Gottfried Wilhelm Leibniz

Character's life

Early life, forging life

On July 1, 1646, Gottfried Wilhelm Leibniz was born in Leipzig in the Holy Roman Empire His grandfather had served in the Saxon government for three generations. His father was Friedrich Leibnütz and his mother was Catherina Schmuck. After growing up, the spelling of Leibniz's name was changed to "Leibniz", but most people are used to writing "Leibnitz". In his later years, his signature was usually written "vonLeibniz" to show his noble status. Leibniz’s work was released to the world after Leibniz’s death. The author’s name is usually "Freiherr[Baron]G.W.vonLeibniz.", but no one is sure whether he actually has the title of noble baron.

Leibniz’s father was a professor of ethics at Leipzig University. He died when Leibniz was 6 years old, leaving behind a private library. At the age of 12, he taught himself Latin and started to learn Greek. At the age of 14 he entered the University of Leipzig to study. He completed his studies at the age of 20, specializing in law and general university courses. In 1666 he published the first book on philosophy, titled "Deartecombinatoria" (Deartecombinatoria).

Serving as a court, fiercely fighting the altar

After Leibniz received his doctorate in Altdorf in 1666, he rejected the appointment as a faculty member, and was introduced by the then politician Baron Boineburg. Served in the High Court of Johann Philippvon Schönborn, the elector archbishop of Mainz.

In 1671, he published two papers "Theoriamotusabstracti" (Theoriamotusabstracti) and "Hypothesisphysicanova" (Hypothesisphysicanova), which were dedicated to the Academy of Sciences in Paris and the Royal Society in London. The world has increased its popularity.

In 1672, Leibniz was sent to Paris by Johann Philipp to shake Louis XIV's interest in invading the Netherlands and other neighboring countries in Western Europe and Germany, and to focus on Egypt. This political plan did not succeed, but Leibniz entered the Parisian intellectual circle and got acquainted with Malebranches and the mathematician Huygens. During this period Leibniz studied mathematics in particular and invented calculus.

Boineburg and JohannPhilipp passed away in 1672 and 1673, which forced Leibniz to leave Paris in 1676 to serve as Duke of Johann Friedrich in Hanover. When he took office, he visited Spinoza in The Hague and discussed philosophy with him for several days. Leibniz then went to Hanover to manage the library and served as the Duke's legal counsel.

In 1679, Leibniz invented the binary system and studied its system in depth to perfect the binary system.

From 1680 to 1685, he worked as a mining engineer at the Harz Mountain Silver Mine. During this period, Leibniz worked on the design of windmills to extract groundwater from the mine. However, due to technical problems and resistance from miners' traditional ideas, the plan did not succeed.

From 1685, he was entrusted by the successor Duke ErnstAugust and began to study his Braunschweig-Lüneburg aristocratic genealogy. This plan was not completed until Leibniz's death.

Completed "Metaphysique" (Discoursdemétaphysique) in 1686.

In 1689, he traveled to Italy to complete the study of Braunschweig-Lüneburg genealogy. At that time, I got acquainted with the missionaries sent by the Jesuits to China, and began to have a stronger interest in Chinese affairs.

In 1695, "The New System" was published in the journal, which made Leibniz's philosophy of "predetermined harmony" between entities and minds and things widely recognized.

As the dean, reject London

In 1700, Leibniz persuaded the Elector of Brandenburg, Frederick III, to establish the Academy of Sciences in Berlin and served as the first dean.

Completed "New Theory of Human Reason" in 1704. This article uses a dialogue style to criticize Locke’s "A Theory of Human Reason" chapter by chapter. However, because of Locke's sudden death, Leibniz didn't want to fall into the pretext of bullying the dead, so the book was never published during Leibniz's death.

In 1710, out of gratitude to the Queen of Prussia, Sophie Charlotte, who passed away in 1705, the Essais de Théodicée (Essais de Théodicée) was published.

