice and then to Rome. In Rome, he was elected a member of the Roman Academy of Scientific and Mathematical Sciences. In 1690, Leibniz returned to Hanover. For his contribution to writing the history of the Brunzwick family, he was awarded the position of Privy Counselor.

During the transition period of the century in 1700, Leibniz was enthusiastically engaged in the planning and construction of the Academy of Sciences. He felt that scholars 'independent research was a waste of time and had little effect, so he vigorously advocated concentrating talents to study academic, cultural and engineering technology, so as to better arrange social production and guide national construction.

Since 1695, Leibniz has been running around and lobbying for the establishment of the Academy of Sciences in Berlin. In 1698, he personally went to Berlin for this purpose. In 1700, when he visited Berlin for the second time, he finally received the patronage of Friedrich I, especially his wife (daughter of Duke Augustus of Hanover), to establish the Berlin Academy of Sciences, and he became the first dean. In February 1700, he was also elected as a member of the French Academy of Sciences. At this time, Leibnitz was the core member of the four major scientific academies in the world: the Royal Society, the French Academy of Sciences, the Roman Academy of Sciences and Mathematical Sciences, and the Berlin Academy of Sciences.

In early 1713, the Emperor of Vienna granted Leibniz the position of imperial advisor and invited him to guide the establishment of the Academy of Sciences. Peter the Great of Russia also listened to Leibniz's advice several times during a trip to Europe from 17ll to 1716. Leibniz tried to convince the talented emperor of the value of establishing an Academy of Sciences in Petersburg. Peter the Great was interested in this, and in 1712 he gave Leibniz a paid position as a court advisor to mathematics and science. Around 1712, he was employed by the royal families of Vienna, Brunzwijk, Berlin, and Petersburg at the same time. During this period he actively promoted his plans to write an encyclopedia, establish an academy, and use technology to transform society at every opportunity. After his death, the Vienna Academy of Sciences and the Petersburg Academy of Sciences were established successively. It is said that he also advised Emperor Kangxi of the Qing Dynasty to establish an Academy of Sciences in Beijing through missionaries.

Just as Leibniz was favored by various courts, he was already moving towards a miserable old age. On November 14, 1716, a week after being laid in bed due to abdominal colic caused by gallstones, Leibniz passed away alone at the age of 70.

Leibniz never married in his life and did not become a professor at a university. He never goes to church, so he has the nickname Lovenix, who believes nothing. When he died, the priest used this as an excuse and ignored him. The court, which had hired him, did not bother, and no one came to express condolences. On his deathbed, he was only accompanied by the doctor he trusted and his secretary Eckhart. After Ekhart issued the obituary, Fondenauer, Secretary of the French Academy of Sciences, delivered a eulogy to Leibniz, a foreign member, at the regular meeting of the Academy of Sciences. In 1793, Hanover people built a monument to him; in 1883, a standing statue of him was erected near a church in Leipzig; in 1983, the city government of Hanover restored the "Leibniz Former Residence" destroyed in the Second World War as it was for people to pay homage.

personal achievement

Founding calculus

In the second half of the 17th century, science and technology in Europe developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, through the efforts of scientists from all over the world and historical accumulation, the calculus theory based on the concepts of function and limit came into being.

The idea of calculus can be traced back to the Greek method of calculating area and volume proposed by Archimedes and others. Newton invented calculus in 1665, and Leibniz also published treatises on calculus ideas in 1673-1676.

In the past, differential and integral were studied separately as two kinds of mathematical operations and two kinds of mathematical problems. Cavalieri, Barrow, Wallis and others obtained a series of important results for finding the area (integral) and tangent slope (derivative), but these results are isolated and incoherent.

Only Leibniz and Newton truly communicated integral and differential and clearly found the intrinsic direct connection between the two: differential and integral are two inverse operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can systematic calculus be constructed on this basis. From the differential and quadrature formulas for various functions, a common algorithm program is summarized, which universalizes the calculus method and develops the calculus algorithm expressed in symbols. Thus, calculus was "largely completed by Newton and Leibniz, but not invented by them."

