Leibniz's father, an ethics professor at Leipzig University, died when Leibniz was 6 years old, leaving a private library. /kloc-When he was 0/2 years old, he taught himself Latin and began to learn Greek. /kloc-He entered the University of Leipzig at the age of 0/4 and finished his studies at the age of 20, majoring in law and general university courses. 1666, he published the first book about philosophy, entitled de arte combinatoria. 1666 After receiving his Ph.D. in Ortoff, Leibniz refused the appointment of a teaching post and was introduced by Baron Boineburg, a politician at that time, as Johann Philipp von Sch? High Court of Embern.
167 1 year, he published two papers, "Theoria motus abstracti" and "Hypothesis physica nova", which were dedicated to the Academy of Sciences in Paris and the Royal Society in London respectively, which increased the popularity of European academic circles at that time.
1672, Leibniz was sent to Paris by john philip to shake Louis XIV's interest in invading Holland and other Germanic neighbors in western Europe, and turned his attention to Egypt. The political plan didn't succeed, but Leibniz entered the intelligentsia in Paris and met Mahleblanc and mathematician Huygens. During this period, Leibniz specialized in mathematics and invented calculus.
Boynburg and john philip died in 1672 and 1673 respectively, forcing Leibniz to leave Paris in 1676 to work for Johann Friedrich, Duke of Hanover. After taking office, he stopped by The Hague to visit Spinoza and discussed philosophy with him for a few days. Leibniz then went to the Hanover Management Library and served as the Duke's legal adviser.
1680 to 1685 as mining engineer of Hatoyama silver mine. During this period, Leibniz devoted himself to designing windmills to extract groundwater from mines. However, the plan failed because of technical problems and the resistance of miners' traditional ideas.
From 1685, he was entrusted by Ernst August, the successor duke, to study his noble family tree of Brunswick-Lueneburg. The plan was not completed until Leibniz died.
1686, he completed "Metafisik Essays".
From 65438 to 0689, he traveled in Italy and completed the study of the Brunswick-Lueneburg genealogy. At that time, I met the missionaries sent by the Jesuits in China, and I became more interested in China.
1695, the new system was published in a journal, which made the theory of "predetermined harmony" between entities and between mind and things in Leibniz's philosophy widely known. 1700, Leibniz persuaded Frederick III, the elector of Brandenburg, to establish the Berlin Academy of Sciences and served as the first president.
1704 completed the new theory of human rationality. This paper criticizes Locke's theory of human reason chapter by chapter with the genre of dialogue. But because of Locke's sudden death, Leibniz didn't want to be accused of bullying the dead, so this book was never published before Leibniz's death.
17 10, out of gratitude to Sophie Charlotte, Queen of Prussia who died in 1705, Essis de thé odicé e was published.
17 14 wrote "Monologue Theory" in Vienna (La Monadologie；; The title was added by later generations) and "Principles of Nature and Grace Based on Reason". In the same year, Georg Ludwig, Duke of Hanover, succeeded King George I of England, but refused to bring Leibniz to London, alienating him from Hanover. The symbols used in the field of calculus today are still put forward by Leibniz. In the field of advanced mathematics and mathematical analysis, Leibniz discriminant method is used to judge the convergence of staggered series.
The argument between Leibniz and Newton who invented calculus first is the biggest case in mathematics. Leibniz published the first differential paper in 1684, defined the concept of differential, and adopted the differential symbols dx, dy. 1686 published an integral paper, discussed differential and integral, and used the integral symbol ∫. According to Leibniz's notebook, he has completed a complete set of differential calculus in 1675 1 1.
But in 1695, British scholars claimed that the invention of calculus belonged to Newton; 1699 said that Newton was the "first inventor" of calculus. 17 12, the royal society set up a committee to investigate the case, and announced in early 17 13: "Newton was confirmed as the first inventor of calculus." Leibniz received a cold shoulder 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, but dismissing Leibniz's superior symbols, which made British mathematics out of the trend of mathematical development.
However, Leibniz spoke highly of Newton. 170 1 At a banquet in Berlin, King Frederick of Prussia asked Leibniz what he thought of Newton. Leibniz said, "In all mathematics from the beginning of the world to Newton's life, Newton's work exceeded half."
