Our chief writer, Mr. Woofeng.

Editor's Notes:The Western mathematical community has long absolutized the consistency of deduction, which has led to major errors in the field of mathematics, resulting in a great deal of fog in the field of mathematical foundations. A Chinese amateur mathematical scholar, through decades of research, mathematized paradoxes and contradictory ways of thinking, and created "S-type super-coherent logic", which overthrew a number of mathematical theorems that had long been entrenched in the mathematical field, and were regarded as classical guidelines, and his theories provided mathematical language support for the "Wo Xue" system of scientific thought. His theory also provides mathematical language support for the heavenly dialectical logic of "Harmony" scientific thought system, which will lead a new mathematical era!

Vast universe, brilliant stars; long history, heroes!

From nature to human society, from science to religion, from Eastern Tai Chi to Western dialectics ...... paradoxes shape the ultimate laws of the universe.

Paradox is an old and young scientific puzzle! A paradox occurs when the conclusion contradicts the initial conditions. If event A occurs, then non-A is deduced; if non-A occurs, then A is deduced.

There is a famous "Liar's Paradox" in ancient Greece. In the sixth century B.C.Cretephilosopher
(Epimenides) says: "All Cretans are liars." This paradox puts the human mind in a dilemma. Due to its popularity, it can be understood by almost everyone. As a result, the Liar's Paradox has become an after-dinner thinking game.

In 1897, Forte revealed the first paradox in set theory in the field of mathematics, and later the mathematician Cantor found a very similar paradox in his theory of ordinal numbers. 1902 Russel found another paradox in the strict sense of mathematics. Russel's paradox shook the entire mathematical edifice, and the paradox finally aroused the scientific community's "panic" and great attention.

 

The Mist of the West

Russell's paradox shook the entire foundation of mathematics, historically known as theThe Third Mathematical Crisis. In order to solve the paradox, the Western mathematical community has proposed many new theories and methods to seek a breakthrough.

To solve this math crisis.
Russell put forward the program of logicalism; Hilbert (Hilbert) put forward the famous Hilbert plan to establish a foundation of mathematics to thoroughly prove the non-contradiction of mathematics, known as formalism; Brouwer (Brouwer) put forward the constructive mathematics, opposed to the use of the law of rows and antidotes in the infinite set, known as intuitionism. Formalism, Logicism, and Intuitionism are the three famous schools of thought in mathematical logic.

There is also the school of axiomatic set theory, which, in order to overcome set theory paradoxes, attempts to axiomatize set theory by using theaxiomaticRestrictions on sets.Chemero (surname)(Zermelo) and the ZF system proposed by Fraenkel et al.

All of the above programs, in essence, seek consistency in the system and are built to prevent contradictions. History has proved that all the above schools of thought have their own merits and defects, making up for the many deficiencies of the mathematical foundation. However, they do not have a unified understanding of each other, and their respective goals have not been fully realized, not to mention explaining the paradoxes clearly.

The classical logical system is a compatible logical system that "breaks down" if there are paradoxes. In contrast to the above coherent research program, recently there are some international logical systems that accommodate contradictions and paradoxes, which are different, but most of them are restrictive of the law of contradiction. By modifying the negations of classical logical systems, the system can accommodate contradictions without causing the system to collapse. For example, the Brazilian Dakshta (Da.
Costa's "subcoherent logic", R. Brandow's "incoherent logic", and R. Routley's "supercoherent logic", all of which are of this type, as well as G. Priest's "paradoxical logic", all of which are of this type. " in the United States, R. Brandow's "Uncoordinated Logic" in the United States, and R. Routley's "Hypercoordinated Logic" in Australia, as well as G. Priest's "Paradoxical Logic" in Australia, are all logical systems of this type.

Russell's paradox is related to a diagonal method. The "diagonal construction method" is also a classical method of proof in mathematics.
Cantor used it to prove that "the set of powers of the natural numbers is uncountable" and "the set of real numbers is uncountable"; Gödel used it to prove that "the system of natural numbers PA is incomplete"; Turing used it to prove that "the shutdown problem" is undecidable; and in recursion theory, it was used to prove that "there is a non-recursive set on the set of natural numbers". Gödel used it to prove that "the system of natural numbers PA is incomplete", Turing used it to prove that "the shutdown problem" is undecidable, and recursion theory used it to prove that "there exists a non-recursive set on the set of natural numbers" and so on, the proofs of these important propositions use the same mathematical method, which is known as the "recursion method". The proofs of these important propositions use the same mathematical method, which has been called "a golden diagonal".

Since the "Gödel's Incompleteness Theorem", "Cantor's Diagonal Proof Method", the international community has raised a lot of skepticism. For example, the famous Austrian philosopher, mathematical logician Wittgenstein (Wittgenstein), does not recognize Cantor and Gödel's proof. Priest, the founder of paradoxical logic in Australia, both denied the validity of Gödel's proof of the incompleteness theorem. However, their views are fragmentary, philosophical and not very mathematical. They did not make the problem clear and thorough, and therefore were not accepted by the mainstream school of mathematics.