However, the priority of the establishment of calculus has caused a fierce debate in the history of mathematics. In fact, although Newton's research on calculus preceded Leibniz, Leibniz's results were published before Newton.

Leibniz's paper "A Wonderful Type of Calculation for Finding the Maximum and Minimum" published in the "Teachers 'Journal" in October 1684 is the earliest calculus document. This six-page paper is not rich in content and vague in reasoning, but it has epoch-making significance.

Newton also wrote in the first and second editions of "Principia Mathematica of Natural Philosophy" three years later, published in 1687:"Ten years ago, in a correspondence between me and Leibniz, the most outstanding geometrically, I showed that I already knew the method of determining maxima and minima, the method of making tangents, and similar methods, but I concealed this method in the exchange of letters... The most outstanding scientist wrote in reply that he had also discovered the same method. He also recounted his method, which was hardly different from mine except for his wording and symbols "(but this passage was deleted in the third edition and subsequent reprints).

Therefore, it was later recognized that Newton and Leibniz created calculus independently.

Newton started from physics and used the set method to study calculus. Its application combined more with kinematics, and his attainments were higher than Leibniz. Leibniz started from geometric problems, used analytical methods to introduce the concept of calculus and obtain operating rules. Its mathematical rigor and systematicness were beyond Newton's reach.

Leibniz realized that good mathematical symbols can save mental labor, and the use of symbols is one of the keys to mathematical success. Therefore, the calculus symbols he created were far superior to Newton's symbols, which had a great impact on the development of calculus. In 1713, Leibniz published the article "The History and Origin of Calculus", which summarized his ideas for founding calculus and explained the independence of his achievements.

Bagua Square Diagram and Binary

There are many textual research on the relationship between Leibniz's binary system and China's Eight Diagrams, but so far there seems to be no final conclusion as to whether Leibniz invented binary system under the influence of the Eight Diagrams or invented binary system alone. Hu Yang and Li Changduo's book "Leibniz-Binary System and Fuxi Eight Trigrams" provides relatively credible material, showing that Leibniz's binary system is at least to some extent inspired by the Eight Trigrams.

According to Leibniz himself, he had invented binary arithmetic before 1679, but it was not until April 1, 1703 that he received the Fuxi Bagua diagram sent by the Jesuit Bai Jin. Only then did he begin to formally study the Bagua symbols and discover the consistency of his binary system with the Fuxi Bagua diagram. A few days later, he wrote a paper "Explanation of Binary Arithmetic - On the Use of Only Zero and 1 and the Meaning of Fuxi's Numbers", published in the Proceedings of the Royal Academy of Sciences in France. According to Leibniz himself, many researchers believe that Leibniz did not invent binary based on the Fuxi Bagua diagram.

However, Hu Yang and Li Changduo's book "Leibniz-Binary and Fuxi Eight Trigrams" proved that although Leibniz did not see the Fuxi Eight Trigrams graph brought to him by Bai Jin until 1703, it did not mean that this was the first time he had seen the Fuxi Eight Trigrams graph, but that Leibniz had already seen the Fuxi Eight Trigrams graph as early as 1687.

In 1687, Jesuit Shipai published the book "Confucius, the Chinese Philosopher", in which a total of 13 pages introduce the Fuxi Eight Trigrams. The book is equipped with the order map of Fuxi Eight Trigrams, the orientation map of Fuxi Eight Trigrams, and the sixty-four hexagrams of the King of Wen. It is worth mentioning that in the order map of Fuxi Eight Trigrams, the orientation map of Fuxi Eight Trigrams, and the sixty-four hexagrams of the King of Wen, the corresponding hexagrams are marked with Arabic numerals 1 to 64.

In Leibniz's binary system, through the extension of 0 and 1, all numbers can be represented, such as 000, 001, 010, 011, 100 represent the numbers 0-4 respectively. In the Gossip of the Book of Changes, through the extension of yin and yang, the principle of everything in the universe can be expressed. If the Yin Yao is regarded as 0, and the Yang Yao is regarded as 1, all the hexagrams can be regarded as a combination of 0 and 1. For example, the Kun hexagram is 000000, the Qian hexagram is 111111, and the Da You hexagram is 111101. The sixty-four hexagrams of the Fuxi diagram can also be regarded as the numbers from 0 to 63 in binary arithmetic.

