Gottfried Wilhelm Leibniz (July 1, 1646 November 14, 1716), a German philosopher and mathematician, is rare in historyGeneralist, known as the 17th centuryAristotle。
He himself is a lawyer and often commutes betweenBig townMany of his formulas were completed on a bumpy carriage, and he also claimed to be a baron.[1]
On July 1, 1646, Gottfried William Leibniz was born inHoly Roman EmpireOfLeipzigHis grandfather, Friedrich Leibn ü tz and Catherine Schmuck, worked in the Saxony government for three generations.When I grow up, LeibnizSpellingIt was changed to "Leibniz", but most people used to write it as "Leibnitz".In his later years, his signature was usually written as "von Leibniz" to show his aristocratic status.Leibniz's works were published after his death, and the author's name is usually "Freiherr[Baron] G. W. von Leibniz.”，But no one was sure whether he really had the baronial title.
Leibniz's father wasUniversity of LeipzigLeibniz died at the age of 6, leaving behind a private library.Self study at the age of 12LatinAnd start learningGreek 。He entered the University of Leipzig at the age of 14.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, called "de arte combinatoria".
Serve in the court and fight in the legal arena
Leibniz
In 1666, Leibniz refused to be appointed as a teacher after he received his doctor's degree in Altdorf, and was introduced by the then politician Baron Boineburg to serve Mainzelector High Court of Archbishop Johann Philipp von Sch ö nborn.
In 1671, he published two papers, Themia motus abstracti and Hypothesis physics nova, which were dedicated to the Academy of Sciences in Paris andLondonOfroyal society At that time, it increased its popularity in European academic circles.
In 1672, Leibniz was sent by Johann Philipp toParis, to waverLouis XIVTo invadeNetherlandsAnd othersWestern EuropeGermanicNeighbouring countries have turned their attention to Egypt.This political plan did not succeed, but Leibniz entered the knowledge circle of Paris and metNicolas Malebranche And mathematician Huygens et al.Leibniz in this period specially studied mathematics and inventedCalculus。
In 1672 and 1673, Boineburg and Johann Philipp died one after another, forcing Leibniz to finally leave Paris in 1676 and transfer to serve inHanoverDuke Johann Friedrich of.I stopped by The Hague when I took officeSpinozaAnd discuss philosophy with him for several days.Leibniz then went to Hanover to manage the library and served as the Duke's legal adviser.
Operation diagram of calculator designed by Leibniz[7]
In 1679, Leibniz inventedBinary, and the systematic in-depth study, improved the binary system.
From 1680 to 1685Haz MountainSilver oreMining engineer.During this period, Leibniz devoted himself to the design of windmill to extract groundwater from the mine pit.However, due to technical problems and minerstraditional ideasThe plan did not succeed.
From 1685, entrusted by Ernst August, the successor duke, he began to study his Braunschweig-L ü neburg aristocratic genealogy.This project was not completed until Leibniz died.
In 1686, he completed Discours de m é taphysique.
In 1689, he traveled inItaly。At that time, I got to know the missionaries sent by the Jesuit Society in China, and began to have a stronger interest in Chinese things.
In 1695, he published the "New System" in a journal, which further made Leibniz's philosophy about“Predetermined harmony”Theory is widely recognized.
Served as dean and refused to accept London
Leibniz persuaded in 1700Brandenburg ElectorFrederick III established the Academy of Sciences in Berlin and served as the first president.
Completed in 1704《A new theory of human reason》。This article aims at Locke's "Theory of Human Reason", and uses the genre of dialogue to criticize chapter by chapter.However, because of the sudden death of Locke, Leibniz did not want to fall into the pretext of bullying the dead, so this book was never published in Leibniz's lifetime.
In 1710, out of gratitude for Sophie Charlotte, the Queen of Prussia who died in 1705, he published Essais de Th é odic é e.
In 1714ViennaWriting《Monadic theory》(La Monadologie; title added by later generations) and Principles of Nature and Grace Based on Rationality.In the same year, George Ludwig, Duke of Hanover, succeeded toKing of EnglandGeorge IBut refused to bring Leibniz to London and alienated him from Hanover.
Death in old age
Leibniz on November 14, 1716HanoverHe died alone, except for his own secretary, even though George Ludwig himself happened to be inHanoverNo one else in the court attended his funeral.Only a few months before his death did he finish writing about the Chinese peopleReligious thought"On Chinese Natural Theology".
