Zhou Yongkun:

We often turn a blind eye to many things, and the relationship between mathematics and law is one of them. [2] Many years ago, Bai and I went to a meeting and went out to sit next to him by car. When I asked him what he was studying, he immediately explained. It turned out that he was studying the relationship between mathematics and law. At that time, he felt refreshed and gradually forgot afterwards. Who knows today gave him a thick book-"Mathematical Interpretation of Legal Culture". [3]

Think about it carefully, the relationship between mathematics and law can be seen everywhere, and it can even be said that law deals with mathematics every day. Conviction and sentencing in criminal law, property rights and their exchange in civil law, marriage age, property inheritance, damages, tax calculation and interest calculation in economic law, evidence in procedural law, composition and voting of collegiate bench, etc. , are inseparable from the numbers. As far as the modern constitutional system is concerned, it can be said that it is based on "counting", such as the electoral system. The electoral system, from the division of constituencies to the emergence of candidates, to the final voting and counting, is full of "head counting". Sometimes, the difference between a few votes determines who gets on and who gets off.

The American presidential election adopts the "voter" system. Regardless of the size of the state, each state has two electoral places. In addition, the number of electoral places is distributed among the states according to the proportion of the population, which is roughly one for every 500,000 people. Therefore, each voter in a populous state represents more voters than each voter in a less populous state. In addition, the American presidential election adopts the principle of "winner takes all", that is, as long as a presidential candidate gets more than half of the votes in a state, all the electoral votes in that state belong to him. So sometimes it happens that if a candidate wins electoral votes from many populous states, and his opponent mainly wins electoral votes from small populous states, then the latter is likely to be elected because he gets more electoral votes than the former, although he may get less total electoral votes than the former.

In the 2000 US presidential election, Bush and Gore almost tied, and the Democratic Party and the Democratic Party fought a "century judicial war" for 36 days to "count the votes". 165438+1October 7 th, which is about 2: 00 am EST. According to the forecast, CNN claimed that George W. Bush narrowly defeated Al Gore with 27 1 electoral votes. After that, Gore called George W. Bush as usual to congratulate his opponent on his election, and then drove to the Tennessee Capitol to openly admit defeat. However, just as Gore's motorcade was about to reach its destination, a dramatic scene happened: the state attorney general in charge of Florida's election affairs telegraphed Gore and slowly gave up because the difference between Gore's and Bush's votes in Florida was less than 0.5%. According to Florida's election law, this situation requires a recount. If the counting results are reversed and 25 electoral votes from Florida are voted for Gore, Gore will win.

165438+1On the afternoon of October 8, Florida finally completed the counting of votes in 67 counties: out of about 6 million voter votes, Bush won 2909 135, Gore won 290735 1, and other candidates won1. This led to more than a dozen legal cases about whether to manually recount the votes. Gore advocated continuing the recount, while Bush was afraid of a reversal and opposed the recount. The lawsuit went from the Florida District Court to the Federal Supreme Court twice.

On the morning of February 9, 65438, just two hours after the manual counting of votes began in Florida counties, the Supreme Court suddenly issued an urgent order, demanding that Florida immediately stop the manual counting of votes, announcing that the court debate would be held again on February 9, 1 1, and officially named the case Bush v. Gore. 65438+February 65438+On the evening of February 2, the Federal Supreme Court ruled with 5 votes to 4 votes, "overturning the decision of the Florida Supreme Court to order the manual counting of votes to continue". The Supreme Court ruled that the previous vote count was valid, which meant that Bush was elected and Gore subsequently admitted defeat. 200111On October 6th, the 7th Congress of the United States opened. Gore, as the speaker of the Senate, read out the election results that he didn't agree with: Bush got 50,456141voter votes (accounting for 47.87% of the total votes), and Gore * * *. But among the 538 electoral votes, Bush got 27 1 and Gore got 266. Although Bushby Gore lost nearly 540,000 electoral votes, he won the presidential election with five electoral votes and became the 42nd president of the United States. It can be seen that this whole process is a numbers game.

Although in fact mathematics and law are inseparable, there are very few works that really study the relationship between mathematics and law. The author's search results only show two Chinese works and one translation. [4] There are only 17 papers in this field in journals. [5] Mathematical Interpretation is the only two monographs on the relationship between law and mathematics in mainland China. It is commendable to think about people without thinking and feel that people are unconscious. This is a book of philosophy of law that studies legal culture from a mathematical point of view, and has made many achievements. After systematically sorting out the mathematization process of social science and the three periods when mathematics influenced western legal culture, the author made a comprehensive and in-depth study on the influence of mathematics on western legal culture. The author first discusses the relationship between mathematical rationality and western law in two chapters (Chapter IV and Chapter V), and the process of mathematization and rationalization of law. Then in three chapters (Chapter VI, Chapter VII and Chapter VIII), the author discusses the mathematical factors in the formalization of western law, the influence of axiomatic method as a mathematical method on western legal theory and law, the quantification of legal value and other important theoretical issues in the relationship between mathematics and western legal culture.