Newton also wrote in the first and second editions of Mathematical Principles of Natural Philosophy published in 1687: "Ten years ago, in my correspondence with Leibniz, the most outstanding geometer, I indicated that I already knew the method of determining the maximum and minimum, tangent method and so on, but I concealed this method in my correspondence ... The most outstanding scientist wrote in his reply that he also He also described his method, which is almost no different from mine except for words and symbols "(but this passage was deleted in the third edition and later editions). So it was later recognized that Newton and Leibniz created calculus independently.
Newton started from physics and studied calculus by set method. His application is more combined with kinematics, and his accomplishments are higher than Leibniz's. Leibniz, on the other hand, started from geometric problems, introduced the concept of calculus by analytical method, and got an algorithm, which was more rigorous and systematic than Newton's algorithm.
Leibniz realized that good mathematical symbols can save thinking labor, and the skill of using symbols is one of the keys to the success of mathematics. Therefore, the symbols of calculus he created are far superior to Newton's symbols, which has a great influence on the development of calculus. During the period from 17 14 to 17 16, before his death, Leibniz drafted the article "History and Origin of Calculus" (this article was not published until 1846), which summarized his thought of establishing calculus and expounded the independence of his achievements. Topology was first called "analytical position" and was put forward by Leibniz in 1679. It is a subject that studies topography and landforms. At that time, I mainly studied some geometric problems arising from the needs of mathematical analysis. There is still controversy about Leibniz's contribution to topology. Mates quoted a paper by Jacob Freudenthal 1954 and said:
Although Leibniz thinks that the position of a series of points in space is only determined by the distance between them-when and only when the distance changes, the position of the points changes accordingly-his admirer Euler used the "geometric position" in his famous paper (published in 1736, which solved the problem of the Seven Bridges in Konigsberg and its popularization). He ..... People often don't realize that Leibniz used this term in a completely different sense, so it is inappropriate to regard it as the founder of this branch of mathematics.
But Ye Ping Xiuqiu holds a different view. He quoted Benhua Mandelbo as saying:
It is a thought-provoking experience to explore Leibniz's great scientific achievements. In addition to the completed research such as calculus, a large number of extensive and forward-looking research has an unstoppable driving force for scientific development. There is an example in the "filling theory" ... after discovering that Leibniz once paid attention to the importance of geometric measurement, I became more enthusiastic about him. In Euclid's Principle, he made Euclid's axiom stricter. He said, "I have several different definitions of straight lines. The 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 curves, but also to sets. This assertion can be proved today.
Therefore, the theory of fractal geometry (developed by Benhua Mandelbo) seeks support in Leibniz's self-similarity thought and continuity principle: nature does not jump (Latin "natura non facit saltus", English "nature does not make jumps"). When Leibniz wrote in his metaphysical works that "a straight line is a curve, and any part of it is similar to the whole", he actually predicted the birth of topology two centuries in advance. Regarding the "filling theory", Leibniz said to his friend Des Bos, "You imagine a circle and then fill it with three congruent circles with the largest radius. The next three small circles can fill smaller circles with the same process." This process can continue indefinitely, and the idea of self-similarity also comes into being. Leibniz's improvement of Euclid's axiom also contains the same concept. Leibniz has an extraordinary belief that many human reasoning can be attributed to some kind of operation, which can solve the differences in views:
"The only way to refine our reasoning is to make them as practical as mathematics, so that we can find our own mistakes at a glance. When people have an argument, we can simply say, Let's calculate [calculatemus] and see who is right without further fuss." (the art of discovery 1685, W 5 1)
Leibniz's calculus inference device is very reminiscent of symbolic logic and can be regarded as a method to make this calculation feasible. The memorandum written by Leibniz (translated by Parkinson 1966) can be regarded as an exploration of symbolic logic-so his calculus is on its way. However, Gerhard and Kutulat published these works only after the modern formal logic was formed in Frege's conceptual text in 1880 and Charles Peirce and his students' works, so it was even after george boole and Augustus de Morgan started this logic in 1847. Leibniz is not only an outstanding gifted mathematician, but also the pinnacle of European rationalism philosophy. He inherited the thought of western philosophical tradition and thought that the world must be composed of self-sufficient entities because of its certainty (in other words, the knowledge about the world is objective, universal and inevitable). Self-sufficiency means being recognized without anything else. Spinoza, Leibniz's predecessor, believed that there was only one entity, namely God/Nature. Leibniz disagrees with this. One of the reasons is that there is an obvious conflict between his pantheism and biblical theology. Secondly, because his theory failed to solve the dualism from Descartes, there is a fault in the world (although he emphasized that the world is one, he did not explain how the unification of this seemingly binary world is possible).