For centuries, the diagonal method, and the paradoxes associated with it, its laws of existence and inner mechanism have remained unclear. The foundations of Western mathematics are shrouded in a heavy fog, with no direction or future in sight. This also means that the paradox is not a localized problem in a particular field of mathematics, but rather it breeds a breakthrough in a completely new approach.

 

"Stunning" proof.

 

In recent years, a Chinese amateur logic researcher-Zhang Jincheng-created a brand-new logic system-S-type supercoordinated logic based on the failure of generalized Western mathematics.
S-type supercoherent logic completely unifies all kinds of "mathematical paradoxes", "Gödel's undecidable propositions", "Cantor's diagonal method proofs", etc., which have long been unsolved, and finds their common mathematical forms to be completely equivalent, and concludes that they are completely equivalent, which astonishes the world. They discovered their common mathematical form, which is completely equivalent, and came to a conclusion that shocked the world.

S-type supercoordinated logic makes only a very small modification to the classical logical system, and its inferences are subversive and revolutionary. A large number of Western mathematical theorems are denied, all of which are false.

Specifically:

1. The proof of Gödel's Incompleteness Theorem is rejected.

In 1931 Gödel proved that "the formal system containing the natural numbersThis is the famous Gödel's Incompleteness Theorem, which is regarded as an epoch-making contribution to the field of mathematics in the twentieth century, and a "milestone in the history of the development of mathematics and logic". It has permeated all corners of mathematics, logic, language, artificial intelligence, natural science, thinking science and epistemology, and even the humanities. "Gödel's Incompleteness Theorem has been regarded as a golden rule by the mainstream school, and enjoys the highest honor. s-type supercoherent logic proves that "Gödel's undecidable proposition" is an extradimensional term in the system of natural numbers, and then obtains "Similar undecidable propositions exist outside the general recursive set". Gödel's undecidable proposition does not affect the completeness of the system, and the proof of "Gödel's Incompleteness Theorem" is not valid. Due to the limitations of conventional thinking, Gödel discovered the extra-territorial term, but he did not recognize it and mistakenly thought that he had proved the "Incompleteness Theorem". This is like Columbus discovering the New World in the 15th century, but mistaking it for India. Gödel made a similar mistake.

2. The proof of "Cantor's theorem" was rejected.

In 1873, Cantor defined countable and uncountable sets by the method of one-to-one correspondence; he proved by the "diagonal method" that the infinite set cannot establish one-to-one correspondence with its power set; the power set of the set of natural numbers is uncountable, and the real numbers are uncountable. These theories have permeated all specific areas of modern mathematics. s-type supercoherent logic proves that Cantor used the "Diagonal method"The terms constructed by the term are all extraterritorial, and are formally the same as "paradoxes" and "extraterritorial undecidable propositions", which is an extraterritorial "unclosed term ". Therefore, Cantor's proof is not valid.

Rejects the proof that the "Turing stopping problem is undecidable". Turing
The proof of the "Undecidability of the Shutdown Problem" is an important theorem in the traditional Theory of Computability, and the proof of this theorem in S-type hypercoherent logic is also a diagonal approach, where the terms constructed are extra-domain terms, as in the case of Gödel's Incompleteness Theorem, "Cantor's uncountability of the real numbers" is formally proved to be the same as "Turing's downtime problem is undecidable".
The proof is wrong. An undecidable "Turing machine" is an extra-domain "unclosed term".

3. The universal validity of the counterfactual is denied.

The antidiagonal method is a classical method of proof in mathematics. All diagonal proofs are antidemonstrative, and S-type supercoherent logic suggests that antidemonstration can only be effective in a closed domain, and beyond that, antidemonstration is invalid. As long as there is self-referential, may produce "not closed terms", on the basis of the blind use of "counterfactual", can only lead to wrong conclusions. Therefore, not only the proof of "Gödel's Incompleteness Theorem" is wrong, but also many theorems and theories similar to or based on "Gödel's Incompleteness Theorem", such as "Turing machine's stopping problem, recursive set determination problem," etc., all of them are wrong. The "Turing machine downtime problem, the recursive set determinability problem," and so on, must be re-examined, and this will involve the Philosophy of Mathematics, Mathematical Logic, Theory of Computing, Theory of Functions, Theory of Measurement, and so on, and so on, in many fields of science based on Cantorian Incompleteness Theorem.

 

The preeminent mathematical genius of our time.