Inspired by the author, we find that mathematics has a lot of influence on law.

First, numbers are tools to express laws. Without numbers, many laws cannot be expressed, and laws cannot form a meaningful knowledge system. For example, "code of hammurabi" stipulates: "Whoever steals cattle, sheep, pigs or goats, if it belongs to God or the court, the pickpocket will pay 30 times the price; If they belong to the king's freemen, he only needs to pay ten times the price ... "This is a number indicating the severity of punishment. "Twelve Copper Tables Law" stipulates: "The debt you admit or judge has a statutory grace period of 30 days." This is the time limit for expressing common legal acts in law by numbers. The system of "incriminating" in China's Tang Law not only stipulates the corresponding amounts of various kinds of punishment, but also stipulates the complicated conversion standards and methods among punishment, staff, apprentice and vagrant. With the development of modern law, mathematics has penetrated into all departments and fields of law, and all kinds of "standards" in modern law have been quantified or expressed in quantitative ways.

Secondly, mathematics is a tool of legal research, which is particularly prominent in modern times. More than 30 years ago, Soviet jurists said that for law, "quantitative research methods are never unfamiliar to law." For example, judicial statistics is to calculate indicators according to the number of illegal acts and the number of people who commit illegal acts, and provide methods to analyze these data. However, judicial statistics mainly rely on descriptive methods and statistical means (percentage of average scores). The achievements of cybernetics, computing technology and classification have pushed the application of mathematics in law to a new stage. "[6] If we broaden our horizons, we will find that legal modernization is a part of knowledge modernization, and the important content of knowledge modernization is the quantification of knowledge. The historical trend of knowledge quantification has undoubtedly had a great influence on law.

Mathematicization of scientific knowledge is inseparable from the names of these three great men: Galileo (1564- 1642), Descartes (1596-1650) and Newton (1643-/kloc-0). It is said that Descartes had a strange dream. In his dream, he was possessed by fate and blinded by a strong light, which seemed to imply that he would find the answer to the question that had been bothering him. After that, he had three more dreams. He saw strange fruit, and suddenly there was lightning and thunder in the room, and then everything was silent. In the silence, he found himself holding a poem in his hand and discussing with a man a sentence he wrote at the end of each poem: "Which way should life take?" In his dream, he thought it was a ghost, so he immediately prayed to the Virgin Mary and vowed to make a pilgrimage on foot. Descartes' answer to the question in his dream is this: unify all knowledge with the precise reasoning method of geometry and mathematize the world. [7] "Galileo (1564- 1642) changed everything, making quantitative analysis method replace qualitative analysis method and become the basic method of scientific research." [8] 1687, Newton (1643-1727) published Mathematical Principles of Natural Philosophy, which is probably the most important work in the history of physical science, and truly realized the mathematicization of natural science. With the promotion of natural science, the mathematicization of knowledge has also entered the field of social science, and mathematical methods such as mathematical statistics and games have become important tools to promote legal progress. Mathematics has contributed "concepts, laws, principles, theories, standards and values" to social sciences, including law. [9]

Third, the influence of mathematics on legal concepts. As long as there are rules-even the most primitive rules-it is inseparable from the concepts of number and quantity. As an equivalent exchange of basic legal rules, it implies the presupposition of "equivalence". Revenge is the "equivalent exchange" between the victim and the injured. It is no exaggeration to say that "equivalent exchange" is a universal basic legal principle, which is itself a calculation process. It needs to "homogenize" people and behaviors and "quantify" interpersonal relationships in mathematics. If we go further and treat homogeneous people equally, it will not be far from a democratic society. Alkita, a city-state politician and a member of Pythagoras School, said, "Once the correct counting standard is found, conflicts among citizens can be controlled and coordination can be promoted. Because if this is done there, there will not be too many rights and interests, and equality will dominate. It is this (the correct counting standard) that brought us the contract. The poor get things from people with property, and the rich give things to the poor, treating each other fairly and trusting each other. As a standard, as a deterrent to people who do bad things, it makes people who are doing bad things stop, can calculate the results, and convince them that when they try to resist, they will inevitably be exposed; And when they can't (calculate this result), they can also see that they have done something wrong because of this, thus preventing them from committing crimes. " [10] It can be seen that the concepts of contract and equality, as the basis of ancient Greek democratic system, are closely related to developed mathematics.