Leibniz andIsaac NewtonWho invented firstCalculusThe dispute over "" is the biggest case in the mathematical world so far.Leibniz published his first differential paper in 1684, defined the concept of differential and adoptedDifferential signDx, dy. In 1686, he also published a paper on integration, discussed differential and integral, and usedIntegral sign∫。According to Leibniz's notebook, on November 11, 1675, he had completed a complete set ofDifferential calculus。
However, in 1695, British scholars declared that:Right of inventionbelong toIsaac Newton；In 1699, he said:NewtonHe is the "first inventor" of calculus.1712Royal SocietyA committee was set up to investigate the case. At the beginning of 1713, an announcement was issued: "ConfirmIsaac NewtonHe is the first inventor of calculus. "Leibniz was treated coldly until a few years after his death.Because of the blind worship of Newton, British scholars have long adhered to Newton'sNumber of streamsIt only uses Newton's stream number symbols, and disdains to use Leibniz's more superior symbols, so that English mathematics breaks away from the trend of the times of mathematical development.
However, Leibniz spoke highly of Newton. In 1701, at a banquet at the Berlin court,King Of Prussia Frederick asked Leibniz what he thought of Newton. Leibniz said: "In all mathematics from the beginning of the world to the age of Newton's life, Newton's work exceeded half."
Leibniz commemorative stamps[5]
NewtonPublished in 1687《Mathematical Principles of Natural Philosophy》The first and second editions ofmaximum valueandMinimumMethod and operation oftangentThe most outstanding scientist wrote in his reply that he also found a similar method.He also recounted his method, which is almost the same as mine, except for his wording and symbols "(but this paragraph was deleted in the third edition and later editions).Therefore, it was later recognized that Newton and Leibniz wereIndependentTo create calculus.
NewtonStarting from physics, using geometrymethod studyCalculus, its application is more integratedkinematicsAnd his attainments are higher than Leibniz's.Leibniz started from geometric problems and appliedAnalyticsMethods The concept of calculus was introduced andAlgorithmIts mathematics is more rigorous and systematic than Newton.
Leibniz realized that goodMathematical symbolThe skill of using symbols is one of the keys to the success of mathematics.Therefore, the calculus symbol created by him is far superior to Newton's symbol, which has a great impact on the development of calculus.From 1714 to 1716, before his death, Leibniz drafted the article "History and Origin of Calculus" (this article was not published until 1846), summarized his ideas of establishing calculus science, and explained the independence of his achievements.
Picture:[4][6]
topology
topologyIt was first called "analysis situs", which was put forward by Leibniz in 1679. It was a discipline studying similar topography and geomorphology. At that time, it mainly studied some geometric problems arising from the need of mathematical analysis.There is still controversy about Leibniz's contribution to topology.Mates quoted Jacob Freudthal's 1954 paper as saying:
Although Leibniz believes that the position of a list of points in space is determined solely by the distance between them——if and only ifWhen the distance changes, the position of the point changes correspondingly - his admirerEulerIn his famous paper (published in 1736)（Kaliningrad）Seven bridge problemAnd its promotion), but in“topologyThe term "geometric position" is used in the sense that the position of the point does not change during deformation.He mistakenly believed that Leibniz was the founder of this conceptPeople often do not realize that Leibniz uses the term in a completely different sense, so it is inappropriate to be respected as the founder of this branch of mathematics.
But Hideki Hirano held a different view, and he quotedBenoit Mandelbrot In his words:
In LeibnizScientific achievementsChinese exploration is a thought-provoking experience.In addition to calculus and other completed research, a large number of extensive and forward-looking research on scientific developmentimpetusbe a trend which cannot be halted.There are examples in the 'filling theory'...... Leibniz also paid attention toGeometric metricAfter that, my enthusiasm for him became even more intense.On“Euclid"Prota", which makes Euclid's axiom more strict, he stated that... '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.
thusfractal geometry (byBenoit Mandelbrot Carry forward) theory in Leibniz'sSelf similarityThought andContinuity principleSeeking support in: nature does not jump（Latin"Nature does not make jumps").When Leibniz wrote in his work Metaphysics that "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 ahead of time.As for the "filling theory", Leibniz said to his friend Des Bosses, "You can imagine a circle, and then fill it with three congruent circles with the largest radius. Later three small circles can be filled with smaller circles in the same process".This process can continue indefinitely, and the idea of self similarity arises from it.Leibniz's improvement of Euclidean axiom also includes the same concept.