Leibniz read "Confucius, the China Philosopher" the year it was published. In a letter to his friend Von Hesen-Reinfel, he introduced him that he had read the book. In this letter, the word "Fohi" also appears, which translates into Chinese as "Fuxi." Through these facts, it is not difficult to prove that Leibniz had seen the sequence diagram of Fuxi's Eight Trigrams, the location diagram of Fuxi's Eight Trigrams, and the sixty-fourth hexagram diagram of King Wen.

But Leibniz claimed in a letter dated May 17, 1698 that thinking about binary had been for more than twenty years. A letter back to Bai Jin on May 18, 1703 also stated that he had invented binary more than 20 years ago. In its museum, there is also "Binary Mathematics" published in 1679. Based on this situation, Bai Yingli's book "Confucius, the Philosopher of China" should have no influence on his invention of binary.

However, Hu Yang and Li Changduo's book "Leibniz - Binary and Fuxi Eight Diagrams" also has material to prove that as early as 1679, that is, before he invented the earliest time of binary, there were books on Eight Diagrams published in Europe, and Leibniz saw Easy Diagrams before 1679.

Hu Yang and Li Changduo's book "Leibniz-A Survey of Binary and Fuxi Eight Trigrams" introduced that in 1660, scholar Speissel published the book "An Analysis of China Literature and History" in the Netherlands, which records I Ging(Book of Changes). Speissel had a close relationship with Leibniz, and this book was a book Leibniz referred to understand China. The two parts of the book introduce the Book of Changes, introducing the Dragon Horse's negative diagram to the river, Fuxi's diagram to make the Eight Trigrams, and the Tai Chi Yin-Yang Eight Trigrams theory.

In addition, from the book "Analysis of Chinese Literature and History", it can be seen that before 1660, Spisel's reference to Chinese cultural documents included the "Ancient History of China" published by the Jesuit Wei Kuangguo in 1658 and the "Empire of China" published by Zeng Dezhao in 1642. The "Empire of China" only briefly introduces the theory of yin and yang gossip, but it is very detailed in the "Ancient History of China". The book details the evolution process of Tai Chi gossip in which yin and yang gave birth to two rites, two rites gave birth to four elephants, and four elephants gave birth to gossip. Some scholars believe that "Ancient History of China" may have been the first to introduce the sixty-four hexagrams to Europe and influenced Leibniz.

Numerous achievements in advanced mathematics

Leibniz's achievements in mathematics are huge, and his research and achievements have penetrated into many fields of higher mathematics. His proposed a series of important mathematical theories laid the foundation for subsequent mathematical theories.

Leibniz discussed the properties of negative and complex numbers, and came to the conclusion that the logarithm of complex numbers does not exist, and the sum of conjugated complex numbers is a real number. In later studies, Leibniz proved his conclusion was correct. He also studied the system of linear equations, discussed the elimination method theoretically, and first introduced the concept of determinants and put forward some theories of determinants. In addition, Leibniz also founded the basic concept of symbolic logic.

Computer Science Contributions

In 1673, Leibniz went to Paris to build a computer that could perform addition, subtraction, multiplication, division, and square operations. This was another advance in computing tools after Pascal's addition machine. After Pascal's death, Leibniz discovered a paper on the "adder" written by Pascal himself, which aroused his strong desire to invent and determined to expand the function of this machine to multiplication and division. Leibniz had a difficult early life. After being given a trip to France, he created an opportunity to realize his long-cherished dream of building a computer. In Paris, Leibniz hired some famous mechanical experts and skilled craftsmen to assist him, and finally built a more complete mechanical computer in 1674. The machine invented by Leibniz was called the "multiplier". It was about 1 meter long and had a series of gear mechanisms installed inside. In addition to its large size, the basic principle was inherited from Pascal. However, Leibniz added a device to the computer called the "stepper wheel". The stepper wheel is a long cylinder with 9 teeth, which are distributed on the surface of the cylinder in sequence; there is another pinion next to it that can be moved along the axial direction to engage with the stepper wheel one by one. Every time the pinion rotates once, the stepping wheel can rotate 1/10 and 2/10 turns respectively according to the number of teeth it engages with the pinion gear... until 9/10 turns, so that it can repeatedly do addition and subtraction, and in the process of turning the handle, this repeated addition and subtraction is converted into multiplication and division operations.