Leibniz thinks that there are many entities, and they are infinite. Following Aristotle's view of entity, he thinks that entity is the subject of proposition. In the proposition that s is p, s is an entity. Because the entity is self-sufficient, it should contain all possible predicates, that is, "... is p". From this, we can deduce that the entity has four characteristics: indivisibility, closeness, unity and morality.
Indispensable means that anything with universality, that is, something with length, can be divided. Divided things contain all their own possibilities. If they are self-sufficient, they have the content of extensive things, that is, the possibility of attaching to his part. By analogy, as long as it is extensive, it is not self-sufficient, but is recognized by other things (for Leibniz, real knowledge is the possibility of poverty), so it is not an entity. Therefore, the entity is inseparable and has no extension. In Leibniz's later works (monadic theory), he called it monadic, and the essence of monadic is thought. This vast world is made up of infinite lists.
Closure means that each list must be self-sufficient, independent of other lists and contain all its own possibilities. It is impossible for an only child to interact with another only child. If one list acts on another list, the latter list may not be included in the list, that is, the list cannot contain all its contents, but depends on other contents. Because of the definition of entity, this is impossible. So Leibniz said, "There is no window between lists."
Unity means that every child must look at the whole world from a certain angle. Because the world is closely composed of cause and effect, A acts on B, not only on B, but on the whole world. If the content of a list contains all its possibilities, then each list points to the whole world centered on the list itself. The fact that the world is one does not mean that all the lists are the same, because the same world can be recognized from different angles, but it can be regarded as a unified world.
Finally, the morality of the list is more complicated. There are two reasons for this feature, one is the unity of the world, and the other is the certainty of the world. For the former, all the lists contain the whole world, but from their own point of view, is the unity of the world false? How to talk about reunification? For the latter, the world is composed of a list, and the list is only a collection of its possibilities, and the world is only a possibility. Can't we have a kind of knowledge that is not only possible but also inevitable? In what sense can we say that the knowledge about the world is true and certain? Leibniz attributed it to a God, the creator of the world. On the one hand, before God created the world, there was no established material, so there was no established limited situation, so creation was pure will creation, and God created the world only by his perfection.
Therefore, as Leibniz famously said, this truly completed world is "the best of many possible worlds." This is almost in line with Leibniz's belief requirements. On the other hand, if you want to know something exactly, you should know its reason. To understand this reason, we must also trace the reason. By analogy, the deterministic knowledge of the world cannot be an efficient reason within a world, but a metaphysical reason beyond it.
Leibniz said that this theoretically necessary setting is metaphysical attribution to God. Therefore, this world is so because it is the best and possibly the best. People can't fully understand this kind of God's goodwill, but they can move in this direction, because people's minds have made a special list, which contains memories and can plan their future according to the past. This is the common divinity of human beings, that is, the possibility of morality People can learn about the world created by God and how to become a moral person by opening possibilities.
This moral worldview can be regarded as the pioneer of Kant, that is, Leibniz arbitrarily put forward the perfection of God as morality, and described the possibility as the reality in God's eyes, but did not really regard the possibility of the world as the possibility. Moreover, Leibniz's criticism of innate ideas is Hegel's criticism of Kant. In this sense, on the one hand, Kant was awakened by Hume from Leibniz's arbitrary dream, but at the same time, he was polluted by Locke's philosophical pathological change-the examination of rational boundary. Leibniz is one step ahead of Kant in this respect. Leibniz is the most important logician between Aristotle and george boole. Augustus de Morgan's works were published in 1847 respectively, which initiated modern formal logic. Leibniz expounded the basic properties of conjunction, disjunction, negation, identity, set inclusion and empty set. Leibniz's logical principles and his whole philosophy can be summed up in two points:
All our ideas (concepts) are made up of a few simple ideas, which constitute the letters of human thinking.
Complex ideas come from these simple ideas, which are unified and symmetrical combinations obtained through analog arithmetic operations.