Symbolic thinking
Leibniz has a remarkable belief that a large amount of human reasoning can bereductionIt is a kind of operation, which can solve the differences in views:
"The only way to refine our reasoning is to make it as practical as mathematics, so that we can find out our mistakes at a glance, and when people have disputes, we can simply say: Let us calculate [calculemus], without further confusion, we can see who is right." (Art of Discovery 1685, W 51)
Leibniz's calculus inference device is very reminiscentSymbolic logic, can be seen as a way to make this calculation feasible.The memos written by Leibniz (translated by Parkinson in 1966) can be seen as an exploration of symbolic logic - so his calculus - is on its way.But Gerhard and Couturat did not publish these works until modern timesformal logicIt was formed in the concept text of Frege and the works of Charles Peirce and his students in the 1880sGeorge Boole andDe Morgan It was after 1847 that this logic was created.
Monadic theory
In addition to being an outstanding genius mathematician, Leibniz is alsoEuropean rationalismThe peak of philosophy.Inheritedwestern philosophy In traditional thought, he believed that the world, because of its certainty (in other words, the knowledge about the world is objective, universal and inevitable), must be composed of self-sufficient entities.The so-called self-sufficiency is noAccording to himThings exist and are not recognized according to other things.Lebniz's predecessorBaruch SpinozaIt thinks that there is only one entity, namely God/Nature.Leibniz disagrees with this, one reason is that his pantheism has obvious conflict with the theology of the Bible, and the other reason is that his theory has not been able to solve the problem caused byDescartesDescendingdualism, making the world a fault (although he stressed that the world is one, he did not say that this one seems to bebinary oppositionHow is the unification of the world possible.
Leibniz believes that there are many entities, and there are unlimited entities.followAristotleHe thinks that entity is the subject of a proposition.In a proposition S is P, S is entity.Because an entity is self-contained, it must contain all possible predicates, that is, "... is P".From this, we can conclude that entities have four characteristics: indivisibilityClosure, unity and morality.
Indivisibility means that anyExtensive extensionThings with length can be divided.The divided things contain all their own possibilities respectively, and are self-sufficient, so they have the content of extensive things, that is, the possibility that the possibility depends on his part.By analogyductilityIf you are not self-sufficient, but want to be known by other things (for Leibniz, real knowledge is the possibility of lacking one thing), you are not an entity.Therefore, entity is indivisible, and it is something that has no extensive extension. In Leibniz's late works (Monadology), he called it Monad. The nature of monad is thinking（thought）。This extensive world is composed of an infinite number of monads.
The closeness means that each list must be self-sufficient, independent of others, and contains all its own possibilities.Then one order can't have it with anotherInteraction（interaction）。If one monad acts on another monad, the latter monad may not be included in the list, that is, the list does not contain all its own content, but needs to attach to other things.Because of the definition of entity, this is impossible.So Leibniz said: "There is no window between the lists."
Uniformity means that every monad must include the whole world in a certain perspective.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 includes all the possibilities of its own, then each list points to the world with the list itself as the center.But the world is unified, which does not mean that all monads are the same, because the same world can be perceived from different perspectives, so it is a unified world.
Finally, the morality of monads is more complex.This feature is proposed for two reasons, one is the unity of the world, and the other is the world'scertainty。For the former, all lists contain the whole world, but from their own perspectives, is the world's unity false?If we want to talk about unification, how can we talk about it?For the latter, the world is composed of monads, which are just a collection of possibilities, and the world is also just a possibility.Is it impossible for us to have a kind of knowledge that is not only possible, but also inevitable?In what sense can we say that knowledge about the world is true and certain?Leibniz attributed it to one god, the creator of the world.On the one hand, before God created, there was no established material, so there was no established limited situation, then creation was a pure will creation, and God created this world by virtue of his perfection alone.
Therefore, as Leibniz famously said, this truly accomplished world is "the best of many possible worlds".This almost meets Leibniz's belief requirements.On the other hand, if you want to know something for sure, you should know its reason.We should understand this reason and pursue the reason.By analogy, the deterministic knowledge of the world cannot be an effective cause within a world, but a transcendental metaphysical cause.
Leibniz said that it was theoretically necessary to set the metaphysical cause of God.Therefore, the reason why this world is like this is that it is the best and the bestPossible world。It is impossible for people to fully understand the supreme good will of the God, but they can move forward in this direction, because the human mind makes a special list, which has memory and can chart their own future based on the past. This is the divinity shared by human beings, that is, the possibility of morality.People can understand the world created by God and how to become a moral person through open possibilities.