Leibniz's contribution to computers not only lies in multipliers. Around 1700 AD, Leibniz was inspired by the China "Yi Tu"(Eight Trigrams) given to him by a friend, and finally realized the true meaning of binary numbers. Although Leibniz's multiplier still uses decimal, he took the lead in systematically proposing binary arithmetic rules for the design of computers, laying a solid foundation for the modern development of computers.

Rich achievements in physics

Leibniz's achievements in physics were also extraordinary. In 1671, Leibniz published the article "New Hypothesis of Physics", which proposed the specific principle of motion and the abstract principle of motion, believing that a moving object, no matter how small, will carry parts of the object that are in a completely static state. Move together. He also carefully discussed the principle of conservation of momentum proposed by Descartes, proposed a prototype of the principle of conservation of energy, and published "On Descartes and Others 'Significant Mistakes in the Laws of Nature" in the "Teachers' Journal". Short Proof "raised the question of the quantity of motion, proved that momentum cannot be used as a unit of measure of motion, and introduced the concept of kinetic energy, believing for the first time that the conservation of kinetic energy is a common physical principle.

He also fully proved the view that "perpetual motion machines are impossible". He also opposed Newton's absolute view of time and space, arguing that "without matter there is no space, and space itself is not an absolute reality". "The difference between space and matter is the same as the difference between time and motion, but although these things are different, they are inseparable." This idea later attracted the attention of Mach, Einstein and others.

In 1684, Leibniz pointed out in the article "New Analytical Proof of the Force on a Solid" that fibers can be extended and their tension is proportional to elongation, so he proposed applying Hooke's Law to a single fiber. This hypothesis later became known in material mechanics as the Mariot-Leibniz theory.

Leibniz also made achievements in optics. He used the extreme value method in calculus to derive the law of refraction and tried to explain the basic laws of optics by using the extreme value method. It can be said that Leibniz's physics research has always been moving towards the goal of establishing a system of axioms similar to Euclidean geometry for physics.

Monotheism of philosophical contributions

Monadism.

Monadologie

The work of the modern German philosopher G.W. Leibniz. The original text of "Monad Theory" is in French, without title. Koehler published in 1720, a German translation of this article, and in 1721 Diton translated it into Latin. In 1840, J.E. Ertmann found in the Leibniz manuscript, the original text, included in the compilation of "The Complete Works of Leibniz Philosophy", and added the title. This article is a highly condensed work of Leibniz's main ideas expounded in many philosophical works. Although short, it is rich in content. The full text consists of 90 sections, which can be roughly divided into two parts: Sections 1 to 48 mainly discuss the nature of all entities, including that entities should be the final unit of the complex, which has no parts in itself, and is a simple thing, that is, a spiritual monad; entities themselves should have intrinsic active principles and so on. Sections 49 to 90 mainly discuss the relationship between entities, including the pre-determined harmony and the theory that this world is "the best of all possible worlds" and so on. Leibniz's monad theory is a system of objective idealism, which has a tendency to compromise with religious theology, but also contains some reasonable dialectical elements, such as the idea that all things move by themselves.

Leibniz's epistemology

Leibniz's epistemology is in the same vein as his monism. Starting from the hierarchy of monads, he devalues sensibility and elevates reason, and regards sensual knowledge as purely animal knowledge. For this reason, he opposes empiricism, especially Locke's empiricism. His New Theory of Human Reason was written specifically to oppose Locke's Theory of Human Reason. He believes that empiricism grasps only individual things, and cannot grasp general and necessary things. If it is based on experience alone, this is animal behavior. He said: "The beast guides himself purely by experience, only by example." The association of beasts is as pure as the association of mere empiricists, who assume that everything that has happened before will happen again in a situation that makes them feel similar, and cannot judge whether the same reasons are still valid. This is why man is so easy to capture beasts, and why mere empiricists are so prone to mistakes. 'Leibniz's critique of empiricism from the perspective of the distinction between the general necessity of scientific knowledge and the individual accidental sensory experience is profound.

