Original The Fuzzy Completeness Theory

The Two Incompleteness Theorems of Kurt Friedrich Gödel and the Impossibility Theorem of Kenneth Arrow claim that logic, the most reliable of human knowledge, is incomplete or can be inconsistent. The Fuzzy Completeness Theory states that the Fuzzy Logic of Lotfi A. Zadeh has resolved the incompleteness and impossibility in logic and made logic complete and knowledge reliable with the new concept of Range of Tolerance, within which logic is still complete and knowledge, valid. In the Age of Reason about 300 years ago just prior to the Age of Science, reasoning is free for all, without the constraint of the laws of nature, which would be discovered in the Age of Science. However, the Scientific Method of reasoning by empirical verification depends so much on faith that it is logically and empirically dismissed by mathematicians and logicians, especially, after the exposure by Thomas Kuhn and Paul Feyerabend that a scientific advancement is akin to a religious conversion. On the other hand, mathematicians and logicians have been working steadily to find the limit of reliable knowledge. In the current state of knowledge, Kurt Gödel has the last word with his Two Incompleteness Theorems, which conclude that the most reliable of human knowledge, logic, is incomplete, casting doubt whether knowledge is completely reliable. Gödel’s view is further supported by the Impossibility Theorem of Kenneth Arrow. However, Zadeh and the author of this paper extend Zadeh’s concept of Range of Value in Fuzzy Logic to that of Range of Tolerance. Accordingly, Fuzzy Logic deals with the sacrifice of precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility of an uncertain future. In knowledge, incompleteness


When a solution is newly defined as an answer within the Range of Tolerance of the solution, Fuzzy Logic resolves the incompleteness in logic and becomes the new foundation of knowledge, replacing
Exact Logic. With this definition of a solution, Fuzzy Logic covers the incomplete or the impossible parts of the solution by expanding sufficiently the Range of Tolerance to make reason complete and knowledge reliable, but only within the Range of Tolerance.
To summarize, even though the world's leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still operating smoothly, and science has even demonstrated the power of knowledge. The conflict between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, reality is fuzzy, not exact.
The breakthrough impact of this paper centers around completeness theory and Fuzzy Logic. In the early 21st century, the mainstream knowledge is still not aware that the supply and demand model is incomplete, and that the DNA-protein system resembles computer science based on logic more than science based on experimentation. The current computer is based on exact logic and is designed for temporary existence, while the living system is design for permanent existence and must depend on the Range of Tolerance based on Fuzzy Logic to survive permanently in an uncertain future. Financial crises will be caused by the unstable investment return, which is the incomplete part in the supply demand model. Complexity crises will be caused by the lack of the requirement of permanence or complete automation, which is the ultimate solution to unlimited complexity. The 16 Methods of Reason correspond roughly to Culture Level Quotient (CLQ), which is a non-technical measure of a person, a people or a nation.

The Limit of Reason
The Completeness Theory is to complete the Two Incompleteness Theorems of Kurt Gödel (Smullyan, 1992) and to make possible the Impossibility Theorem of Kenneth Arrow (Arrow's impossibility theorem entry in the Stanford Encyclopedia of Philosophy), using Fuzzy Logic of Lotfi A. Zadeh (Lotfi, 1965). The Fuzzy Completeness Theory is supported by the demonstration of a Complete Mathematically Rigorous System by the solution of value (2000) and of a Completely Logically Rigorous System by the solution of Complete Automated Software (1996) of the author. However, the best-proven illustration of the Fuzzy Complete Theory is the operational living system (Miller, J. L., & Miller, J. G., 1992;Schrodinger & Penrose, 1974), which, however, is still very far from being understood by scientists of the twenty-first century. The author has extended the concept of Range of Value of the Fuzzy Logic of Zadeh to the new concept of Range of Tolerance and, thus, has expanded the application of Fuzzy Logic beyond science, which is characterized by precision, into post-science.
Fuzzy Logic is a post-creational technology, which sacrifices precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility 53 automated software is explained in "Completely Automated and Self-generating Software System" (Pat. No. 5,485,601). Complete Automation will be achieved through Self-Manufacture General-Purpose Robot with the ability of touch, where the Robot will be developed and controlled by the completely automated software. The solution of touch is the same as the solution of the 300-year-old unsolved contact problem, which has eluded Isaac Newton and all the scientists since Newton and is explained in a book on prolonged contact (http://www.jumpulse.com/jbook.pdf). The solution of touch is based on a Fuzzy Jumpulse Mechanism. Jumpulse is a word coined by Ta-You Wu (1999) to denote a sudden change of force, as Newton's impulse is a sudden change of momentum. Prolonged contact or touch can be achieved by applying a jumpulse within the Range of Tolerance of a very short interval during impact. Touch is achieved when the two colliding objects have the same position, velocity, and acceleration. The Law of Touch states that acceleration and all higher derivatives can change instantly and is necessary to achieve touch. Ultimately, the Robot will become the human and the software, DNA, as part of the process of the self-creation of the living system. Mankind's self-creation (Explanation of self-creation, http://www.self-creation.org) will reveal from the design specification the meaning of life and the purpose of existence. From the vision of knowledge of the future, the meaning of life is in its value, and self-creation is the purpose of existence, for what is self-created will be able to do whatever the creator can do. Only after self-creation, the living system can be improved by mankind. The Fuzzy Completeness Theory will be the foundation of Knowledge-Oriented Society (2016).