This kind of worldMorality, can be regarded asKant Leibniz's pioneers, respectively, arbitrarily put forward that God is the perfection of morality, and said that the possibility is the reality under the eyes of God, but did not really regard the possibility of the world as the possibility.And Leibniz is rightInnate ideas(inland idea)HegelyesKant In this sense,Kant On the one handHume(Hume) Awakened from Leibniz's arbitrary dream, but at the same time, it was also polluted by Locke's philosophical pathological change - the examination of rational boundaries.In this respect, Leibniz took a step ahead of Kant.
formal logic
Leibniz wasAristotleThe most important works between George Burr and De Morgan, who respectively published the works that created modern formal logic in 1847logician。Leibniz expounded conjunction, disjunction, negation, identity, set inclusion andempty setThe primary nature of.LeibnizLogic principleAnd his whole philosophy can be reduced to two points:
All our ideas (concepts) are compounded from a very small number of simple ideas, which form the letters of human thinking.
Complex ideas come from these simple ideas, which are simulated by themArithmetic operationA unified and symmetrical combination of.
Leibniz was the first to contactChinese cultureFrom some missionaries who had gone to China to preachChinese culture, should have been taken fromMarco PoloI have also learned about Chinese culture from the influence of the oriental fever.FranceSinologyMaster Joachim Bouvet, HanNameless whiteJin, 1662-1732) introduced to Leibniz《Zhouyi》And gossip system.In Leibniz's eyes, "yin" and "yang" are basically hisBinaryChinese version of.He once asserted: "Binary is the worlduniversalityThe most perfect logical language ".Now in GermanyThuringiaIn the famous Schlossbibliothek zu Gotha, there is still a copy of Lester's manuscript with the title "1 and 0, the magical origin of all numbers"
The full text of the title of the manuscript is: "1 and 0, the magical origin of all numbers... This is a wonderful example of the secret of creation, because everything comes from God." And Leibniz himself wrote to Joachim Bouwe, saying in his letter: "The first day begins with 1, which is God. The second day begins with 2,... By the seventh day, everything is there.So, this last day is also perfect.Because, at this time, everything in the world has been created.Therefore, it is written as' 7 ', that is,' 111 '(111 in binary is equal to 7 in decimal), and does not contain 0.Only when we express this number with 0 and 1 can we understand why the seventh day is perfect and why 7 is a sacred number.It is particularly noteworthy that its (seventh day) characteristics (111 for writing binary) are related to the trinity. "
Guo ShuchunOn《Liu Hui, an ancient world leader in mathematics》It is said on page 461 of a book: "There is a saying in China that the Book of Changes created binary. The myth that Leibniz was influenced by the Eight Diagrams of the Book of Changes to create binary and use it in computers is even more widespread. The fact is that Leibniz first invented binary, and later saw the rearrangement of the Book of Changes by scholars in the Song Dynasty brought back by missionariesBagua, and found that Bagua can be explained by his binary system. "For this reason, it is believed that Leibniz did not seeYin Yang Eight TrigramsBinary was invented.Liang Zong's great book Mathematical Historical Allusions (published in 1995) has the same view on this historical case on pages 14-18.
Hu Yang and Li Changduo in "Did not Leibniz See the Congenital Map Before Inventing Binary System -- A Textual Research on the Existing European Documents of Sino Western Exchange in the 17th Century"[2]Through the research and textual research on the existing European documents of Sino Western communication in the 17th century, the argument that Leibniz saw the congenital diagram only after he invented the binary system was denied.Before Leibniz invented the binary system, the congenital diagram was called the binary system by Spencer.[2]
On Leibniz Binary System and Ancient Chinese Books《I Ching》The discussion of the relationship involves how to look at the respective characteristics of modern Chinese and Western cultures and the interaction between them.Although binary is only an arithmeticNumerationandCounting methodHowever, it is actually the product of a specific culture (including mathematics, language, symbols, logic, philosophy, etc.).One of the obvious shortcomings of the existing views is that the formation and development of concepts and theories (principles, symbols, etc“All or none”It ignores the formation and change process of concepts and theories, and is easy to lead to two extreme judgments.[3]
Therefore, based on the background of modern cultural exchanges between China and the West, starting with conceptual and cognitive analysis, the formation process of Leibniz's binary thought can be placed in the concept woven by modern cultural exchanges between China and the WestNetwork systemAnd then sort out Leibniz's inheritance of western modern timesMathematical conceptHow to acquire and absorb《I Ching》The context of creative transformation of concepts through conceptual resources.We can see that, in addition to Leibniz's great contribution of personal originality, binary in modern sense is actually the product of "Chinese and Western combination".[3]