Fourthly, mathematics has a great influence on legal practice. Since the era of big data, various computing tools have been directly applied to the judicial and law enforcement process. From about 1990, the court work in developed countries began to be digitized: juries were drawn by computers, simple judgments (such as customs rulings) could be made by "legal expert system", and judgment documents could be found directly on the Internet. Even in China, a rising star in this field, the current court work is inseparable from mathematical tools.

Fifth, it promotes the formalism of law. This is undoubtedly the greatest contribution of mathematics to law, and it is also the focus of mathematical interpretation. The influence of mathematical interpretation on mathematics and legal formalism is mainly proved by the analysis of Weber's thought. As stated in the preface of this book, the author of Mathematical Interpretation fully discusses Weber's theoretical analysis of rational and formalistic rational legal issues, follows Weber's ideological path, and highlights the uniqueness and uniqueness of formal rationality required by western formal rationality laws. At the same time, he also noticed Weber's profound revelation of the relationship between the rationalization of economic behavior and the computability and predictability of economic behavior, which really grasped the essence of Weber's thought. Moreover, the author of Mathematical Interpretation tries to emphasize more clearly the decisive role of mathematical factors in the formation of western formalistic rational laws on the basis of Weber's exposition. He believes that in the western civilization system, rationality and rationality are related to calculation, while calculation is related to mathematics, which is the root of rationality and rationality. Without mathematics, rationality would be absent, and rationality would be out of the question. These expositions are undoubtedly of great academic value.

It should be pointed out that the causes of western legal formalism are diverse, not all in mathematics. As the author of Mathematical Interpretation said, western religions, the formalization of Roman law, the rationalization of economy and the technical training of professional jurists all contributed to the formalization of western laws. [12] indeed, the formalism of western law has both the reasons of advanced mathematics and political reasons-democracy. Without democratic institutional conditions, intellectuals' mathematical concepts cannot become social practice, and even authoritarian systems may suppress and destroy mathematical science itself. Pound's theory of stages of legal development can support this view. According to Pound, form has two advantages: first, form can avoid disputes; Second, the form is a safeguard to prevent judicial consuls from acting arbitrarily. Pound not only attributed the strict law-formalism law to tradition, but also called on the Romans to "pay attention to the arbitrary use of state aid." [13] These arguments clearly tell us that the fear of abuse of power is an important cause of western legal formalism, and this social psychological demand is transformed into institutional rationality through democratic system.

Then, according to the author's thinking, let's discuss the China problem of the relationship between mathematics and law.

First, can the judgment that "Western laws are formalistic and China laws are substantive" be established?

Many scholars understand Weber in this way when comparing Chinese and western laws. After careful consideration, this statement may be unacceptable. Weber's classification of formalism and essentialism is only conceptual, which is "ideal type" in Weber's words, and it does not correspond to the specific legal space. Developed form, respect for form, especially in ancient times, even emphasized form to the point of irrationality, which is undoubtedly an important feature that western law is different from and superior to eastern law (not just China law). However, the judgment that "China laws are substantive" may not be valid.

From the experience, in terms of legislation, at least since the Qin Dynasty, China's laws have been highly formalized. As for the Tang law, I'm afraid its formalization degree is the highest in the contemporary world law, and this tradition initiated by the Tang law continued until the late Qing Dynasty. Judicial formalism also appeared as early as the Qin Dynasty. I believe that friends who have read bamboo slips of the Qin tomb in Sleeping Tiger Land can find that at least in terms of law, the justice of the Qin Dynasty is highly formalized. As a judicial philosophy, judicial formalism was formed as early as the Jin Dynasty. Liu Song of Jin Dynasty systematically discussed the judicial formalism in The Record of Playing the Emperor, that is, judicature should be determined by law (form), judicature should be a "small skill" (pursuing legal justice), and judicature should be opposed to the pursuit of perfection (surpassing the goodness of law), and clearly put forward that "a statutory crime should be based on law. If there is no text, it is necessary to use examples to judge, and its text cannot be compared with examples ... "

However, China's judicial practice does have the characteristics of essentialism, and it pursues "substantive justice" rather than "formal justice". China's justice lacks respect for form, and the above-mentioned formalistic judicial view has limited influence on judicial practice. This is not to say that China's judicature generally does not respect the form, but that when the law encounters the power to intervene in the judiciary and when the law encounters various policies with Confucian authority, the law makes way for it and replaces it with political, moral and utilitarian policy considerations. This is fully reflected in Bao Gong's plays. You see, in order to pursue substantive justice, Bao Gong can have a "negative trial" that completely ignores the trial procedure. [ 14]