As a rationalist, Leibniz attempted to reconcile empiricism and rationalism in an attempt to find a middle way between Descartes and Locke's theories. After a detailed analysis of Locke's empiricism, he wrote: "I have always been and still am in favor of the innate concept of God advocated by Mr. Descartes, and therefore also believe that there are other innate concepts that cannot come from feeling." Now I have gone further in accordance with this new system; I even believe that all thoughts and actions of our soul come from within itself and cannot be given to it by senses. Leibniz inherited Descartes 'rationalism and advocated the theory of "natural concept". In his view, the list has no "window" for external things to enter and exit, and cannot accept the influence of any external things. Therefore, knowledge cannot have any objective source, but can only be innate. However, Leibniz did not agree with Descartes 'assertion that the human mind is born with a clear concept of talent. He said: "We cannot imagine that in our souls we can read the eternal laws of reason as we read an open book, as we read the judges 'decrees on a bulletin board without difficulty or inquiry." In his view, the concept of talent is not always clear from the beginning (except in God), but gradually develops from a relatively vague perception of talent. "Ideas and truth are innate in us as tendencies, endowments, habits, or latent abilities of nature, not as practical effects. It can be seen that when Leibniz promoted the theory of talent, he emphasized the "latent" nature of the concept of talent. He emphasized the role of sensory experience when describing how to turn potential things into reality. He said: "As long as we rely on the opportunities provided by our senses and focus, we can discover these laws in our hearts. It can be seen that Leibniz did not deny that feelings play a certain role in the process of cognition. However, Leibniz believed that although perceptual experiences of individual things are necessary, they can only provide us with some special individual examples and cannot provide universal truths. Here he is implying that since the knowledge of universality and necessity does not come from sensory experience, it can only be innate in the mind. Locke adheres to the materialist empiricism principle that "everything that is in reason is in feeling." He asserts that all our knowledge is based on experience, and that our hearts are something like a blank board, and experience can be written on it. Leibniz proved that the mind is essentially active. Therefore, he added a supplement to Locke's principle in "A New Essay of Human Reason", that is,"Everything in the mind preexists in feelings, except reason itself." He believes that since the mind is dynamic, it will not be a blank board. He compared the human soul to a piece of textured marble. Although the patterns on marble are not ready-made images, the existing patterns of marble determine what kind of image it is suitable for carving into. "If there were originally some lines on this stone, indicating that the image of Herkule was better than other images, this stone would have been more decided to be used to carve this image, and the image of Herkule could be said to be In some way, he was gifted in this stone. It can be seen that on the one hand, Leibniz, like Descartes, advocated the theory of "natural concepts"; on the other hand, he was different from Descartes, believing that concepts were potentially natural, that is, concepts were originally hidden in the human heart and needed to be rationally processed and pondered before they could be turned into clear concepts. Here, Leibniz stated the valuable dialectical thought that cognition is a process of development, and also showed that his rationalism was a rationalism that gave way to empiricism.

On the question of whether the subject of knowledge is a matter or a spiritual entity, Leibniz opposed Locke's view that God might give thought power to matter. He believes that the spiritual monad is the only entity, there is no material entity, and the subject of cognition naturally cannot be a material entity. He said: "A thing that can feel or think cannot be mechanical. "The ability of matter to feel and think is not a natural thing, but it can do so in two ways, one way is that God connects it to another entity that naturally can think, and the other way is that God places thoughts in matter in a miraculous way.¡»

