Abstract:
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.

Abstract:
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.

Abstract:
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”.

Abstract:
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.

Abstract:
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).

Abstract:
Rural communities are disappearing in Japan due to aging, depopulation, and changes in lifestyles. Recently, outsiders such as immigrants, volunteers, and tourists cooperate with residents to revive and maintain rural communities. This paper uses my fieldwork in the rural areas of Takachiho, where the Japanese traditional dance kagura is well-known, to consider the possibility that residents and tourists cooperatively create shared communities. Actually, an increasing number of tourists visit Takachiho to see kagura. Consequently, some dancers miss “classical” kagura, which involved almost exclusively local residents in intimate interactions. Nonetheless, many dancers welcome the influx of tourists and its stimulation of community festivals. Some tourists are attracted to kagura at community festivals, and some dancers and tourists have tried to forge bridges between their groups to create a shared community. The existence of kagura becomes an important common symbol that connects members of local communities.

Abstract:
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.

Abstract:
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.

Abstract:
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).

Abstract:
Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. We believe that quantum language is not only the scientific final goal of dualistic idealism but also the language in which science is written. Hence there is a reason to want to clarify, from the quantum linguistic point of view, the following problems: “brain in a vat argument”, “the Cogito proposition”, “five-minute hypothesis”, “only the present exists”, “Copernican revolution”, “McTaggart’s paradox”, and so on. In this paper, these will be discussed in quantum language. And we clarify that these are not propositions in quantum language. That is, these are metaphysical and not scientific. Also, we emphasize that Leibniz’s relationalism in Leibniz-Clarke correspondence should be regarded as one of the most important parts of the linguistic Copenhagen interpretation of quantum mechanics.