 

Zhang Jincheng, the original creator of "S-type super-coherent logic", is a contemporary outstanding mathematical genius in China. He was originally an ordinary math teacher in Guangde County, Anhui Province. He made these significant proofs and mathematical discoveries, which are very surprising. He was not a professional scientific researcher or university professor. He was originally engaged in teaching mathematics and philosophy in the Party School. Later, because of the need for research, he resigned and founded a training school by himself to train secondary school students in Olympiads, and persisted in researching mathematics and paradoxes in his spare time for decades.

Zhang Jincheng was particularly fond of mathematics in his junior and senior high school years. When he was in high school, he completed the university's "Calculus" and "Theory of Functions of Complex Variables" on his own, and had a particularly high talent and strong interest in mathematics. He did not go to a formal university to study mathematics, and joined the workforce after graduating from high school. Although later in the party school work through the function to obtain a university degree, are not related to mathematics. All the math knowledge was done by his self-study. Some of the set theory, recursion theory, mathematical logic, and other western mathematical theory content, which is daunting to the doctor, is almost untutored.

In his early years, when he was just in his twenties, he published a paper on mathematical logic in the Wuhan University Newspaper and was highly regarded by Gui Qiquan and Chen Xiaoping, professors of the Philosophy Department of Wuhan University, who wished to admit him as a graduate student of Wuhan University. Due to the obstruction of some dissenting opinions, it did not work out in the end. He published his first formal system Z in Wuhan University Journal, which now seems to be rather naive, but it gave him the right direction to establish "S-type supercoordinated logic" in the future.

He thinks that the pure consistency of mathematical systems in the Western mathematical logic community, excluding the research method of contradiction and paradox, seems to have lost the philosophical guidance and direction, circling around in a dead end without finding a fundamental way out. And Chinese Taoism's Taiji culture contains the dialectical philosophy of yin and yang is a kind of philosophy that accepts contradiction, can we unify the dialectical philosophy and mathematical construction, these two directions of development. The use of pure mathematical methods to study contradictions, paradoxes and other philosophical issues, which is the forefront of the Western mathematical community of thought, and this became his firm research goal. Over the decades, he attended dozens of various related academic conferences in universities and colleges at his own expense, and made hundreds of corrections off and on, finally building the hyper-coordinated logic system.

From 2011-2014, his paper "Immovable Terms and Undecidable Propositions I and II in Logic and Mathematical Algorithms" was published in the Journal of Intelligent Systems, which was highly praised by Prof. He Huacan of Northwestern Polytechnical University, for which he personally wrote a review article.

The basic idea of "S-type supercoordinated logic", partially published in the Journal of Intelligent Systems, has been supported and recognized by some scholars. Some scholars have also published some skeptical and negative articles. Except for a few opinions that can be adopted for further improvement and clarification of the theory, the majority of them have some misunderstanding or blindly believe in the authority and do not understand his paper at all.

 

2015In 2007, in an online "Academic Issues Review Garden", Zhang Jincheng and Prof. He Huacan were leading a historic debate. The "S-type supercoordinated logic" requires a comprehensive understanding of philosophy, logic, set theory, infinity, non-standard analysis, and other cross-cutting fields, and the publication of some poor reviews by authoritative scholars with one-sidedness and blind superstition in some fields of knowledge is a misinterpretation of the "S-type supercoordinated logic". Misinterpretation. The current situation has shown that the influence of new theories is expanding and the traditional forces are losing ground. A fallacy is a fallacy.

 

In 2016, Zhang Jincheng's "S-type supercoordinated logic" has been translated into English, and will be publicized in the United Kingdom, the United States, Australia and other Western countries, so that experts and scholars in the Western mathematical community can understand and accept the S-type supercoordinated logic.

Contribution and significance of the new theory

 

SSupercoordinated Logic System on the one hand is broken, denying that the above theorem proves to be wrong; on the other hand, it is established, also re-establishing some new propositions and new theories. Therefore, it has significant theoretical and practical significance.

1The first is that it overthrew a number of erroneous theorems that had long dominated the field of mathematics.

"The real numbers are uncountable", "The power set of all natural numbers is uncountable","Gödel's incompleteness theorem (math.)" , "The Turing stopping problem is undecidable", "There are non-recursive functions of functions on the set of natural numbers", etc., and the numerous theorems associated with them, are all associatively false.

2, cleaned up a batch of math trash

As a result of the faulty reasoning of the diagonal proof method, a number of useless mathematical garbage such as uncountable, undecidable, non-recursive, ..., etc., have been derived from the theories of Set Theory, Recursion Theory, and Computable Theory, and they must all be discarded once and for all.

3, reconstructed new axioms, new systems, new methods, new theorems

It is proved anew that: the real numbers are a countable set; the set of powers of all natural numbers is countable; Cantor"diagonallyBuddhist teaching"The numbers constructed are hyperreal; it is proved anew that the systemPAis complete; all functions on the set of natural numbers are recursive; the "Turing Shutdown Problem" is decidable, and so on.