In terms of truth, Leibniz believed that there are two types of truths: "truth of inference" and "truth of fact." In determining the difference between the two, he described their principles. One is the principle of contradiction. Because of this principle, we believe that what hides contradictions are false, and what opposes error is real. In "A New Essay on Human Reason", he described the principle of contradiction in more detail: any judgment is either true or false. This involves two true judgments:1. A judgment cannot be both true and false;2. A judgment cannot be both true and false. Therefore, he said: "The truths of reasoning are inevitable, and their opposite is impossible." For example, knowledge deduced based on mathematical axioms and logical rules is the truth of reasoning. Only this kind of truth is inevitable and reliable. The other is the principle of sufficient reason, because of which we can see that no phenomenon can be true or realistic, and no assertion can be fair-because there is no sufficient reason why things are this way and not that way. He said: "If anything is true or real, if any statement is true, there must be a sufficient reason why it is this way and not that way, although these reasons are often never known to us." Thus,"the truths of facts are accidental, their opposites are possible." He believed that what perceptual perception provided was "factual truth," which was accidental and untrustworthy. He wrote: "The original proof of necessary truth comes only from reason, while other truths come from observation through experience or sensation." Our minds can recognize two truths, but it is the source of the former truth; and for a universal truth, no matter how much special experience we have about it, if we understand its inevitability without relying on reason, we will never get a definite guarantee for it by induction. It can be seen that Leibniz advocates a rationalist view of truth, believing that the truth of reasoning comes from the soul, rather than a correct reflection of objective things. In Leibniz's view, since human beings cannot find final or sufficient reasons in their understanding of actual things, these things and the truths that correspond to them are accidental. Leibniz emphasized that "contingency" is only for us humans, because humans cannot find sufficient reasons for the reality of factual truth; for God, all truth is intuitive, and there is no difference between the truth of reasoning and the truth of fact, because the world and its principles are created by God, and God can see everything.

In short, Leibniz elevated the truth of reasoning and showed a tendency towards rationalism, but after all, he admitted the truth of fact and believed that it was provided by perceptual perception, reflecting his concession to empiricism.

In Leibniz, however, "truth of facts" does not mean objectively existing facts. He believed that everything is the sum of the monads, but except that God has absolutely clear and unambiguous consciousness, many monads have only unconscious consciousness, which Leibniz called the "passive activity" of the monads. He believed that matter or object is a combination of these monads. Matter and objects do not exist, they are just vague, unconscious perceptions, they are nothing more than phenomena. However, these phenomena should be subject to certain laws. These laws are not laws of material nature, but laws of the appearance of the monads, they are the highest monad - the purposeful arrangement of God. In this way, teleology is based on the mechanistic interpretation of nature.

The versatile Leibniz

The main goal of Leibniz's struggle was the search for a universal way to acquire knowledge and invent, an effort that led to many mathematical discoveries. Leibniz's versatility is rarely matched in history. His fields of study and achievements span mathematics, physics, mechanics, logic, biology, chemistry, geography, anatomy, zoology, botany, gaseology, navigation, geology, linguistics, law, philosophy, history, and diplomacy.

In 1693, Leibniz published an article on the origin of the earth, which was later expanded into the book "Primitive Earth", proposing the formation of igneous and sedimentary rocks in the earth. As for the fossils of organisms in the strata, he believed that these fossils reflected the continuous development of biological species, and the ultimate cause of this phenomenon was changes in nature, not accidental miracles. His theory of the origin of the earth, especially his ideas on the evolution of the universe and the evolution of the earth, inspired Lamarck, Ryle and others, and to a certain extent promoted the progress of geological theory in the 19th century.

In 1677, he wrote "History of the Discovery of Phosphorus", which discussed the properties and extraction of phosphorus. He also proposed techniques for separating chemicals and desalinating water.

In terms of biology, Leibniz put forward various viewpoints on organic theory from a philosophical perspective in his works such as "Monadology" published in 1714. He believed that there were organisms between animals and plants, and the discovery of hydrops proved his view.

In meteorology. He once personally organized manpower to observe atmospheric pressure and weather conditions.

In formal logic, he distinguished and studied the truth of reason (the proposition of necessity) and the truth of fact (the proposition of chance), and introduced the "law of sufficient reason" in logic, which was later regarded as a basic law of thinking. He envisioned applying mathematical methods to logic, turning logical reasoning into purely symbolic logical calculus, which is the art of logic as a proof, and carried out pioneering research work for this purpose. Although he later interrupted this research, he pointed out a new direction for the development of logic, which played an important role in the later creation of mathematical logic, and is therefore recognized as the founder of mathematical logic.

