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.
Recently we proposed the linguistic Copenhagen interpretation (or, quantum language), which has a great power to describe both classical and quantum systems.Thus we think that quantum language can be viewed as the language of science.Therefore, it makes sense to study, from the quantum linguistic point of view, Wittgenstein's picture theory, since he must have wanted to create a language of science.In this paper, we show that the proposition that Wittgenstein studied in his book "Tractatus Logico-Philosophicus" can be regarded as a binary projective measurement in classical quantum language.And thus, we conclude that Wittgenstein's language (i.e., the language that he supposed in his book) is realized by classical quantum language.Hence, now we can fully understand Wittgenstein's picture theory since the reason his book is incomprehensible is that he did not define his language.
Although there are many different types of philosophy, many philosophers agree that the mainstream of Western philosophy (Socrates, Plato, Aristotle, Descartes, Kant, Wittgenstein) developed toward the perfection of Socrates’ absolutism. But can the absolutism maintain its central position after analytic philosophy? There are pessimistic views on this problem, such as that of R. Rorty, the standard-bearer of neo-pragmatism. Recently, I proposed quantum language (which is including quantum mechanics, statistics, fuzzy sets, etc.). I think that that this theory is not only one of the most fundamental scientific theories, but also the scientific final destination of Western philosophy. If so, Socrates’ dream has come true. The purpose of this paper is to discuss the above and to inform readers that quantum language has the power to create a paradigm shift from the classical mechanical world view to the quantum mechanical worldview.
Recently we proposed the linguistic Copenhagen interpretation (or, quantum language, measurement theory), which has a great power to describe both classical and quantum systems. Thus we think that quantum language can be viewed as the language of science. Further, we showed that certain logic (called quantum fuzzy logic) works in quantum language. In general, it is said that logic and time do not go well together. Then, the purpose of this paper is to show that quantum fuzzy logic works well with time. That is, quantum fuzzy logic has the advantage of being able to clearly distinguish between implication and causality. In fact, we will show the contraposition of the proposition “If no one is scolded, no one will study” (or the negation of “John is always hungry”) can be written in quantum fuzzy logic. However, “time” in everyday language has various aspects (e.g., tense, subjective time). Therefore, it is not possible to understand all of the “time” of everyday language by the “time” of quantum language.
Recently we proposed "quantum language" (or, "the linguistic Copenhagen interpretation of quantum mechanics", "measurement theory") as the language of science.This theory asserts the probabilistic interpretation of science (=the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born's probabilistic interpretation of quantum mechanics.In this paper, we consider the most fundamental problems in philosophy of science such as Hempel's raven paradox, Hume's problem of induction, Goodman's grue paradox, Peirce's abduction, flagpole problem, which are closely related to measurement.We believe that these problems can never be solved without the basic theory of science with axioms.Since our worldview (=quantum language) has the axiom concerning measurement, these problems can be solved easily.Thus we believe that quantum language is the central theory in philosophy of science.Hence there is a reason to assert that quantum language gives the mathematical foundations to science.
Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic turn of quantum mechanics. This turn from physics to language does not only realize the remarkable extension of quantum mechanics but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics). And thus, the turn urges us to dream that traditional philosophies (i.e., Parmenides, Plato, Aristotle, Descartes, John Locke, Berkeley, Hume, Kant, Saussure, Wittgenstein, etc.) can be understood in the quantum mechanical world view. This dream will be challenged in this paper. We, of course, know that most scientists are skeptical to philosophy. Still, we can expect that readers find a good linguistic philosophy (i.e. philosophy of language) in quantum mechanics.
Recently, we proposed measurement theory ( or. quantum language) as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). This theory has a great power of scientific descriptions. In fact, we have continued asserting that even statistics can be described in terms of measurement theory. Thus, we believe that quantum language is future statistics (i.e., statistics will develop into quantum language). However, now we think that our arguments were too abstract and philosophical, that is, we should have presented concrete examples much more. Thus, in this paper, we show that the calculation of Kalman filter is more understandable in terms of quantum language than in terms of usual statistics. For this, we devote ourselves to statistical measurement theory, in which the Bertrand paradox is discussed.