The Sixteen Methods of Reason
The Fuzzy Completeness Theory deals with methods of reason. Before Fuzzy Logic, people use exact reasons as the method to discover truth. And before complete solutions, people arrive at incomplete solutions. For example, the Scientific Method completes reason by introducing the final equation for a deterministic solution, with an equal number of equations and independent variables, from an empirically verified law of nature, which, however, requires the faith in the Law of Uniformity, which states that what happens in the past will happen in the future. Mathematics is more reliable than empirical verification, and logic is even more reliable than mathematics and is the foundation of mathematics. The solution of value identifies an exact complete mathematically rigorous system, which corresponds to reality. The exact solution of completely automated software identifies a complete  We see from the above that Fuzzy makes the Method more accurate than Exact, and Complete, than Incomplete. And Fuzzy could be more important than Complete, whose defects, accordingly, are In practice, very few current solutions in social and life sciences satisfy the rigor required for the reliability or predictive capability. And this observation checks with the incapability of these solutions in predicting the recent financial and medical crises, while the post-science solution of value has 57

Foundation of Knowledge is Faith, Not Reason
Everyone is brainwashed by the establishment at an early age. A good thinker should be able to realize the brainwashing by the establishment and should start to deprogram oneself as soon as the moment of realization, for human progress is based on the struggle between the thinker and the establishment.
On the other hand, if one does not believe that one has been brainwashed or, as one of the most common phenomena in brainwashing, one believes that one is so smart that one can never be brainwashed by anyone or anything, one is definitely brainwashed. Moreover, the establishment, in order to maintain social stability, generally defends itself, at the expense of progress. Also, most people would prefer to bask in the sunshine and the warmth of the establishment, being financially and socially supported by the establishment for their obedience rather than to live the lives of social outcasts and not being fed naturally by the establishment.
One of the most important phenomena in modern society is the brainwash of nearly 100% of the population in science and the scientific method of empirical verification. Yes, science has exposed the brainwashing of religion, which has at one time brainwashed nearly the entire world and is formed out of necessity by the wisest of human beings to set a code of behavior for the foreseeable future from the time of the establishment of religion. Even today, religion could be a better guidance than science for human and social behavior. Bashing religion by science is understandable simply because science is a newer phenomenon than religion and has the advantage of progress since the founding of religion. One day in the distant future, all the knowledge in religion will be replaced by new discoveries in knowledge, as it is replaced by science in the knowledge of the physical world. The focus of the world in the twenty-first century is how to deprogram ourselves from the success of science and the wonders of technology. Post-science, with its solution of value and of software, claims that the foundation of social science and the foundation of computer science are completely wrong. Social science and life science deal with problem of the entire reality and involve, in particular, infinity. Since infinity never arrives, empirical verification in social and life sciences is not possible. Post-science has realized that the solutions in social science, such as the solution of value, must be accepted based on completely mathematical rigor, and the solutions in life science, such as the solution of completely automated software, of which DNA is a prime example, must be accepted based on completely logic.
Trying to change one's own or anyone else's beliefs acquired through brainwashing is generally as hard as trying to discard something, which one can no longer find. The beliefs are hidden in the subconscious, almost as firmly embedded as one's innate beliefs, such as the Human Associative Memory (HAM) and one's language ability. It would take a lifetime of conscious deprogramming to get rid of these beliefs. Some societies even try purposely to inject young minds with dogmatism, which will benefit the society in the short-run or keep the society stable and united. Well, right or wrong, brainwashing is an effective tool when used by authority, but for all the thinking people, deprogramming throughout one's life should also accompany the brainwashing.

Conclusion
This paper deals with the foundation of knowledge. It claims that Fuzzy Logic has resolved the incompleteness of knowledge and made knowledge reliable within the qualification of the most fundamental consideration of the 16 Methods of Reason. In conclusion, even though the world's leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still functioning in an orderly fashion according to empirically verified laws of nature, and science has even demonstrated the power of knowledge. The direct contradiction between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, the reality is fuzzy, not exact. The Fuzzy Completeness Theory is a fuzzy proof of the necessity of tolerance in reality. This paper endorses reason, but admits that the foundation of knowledge is faith, not reason. This paper concludes that we must have faith in reason.

Breakthrough Impact
The current Age of Science deals with finite duration, within which deterministic data can be obtained for empirical verification. The Age of Science also deals with temporary creations, which differ from the living system designed for permanent existence. Empirical verification is only possible for finite duration and temporary creation and is the bulwark of the scientific method. This paper claims that reality in infinite and permanent. The breakthrough of this paper is the achievement of completeness by infinite consideration and of permanence by fuzzy logic, which sacrifices precision in the expansion of the Range of Tolerance in order to survive permanently in an uncertain future. Postmodern knowledge or post-science (Ching, 2019) is knowledge beyond science for solving problems in social and life sciences, which deals with reality, which is infinite and permanent. In relation to infinity and by definition, will never arrive for collecting the complete set of deterministic data. Ching concludes that solutions in social science must be accepted based on complete mathematical rigor, and that solutions in life science must be accepted based on complete logic. Here, he has implied, for the first time in history, the ultimate usefulness of mathematics and logic. Ching is considered the founder of completely mathematically rigorous New Social Science, the founder of the completely logically rigorous New Life Science, the founder of the New Robotics, which will replace all human routine work, the founder of Self-Creation, and the heir to Lotfi A. Zadeh, the Father of Fuzzy Logic. 61