In 1696, Leibniz put forward the theory of mind-body parallelism in psychology. He emphasized the role of synesthesia, and Descartes' interaction theory and Spinoza's monism constituted the three major theories of psychology at that time. He also put forward the preliminary idea of the "subconscious" theory.

In 1691, Leibniz sent a letter to Baben proposing the basic idea of the steam engine.

Around 1700, he proposed the principle of anhydrous air pressure, completely eliminating the liquid column, which played an important role in the history of the development of air presses.

Law is a subject in which Leibniz received a degree. In 1667, he published "New Law on Legal Teaching". He had a series of profound thoughts on law.

In 1677, Leibniz published "Towards a Common Writing". After that, he devoted himself to the study of universal writing ideas for a long time and made certain contributions to logic and linguistics. Today, he is recognized as a pioneer of Esperanto.

As a famous philosopher, his philosophy mainly focuses on "monadalism","predeterminative harmony" and natural philosophical theories. His theory was combined with the theory of his disciple Wolf to form the Leibniz-Wolf system, which greatly influenced the development of German philosophy, especially Kant's philosophical thoughts. The German natural philosophy he pioneered has developed greatly through Wolf, Kant, Goethe to Hegel.

When Leibniz was the historian of the Elector of Braunschweig-Hanover, he wrote three volumes of "History of Braunschweig". His ideas on historical continuity and the method of looking at the small picture from the big picture and the collection and arrangement of historical materials had a great influence on the later German Göttingen School.

During Leibniz's academic research career, he published a large number of academic papers, and many manuscripts were not published during his lifetime. In terms of mathematics, the seven-volume "Complete Mathematics" edited by Gerhardt is a relatively complete representative work of Leibniz's mathematical research. Gerhardt also edited the seven-volume Book of Philosophy. Dozens of various anthologies, collections of works, and collections of letters have been published, from which Leibniz's main academic achievements can be seen. Today, there is also a special academic journal "Leibniz" for Leibniz studies, which shows its important position in the history of science and culture.

An advocate of cultural exchange between China and the West

Leibniz was very concerned about Chinese science, culture and philosophy, and he was the first German to study Chinese culture and philosophy. He learned a lot about China from Grimaldi, a Jesuit missionary who came to China, including sericulture and textiles, paper printing and dyeing, metallurgy and minerals, astronomy and geography, mathematical writing, etc., and edited and published these materials. He believes that a new type of relationship of exchange and understanding should be established between China and the West.

In the introduction to The Current Situation in China, Leibniz writes: "The greatest culture and the most advanced civilization of all mankind seem today to converge at the opposite ends of our continent, that is, in Europe and in the east at the other end of the earth - China." China, an ancient civilization, is comparable in size to Europe, but has a population that exceeds "." We are on equal footing in terms of daily life and the skills of dealing with nature empirically. Each of us has the skills to benefit the other by communicating with each other. In terms of thoughtfulness and rational deliberation, we are obviously better ", but" in terms of the philosophy of time, that is, in terms of ethics and statecraft in terms of life and human reality, we are really dwarfed ".

Here, Leibniz not only showed an open-minded and studious spirit without the color of "Eurocentrism", but also drew a grand blueprint for the two-way cultural exchange between China and the West, and tried his best to promote the in-depth development of this exchange. It is the people of the East and the West who learn from each other, learn from each other's strengths and weaknesses, and prosper and progress together.

Leibniz has made lifelong efforts to promote cultural exchanges between China and the West, which has had a wide and far-reaching impact. His spirit of being open-minded and eager to learn, treating Chinese culture as equals, and free from "Eurocentric" prejudice is particularly commendable, and is worthy of admiration and emulation by future generations.

A versatile and knowledgeable scientific genius who is rare in the world has achieved fruitful results in many fields and made irreplaceable contributions to the continuous enrichment and prosperity of human scientific knowledge.