In 1714, he wrote "Monadologie" (LaMonadologie; title added by later generations) and "The Principle of Nature and Favor Based on Reason" in Vienna. In the same year, Georg Ludwig, Duke of Hanover, succeeded as King George I of England, but refused to bring Leibniz to London, and alienated him from Hanover.

Death in his later years

On November 14, 1716 Leibniz passed away alone in Hanover. Except for his own secretary, even though George Ludwig himself happened to be in Hanover, there was no one else in the court. Attend his funeral. It was only a few months before his death that he wrote a manuscript on Chinese religious thought: "On the Natural Theology of Chinese People".

Character achievement


The symbols used in the field of calculus today are still proposed by Leibniz. In the field of advanced mathematics and mathematical analysis, Leibniz's discriminant method is used to judge the convergence of interlaced series.

The debate between Leibniz and Isaac Newton over who first invented calculus is the largest legal case in mathematics so far. Leibniz published his first differential paper in 1684, which defined the concept of differential and used differential symbols dx and dy. In 1686, he published a paper on integration, discussing differentiation and integration, using the symbol ∫ for integration. According to Leibniz's notebook, he had completed a complete set of differential calculus on November 11, 1675.

However, in 1695, British scholars declared that the invention of calculus belonged to Isaac Newton; in 1699, they said: Newton was the "first inventor" of calculus. In 1712, the Royal Society set up a committee to investigate the case. In early 1713, it issued an announcement: "Isaac Newton was confirmed as the first inventor of calculus." Leibniz received cold reception until a few years after his death. Because of the blind worship of Newton, British scholars have long adhered to Newton's flow number technique, only using Newton's flow number symbols, and disdain to adopt Leibniz's more superior symbols, so that British mathematics has broken away from the trend of mathematics development.

However, Leibniz's evaluation of Newton is very high. At a banquet at the Berlin court in 1701, King Frederick of Prussia asked Leibniz about Newton's opinion. Leibniz said : "In all mathematics from the beginning of the world to the era of Newton's life, Newton's work is more than half."

The first and second editions of "The Mathematical Principles of Natural Philosophy" published by Newton in 1687 The edition also wrote: "Ten years ago, in my correspondence with Leibniz, the most outstanding geometer, I stated that I already knew how to determine maximum and minimum values, how to make tangents, and similar methods. , But I concealed this method in the exchanged letters.... The most remarkable scientist wrote in his reply that he also found a similar method. He also described his method, which is the same as mine. There is almost no difference, except for his wording and symbols" (but this passage was deleted in the third edition and later reprints). Therefore, it was later recognized that Newton and Leibniz created calculus independently.

Starting from physics, Newton used geometric methods to study calculus, and its application was more integrated with kinematics, and his attainments were higher than that of Leibniz. Leibniz started from geometric problems and used analytical methods to introduce the concept of calculus and derive algorithms. The rigor and systematicness of his mathematics was beyond Newton's.

Leibniz realized that good mathematical symbols can save thinking labor, and the technique of using symbols is one of the keys to success in mathematics. Therefore, the calculus symbol created by him is far superior to Newton's symbol, which has a great influence on the development of calculus. Between 1714 and 1716, before his death, Leibniz drafted an article "The History and Origin of Calculus" (this article was not published until 1846), summed up his own ideas for founding calculus, and explained his independence. sex.


Topology was first called "analysissitus", which was proposed by Leibniz in 1679. This is a study of similar topography and geomorphology. At that time, the main research was some geometric problems arising out of the needs of mathematical analysis. There is still controversy about Leibniz's contribution to topology. Mates quoted a 1954 paper by Jacob Freudenthal as saying:

Although Leibniz believes that the position of a list of points in space is uniquely determined by the distance between them-only when the distance changes. The position has changed accordingly-his admirer Euler, in his famous paper (published in 1736, solved the problem of the Seven Bridges of Königsberg (Kaliningrad) and its promotion), but in " The term "geometric position" is used in the sense that the position of a point does not change during topological deformation. He mistakenly believed that Leibniz was the creator of this concept. ...People often don't realize that Leibniz uses this term in a completely different sense, so it is inappropriate to be respected as the founder of this subfield of mathematics.

