Fuzzy Logic in the Quantum Mechanical Worldview;Related to Zadeh, Wittgenstein, Moore, Saussure, Quine, Lewis Carroll, etc.  

作　　者：Shiro Ishikawa Shiro Ishikawa(Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, Japan)

机构地区：[1]Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, Japan

出　　处：《Journal of Applied Mathematics and Physics》2021年第7期1583-1610,共28页应用数学与应用物理（英文）

摘　　要：Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.

关 键 词：Zadeh’s Fuzzy Sets Quantum Language Linguistic Copenhagen Interpretation 

分 类 号：O15[理学—数学]