Then, what are the reasons for the "substantial advantages" in our laws? Of course, the relatively backward mathematics and its concept of number are one of the reasons, but the more important reason is probably the autocratic system of the emperor. Imperial autocracy certainly needs formal legal support, because there is no order without law, and there is no autocracy, because autocracy is also a system, although it is not desirable under the concept of freedom and equality. On the other hand, there is an inherent tension between the autocratic system and the formalistic application of law. Because the ultimate goal of authoritarian law is to maintain authoritarian rule, which conflicts with the main principles of legal formalism, such as the same case and the same sentence, the clarity of law and the predictability of law. Of course, the most important thing is that formalistic justice means personal freedom, which is the last thing a dictator wants to see. As Ye Lin pointed out, "form is the deadly enemy of willful behavior-that is, the twin sister of freedom." ..... The definite form is the foundation of discipline and order, so it is also the foundation of freedom itself. They are fortresses against foreign attacks, because they will only break and will not bend; Moreover, when a nation truly understands the function of freedom, they will instinctively discover the value of form and intuitively realize that what they have and insist on is not purely external things, but the guarantee of their freedom. " [ 15]

In addition to the important reasons of autocratic system, China's legal essentialism has two cultural reasons. One is China's tendency of rational materialism. Weber wisely pointed out that Puritanism and Confucianism hold two different kinds of rationality: "The rationalism of Confucianism aims at rationally adapting to the world; Puritan rationalism aims to rationally dominate the world. " [16] This is actually the characteristic of China culture pointed out by many scholars-Shunsheng culture. In this culture, the highest pursuit of judicial bureaucrats is not the basic judicial goodness of "the same case and the same sentence", but their own political achievements, and judicial goodness often gives way to "good governance"-the stability of kingship. An important cultural reason is the undeveloped logic. China people lack the concept of logos, but adopt the so-called "dialectical thinking". The former is an objective existence that people must abide by and is normative. It exists with the authority of rules and is the basic conceptual tool of judicial formalism. The latter often becomes an excuse to go beyond the rules and is used to prove that it is substantive justice beyond the law. In the west, the basic logical rules are also legal rules, and obeying logic is the basic obligation of judges; In China, on the contrary, people who abide by logic are often regarded as pedantic and even denounced as "cruel officials".

Second, how does mathematics affect the legal issues in China?

The mathematical explanation talked about the legal problems in China in some places, for example, after demonstrating the contribution of western natural law to the rationality of legal form, it mentioned the ancient natural law in China, and [17] mentioned the influence of mysterious numbers on China's legal culture in The Legal Cultural Implication of Mysterious Numbers. [18] But there is always a feeling of unfinished business. In fact, legal culture has both individuality and * * *. Since, like the West, China's mathematics and law also exist in the same time and space, there must be a close relationship between China's law and mathematics. In fact, mathematics has a high status in China. When Song Huizong first introduced arithmetic (mathematics), he discussed who was the ancestor of mathematics. Some people pushed Confucius, but Xu Churen, the magistrate of Jinxiang, Jeju, said, "Zhong Ni's way is all-encompassing, but not specialized. The Yellow Emperor welcomed and pushed, and the number began. It is appropriate to worship the ancestors of the Yellow Emperor. " [19] In a country that regards the Yellow Emperor as the ancestor, the ancestor of mathematics is designated as the Yellow Emperor, which shows that the status of numbers is very high. In terms of numbers, China people especially worship "one", thinking that it is the beginning of all things, and at the same time, they associate the law with the number "one". "Deng Xi Zi" said, "It's not easy to obey the rules, not for Qin Chuzhi's breathing, not for Yue Huzhi's plastic surgery. Without evil, there is no flow. It takes shape in one day and is passed down from generation to generation. " [20]

But on the whole, it is an indisputable fact that the influence of mathematics in China is far less than that in the West. As pointed out by the author of Mathematical Interpretation, western mathematics is developed, especially highly abstract. In addition, an important reason may be that the concept of numbers is different. The western concept of number is "scientific", while China's concept of number is superstitious. "China ancient logarithmic superstition is very different. In ancient China, the conscious level of rational thinking was only the perceptual nature, and numbers were completely understood according to the perceptual nature, without realizing the conceptual difference between them. For example, Zhouyi directly attributed the parity of numbers to the sensibility of yin and yang. This is precisely a big difference in the concept of numbers between the East and the West. " "One of the main consequences of this difference is that pure mathematics has existed in Greece since Pythagoras, but it did not and could not exist in ancient China, because pure mathematics is an inevitable product of the concept of numbers, and its content is only a concrete demonstration of the stipulation of the concepts of numbers and quantities." [2 1] That is to say, western "scientific mathematics" developed strict concepts and formed strict conceptual logic, while China's superstitious mathematics failed to abstract precise concepts and form conceptual logic, which fundamentally weakened the influence of China's mathematics.

We have entered the so-called era of big data. The internet based on mathematics is changing the world, changing interpersonal relationships, and then changing the law. The relationship between mathematics and law is getting closer and closer. It is conceivable that the study of the relationship between mathematics and law also has its brilliant prospects.