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...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.展开更多
It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability th...It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability theory, since it is not guaranteed that mathematics and our world are connected. In order that mathematics asserts some statements concerning our world, a certain theory (so called “world view”) mediates between mathematics and our world. Recently we propose measurement theory (i.e., the theory of the quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. In this paper, we assert that statistics is based on measurement theory. And, for example, we show, from the pure theoretical point of view (i.e., from the measurement theoretical point of view), that regression analysis can not be justified without Bayes’ theorem. This may imply that even the conventional classification of (Fisher’s) statistics and Bayesian statistics should be reconsidered.展开更多
In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statisti...In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.展开更多
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 th...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.展开更多
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 la...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 (<em>i.e.</em>, 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.展开更多
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 tu...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.展开更多
In this paper, we study the principle of equal probability (i.e., unless we have sufficient reason to regard one possible case as more probable than another, we treat them as equally probable) in measurement theory (i...In this paper, we study the principle of equal probability (i.e., unless we have sufficient reason to regard one possible case as more probable than another, we treat them as equally probable) in measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics with the Copenhagen interpretation. This turn from physics to language does not only realize theremarkable extensionof quantum mechanicsbut alsoestablish the method of science. Our study will be executed in the easy example of the Monty Hall problem. Although our argument is simple, we believe that it is worth pointing out the fact that the principle of equal probability can be, for the first time, clarified in measurement theory (based on the dualism) and not the conventional statistics (based on Kolmogorov’s probability theory).展开更多
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 interpretatio...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.展开更多
Recently we proposed “quantum language”, which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. And further we be...Recently we proposed “quantum language”, which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. And further we believe that quantum language is the only scientifically successful theory in dualistic idealism. If this turn is regarded as progress in the history of western philosophy (i.e., if “philosophical progress” is defined by “approaching to quantum language”), we should study the linguistic mind-body problem more than the epistemological mind-body problem. In this paper, we show that to solve the mind-body problem and to propose “measurement axiom” in quantum language are equivalent. Since our approach is always within dualistic idealism, we believe that our linguistic answer is the only true solution to the mind-body problem.展开更多
The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not nec...The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.展开更多
Bell’s inequality itself is usually considered to belong to mathematics and not quantum mechanics. We think that this is making our understanding of Bell’ theory be confused. Thus in this paper, contrary to Bell’s ...Bell’s inequality itself is usually considered to belong to mathematics and not quantum mechanics. We think that this is making our understanding of Bell’ theory be confused. Thus in this paper, contrary to Bell’s spirit (which inherits Einstein’s spirit), we try to discuss Bell’s inequality in the framework of quantum theory with the linguistic Copenhagen interpretation. And we clarify that the violation of Bell’s inequality (i.e., whether or not Bell’s inequality holds) does not depend on whether classical systems or quantum systems, but depend on whether a combined measurement exists or not. And further we conclude that our argument (based on the linguistic Copenhagen interpretation) should be regarded as a scientific representation of Bell’s philosophical argument (based on Einstein’s spirit).展开更多
As the fundamental theory of quantum information science, recently I proposed the linguistic interpretation of quantum mechanics, which was characterized as the linguistic turn of the Copenhagen interpretation of quan...As the fundamental theory of quantum information science, recently I proposed the linguistic interpretation of quantum mechanics, which was characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse (or more generally, the post-measurement state) is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized. That is, the projection postulate is completely clarified in the linguistic interpretation.展开更多
文摘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.
文摘It is a matter of course that Kolmogorov’s probability theory is a very useful mathematical tool for the analysis of statistics. However, this fact never means that statistics is based on Kolmogorov’s probability theory, since it is not guaranteed that mathematics and our world are connected. In order that mathematics asserts some statements concerning our world, a certain theory (so called “world view”) mediates between mathematics and our world. Recently we propose measurement theory (i.e., the theory of the quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. In this paper, we assert that statistics is based on measurement theory. And, for example, we show, from the pure theoretical point of view (i.e., from the measurement theoretical point of view), that regression analysis can not be justified without Bayes’ theorem. This may imply that even the conventional classification of (Fisher’s) statistics and Bayesian statistics should be reconsidered.
文摘In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.
文摘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.
文摘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 (<em>i.e.</em>, 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.
文摘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.
文摘In this paper, we study the principle of equal probability (i.e., unless we have sufficient reason to regard one possible case as more probable than another, we treat them as equally probable) in measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics with the Copenhagen interpretation. This turn from physics to language does not only realize theremarkable extensionof quantum mechanicsbut alsoestablish the method of science. Our study will be executed in the easy example of the Monty Hall problem. Although our argument is simple, we believe that it is worth pointing out the fact that the principle of equal probability can be, for the first time, clarified in measurement theory (based on the dualism) and not the conventional statistics (based on Kolmogorov’s probability theory).
文摘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.
文摘Recently we proposed “quantum language”, which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. And further we believe that quantum language is the only scientifically successful theory in dualistic idealism. If this turn is regarded as progress in the history of western philosophy (i.e., if “philosophical progress” is defined by “approaching to quantum language”), we should study the linguistic mind-body problem more than the epistemological mind-body problem. In this paper, we show that to solve the mind-body problem and to propose “measurement axiom” in quantum language are equivalent. Since our approach is always within dualistic idealism, we believe that our linguistic answer is the only true solution to the mind-body problem.
文摘The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.
文摘Bell’s inequality itself is usually considered to belong to mathematics and not quantum mechanics. We think that this is making our understanding of Bell’ theory be confused. Thus in this paper, contrary to Bell’s spirit (which inherits Einstein’s spirit), we try to discuss Bell’s inequality in the framework of quantum theory with the linguistic Copenhagen interpretation. And we clarify that the violation of Bell’s inequality (i.e., whether or not Bell’s inequality holds) does not depend on whether classical systems or quantum systems, but depend on whether a combined measurement exists or not. And further we conclude that our argument (based on the linguistic Copenhagen interpretation) should be regarded as a scientific representation of Bell’s philosophical argument (based on Einstein’s spirit).
文摘As the fundamental theory of quantum information science, recently I proposed the linguistic interpretation of quantum mechanics, which was characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse (or more generally, the post-measurement state) is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized. That is, the projection postulate is completely clarified in the linguistic interpretation.