But Hideaki Hirano held a different view. He quoted Benhua Mandelberg as saying:

Exploring in Leibniz’s massive scientific achievements is a thought-provoking experience. In addition to calculus and other completed research, a large number of extensive and forward-looking researches are unstoppable for scientific development. There are examples in the ‘filling theory’.... After discovering that Leibniz had also paid attention to the importance of geometric measurement, I became even more enthusiastic about him. In "Euclidean Prota"... which makes Euclid's axioms more strict, he stated,... ‘I have several different definitions of straight lines. A straight line is a kind of curve, and any part of the curve is similar to the whole, so the straight line also has this characteristic; this applies not only to the curve, but also to the collection. 'This thesis can already be proved today.

Therefore, the theory of fractal geometry (developed by Benhau Mandelberg) seeks support in Leibniz’s self-similarity and the principle of continuity: Nature does not jump (Latin "naturanonfacitsaltus", English "naturedoesnotmakejumps"). When Leibniz wrote in his metaphysical work, "A straight line is a kind of curve, and any part of it is similar to the whole", he actually predicted the birth of topology two centuries in advance. As for the "filling theory," Leibniz told his friend DesBosses, "You imagine a circle, and then fill it with three congruent circles with the largest radius, and the three smaller circles can follow the same process. Filled with smaller circles". This process can continue indefinitely, and the thought of self-similarity arises from this. Leibniz's improvement of Euclidean Axiom also contains the same concept.

Symbolic Thinking

Leibniz has a significant belief that a large amount of human reasoning can be reduced to a certain type of operation, and this kind of operation can solve the difference in perception:

"The only way to refine our reasoning is to make them as practical as mathematics, so that we can spot our mistakes at a glance, and when people have disputes, we can simply say: let us Calculate [calculemus], and you can see who is correct without further fuss.” (Discovered Art 1685, W51)

Leibniz’s calculus inferential device is very reminiscent of Symbolic logic can be seen as a way to make this kind of calculation feasible. The memos written by Leibniz (Parkinson translated them in 1966) can be seen as an exploration of symbolic logic—so his calculus—on the way. But Gerhard and Couturat did not publish these works until modern formal logic was formed in Frege's conceptual text and the writings of Charles Peirce and his students in the 1880s, so it was even more invented by George Bull and de Morgan in 1847. After the logic.


In addition to being an outstanding mathematician, Leibniz is also the peak of the philosophy of European rationalism. Inheriting the traditional thinking of Western philosophy, he believes that the world, because of its certainty (in other words, knowledge about the world is objectively universal and inevitable), must be constituted by self-sufficient entities. The so-called self-sufficiency is not dependent on the existence of other things and not dependent on other things to be recognized. Leibniz’s predecessor, Baruch Spinoza, thought that there was only one entity, which was God/Nature. Leibniz disagrees with this. One of the reasons is that there is a clear conflict between the Pantheism of St. Stephens and the theology of the Bible, and the second is that St. Peters's theory has not been able to resolve the dualism from Descartes onwards and make the world appear. (Although he emphasized that the world is one, he did not explain how the unity of this seemingly dualistic world is possible).

Leibniz thought there were many entities, infinitely many. Following Aristotle's view of substance, he thought that substance was the subject of a proposition. In a proposition S is P, S is the entity. Because the entity is self-sufficient, it must contain all possible predicates, that is, " P". From this, we can conclude that the entity has four characteristics: indivisibility, closure, unity and morality.

Indivisibility means that anything with extension, that is, with length, can be divided. The divided things respectively contain all their own possibilities, and self-sufficiency has the content of the extended things, that is, the possibility that the possibility depends on his part. By analogy, as long as it is extensive, it is not self-sufficient, but to be known in terms of other things (for Leibniz, true knowledge is the possibility of one thing), and it is not an entity. Therefore, the entity is indivisible, it is something without extensiveness, in Leibniz’s later works (Monadology)

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