The "axiom of infinity" has been revised, the ordinal and base numbers have been redefined, and there are no longer any uncountable ordinal and base numbers; the method of transcendental induction has been revised, and the method of supernatural number induction has been established. The concept of infinity has been re-conceptualized, and standard analysis, non-standard analysis and set-theoretic infinity have been unified, and so on.

4The first is to solve a number of mathematical problems that have been seemingly unsolved for a long time in the history of mathematics.

The "continuum hypothesis problem" is a Hilbert"23math problem"Fourth periodic report of the Secretary-General1A question.1938In 2007, Gödel proved that the continuum hypothesis is consistent with theZFNon-contradiction of set-theoretic axiom systems.1963In 2007, the American mathematician Korth (P. Choen) proves that the continuum hypothesis is not compatible with theZFThe axioms are independent of each other. Thus, the continuum hypothesis cannot be usedZFAxioms are proved. It is usually assumed that the problem is solved in this sense. However, "S-type supercoherent logic" proves that uncountable bases do not exist at all. The "continuum hypothesis problem" is an erroneous problem that confuses the concept of infinity. There are other problems such as the Axiom of Infinity, the Axiom of Choice, and Transcendental Induction, all of which have definite conclusions.

5,SType Supercoordinated Logic has changed the way we think logically.

Whole over Western classical logic is based on coherent thinking. Western coherent thinking is absolute. Thinking that the whole world is coherent. Does not realize the normalcy of the existence of contradictions outside the domain. Thinks that whenever a contradiction is constructed within a system, the system is wrong. In reality consistency exists only relative to a closed domain that ignores assumptions and microfoundations. The external world is precisely in motion and contradictory. The use of extra-domain contradictions as a basis for reasoning within the domain has led to such approaches as "Cantor's diagonal approach", "G?delIncompleteness Theorem" and other disastrous consequences.SThe creation of type hypercoherent logic negates the absolute validity of consistency and non-contradiction, which are also relatively valid.

The laws of classical logic have historically been considered absolute truths. FromSThis does not appear to be the case for type supercoherent logic. The law of non-contradiction and the law of exclusion also have a scope of application. Extraterritorial terms do not hold for classical logic. This is just like the creation of non-Euclidean geometry, which denied the absolute validity of Euclidean geometry.SThe production of type hypercoherent logics can be analogized to the production of non-Euclidean geometry.

6, transformative for the foundations of mathematics, mathematical logic, basic computer theory, etc.

Zhang Jincheng's discovery was shocking.

He made it clear to the world that such a serious cluster of problems was hidden in the original basic theory of modern mathematics. As people's understanding deepened, theSThe impact of type hypercoherent logic will grow with each passing day. It will affect many fields of science that think in terms of counterfactuals. Never before in the history of science have there been so many errors as in Gödel's Theorem, Cantor's Theorem, Turing's Theorem, and so on.

Liu Haofeng, the founder of Harmony, a contemporary thinker and philosopher, once pointed out that any stable system must be holistic over local, mathematical-dialectical logic over mathematical-formal logic. Both he and Liu Haofeng saw that the comprehensive use of mathematical dialectical logic and mathematical formal logic to clean up and rebuild these theories would lead to a new scientific revolution for mankind.

Zhang Jincheng'sSType hypercoherent logic is mathematical at the micro level and philosophical at the macro level. It turns out that coherence holds only in closed domains and is contradictory outside them. This law has been philosophically formulated in close proximity in ancient and modern times. However, it is the first time in history that it is precisely expressed mathematically. This is the great achievement of Zhang Jincheng.

SType supercoordinated logic will announce the end of the era of Russell, Cantor, Gödel, and Turing. The Chinese cultural renaissance has ushered in a new pinnacle in mathematics.

The process of mankind's understanding of the objective laws is an ever-approaching process that never has an end.

No doubt about it. Cantor, Gödel. Turing and others are20A generation of great scientists of the century had made epoch-making achievements in the fields of set theory, mathematical logic, computers and philosophy. But like the great men and women of history, they also had more or less historical limitations. Now, their theories will eventually be replaced by new ones.

Taoism says that yin and yang give birth to all things in heaven and earth. If we place the domain of the theory in the context of the entire universe, we can deduce that "contradiction is the fundamental force that drives the development and movement of things".

The mathematical laws of paradoxes are clarified, and paradoxes have not yet ended in nature, human society, and science. Because, paradoxes exist universally.

Whenever there is a disruptive major breakthrough in the field of science, the mysterious power of paradox can always be seen. Paradox is the great driving force of the evolution of nature, and paradox is the heroic epic of the progress of human society!

 (This article refers to Prof. Ho Wah Chan'sSA major breakthrough in type supercoordinated logic", in Zhang Jincheng, Principles of Supercoordinated Logic, Beijing Book Publishing House.2015First edition, year.P2The)