In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary von Neumann algebra. (...) A transfer principle is established that enables us to transfer theorems of ZFC to their quantum counterparts holding in the model. The set of real numbers in the model is shown to be in one-to-one correspondence with the set of self-adjoint operators affiliated with the von Neumann algebra generated by the logic. Despite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model. It is also shown that any observational proposition in quantum mechanics can be represented by a corresponding statement for real numbers in the model with the truth value consistent with the standard formulation of quantum mechanics, and that the equality relation between two real numbers in the model is equivalent with the notion of perfect correlation between corresponding observables (self-adjoint operators) in quantum mechanics. The paper is concluded with some remarks on the relevance to quantum set theory of the choice of the implication connective in quantum logic. (shrink)

This monograph is the first to analyze Julius Caesar Scaliger's Exotericae Exercitationes(1557). In order to make this late-Renaissance work accessible to modern readers, Kuni Sakamoto conducted a detailed textual analysis and revealed the basic tenets of Scaliger's philosophy.

清朝末から中華人民共和国建国までの世界的激動期、中国の知識人は儒教的世界観の更新に立ち会い、西洋の知と格闘した。社会進化論や立憲思想の衝撃はナショナリズムと革命思想に展開し、雑誌メディアには生命論から 民族論まで様々な論争と漫画表現が花開く。貴重な資料と最新の研究から読み解く労作。.

Pierre Gassendi is widely known as a reviver of Epicurean atomism. But he was also regarded as an accomplished astronomer by his contemporaries. Along with the life-long observational pursuits, Gassendi developed his theories of the causes underlying celestial motions. In elaborating them, he absorbed seveal ideas coming from the astronomy of Johannes Kepler. Moreover, Gassendi went further to incorporate some theological principles from the Keplerian cosmology, especially the idea that God is a Geometer. The present paper thus explores Kepler's influence (...) on the philosophy of Gassendi in both astronomical and theological spheres. (shrink)

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum (...) logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context. (shrink)

A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. This provides a new framework of nonstandard analysis with which methods of forcing are incorporated naturally. Various new principles in this framework are provided together with the following applications: An example of an 1-saturated Boolean ultrapower of the real number field which is not Scott complete is constructed. Infinitesimal analysis based on the generic extension of the hyperreal numbers is provided, and the hull completeness theorem (...) and the Loeb measure construction are extended to objects in the generic extension of the internal universe. The reduction theory of the Boolean-valued complex numbers are developed as a prototype of the applications to the topological reduction theory of Boolean sheaves or operator algebras. (shrink)

Quantum set theory and topos quantum theory are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding QM by reformulating parts of the theory inside of nonclassical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, (...) ‘Q-worlds’. Here, we provide a unifying framework that allows us to better understand the relationship between different Q-worlds, and define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches. Along the way, we develop a novel connection to paraconsistent logic and introduce a new class of structures that have significant implications for recent work on paraconsistent set theory. (shrink)

An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to examples of Boolean (...) ultrapowers of the real line which are not Scott complete. (shrink)

Halvorson and Clifton have given a mathematical reconstruction of Bohr’s reply to Einstein, Podolsky and Rosen, and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr’s reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, (...) to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr’s requirements of classicality and objectivity, in a general formulation of algebraic quantum theory. (shrink)

Halvorson and Clifton have given a mathematical reconstruction of Bohr’s reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr’s reply. In the present paper, we generalize the above consistency theorem, with a rather elementary (...) proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr’s requirements of classicality and objectivity, in a general formulation of algebraic quantum theory. (shrink)

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for (...) bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws. (shrink)

In this article, we address the problem of how people understand predicative metaphors such as “The rumor flew through the office,” and argue that predicative metaphors are understood as indirect (or two-stage) categorizations. In the indirect categorization process, the verb (e.g., fly) of a predicative metaphor evokes an intermediate entity, which in turn evokes a metaphoric category of actions or states (e.g., “to spread rapidly and soon disappear”) to be attributed to the target noun (e.g., rumor), rather than directly evoking (...) a metaphoric category as argued by CitationGlucksberg's (2001) categorization theory. We test our argument using two experiments, namely, offline comprehension and online priming. The offline comprehension experiment showed that interpretation of predicative metaphors had greater overlap with words indirectly associated with the verb than those directly associated with the verb. The online priming experiment demonstrated that indirectly associated words were activated during predicative metaphor comprehension, but directly associated words were not. These results provide convergent evidence for our argument, and thus the psychological validity of two-stage categorization as a process of predicative metaphor comprehension was confirmed. (shrink)

Background: Advocacy is an important role of psychiatric nurses because their patients are ethically, socially, and legally vulnerable. This study of Japanese expert psychiatric nurses’ judgments of interventions for patient advocacy will show effective strategies for ethical nursing practice and their relationship with Japanese culture. Objectives: This article explores Japanese psychiatric nurses’ decision to intervene as a patient advocate and examine their ethical, cultural, and social implications. Research design: Using semi-structured interviews verbatim, themes of the problems that required interventions were (...) inductively summarized by a qualitative analysis and their contexts and nursing judgments were examined. Participants and research context: The participants were 21 nurses with 5 or more years of experience in psychiatric nursing. Ethical considerations: The research was approved by Institutional Review Board of research site and study facilities. The participants gave written informed consent. Findings: Analysis of 45 cases showed that nurses decided to intervene when surrounding people’s opinions impeded patients’ safety, healthcare professionals’ policies impeded patients’ decision-making, own violent behaviors impeded treatment and welfare services for patients, own or families’ low acceptance of illness impeded patients’ self-actualization, inappropriate treatment or care impeded patients’ liberty, and their families abused patients’ property. Discussion: To solve conflicts between patients and their surrounding people, the nurses sought reconciliation between them, which is in accordance with Japanese cultural norms respecting harmony. When necessary, however, they protected patients’ rights against cultural norms. Therefore, their judgments cannot be explained by cultural norms alone. Conclusion: The findings indicate that the nurses’ judgments were based on respect for patients’ rights apart from cultural norms, and they first sought solutions fitting the cultural norms before other solutions. This seems to be an ethical, effective strategy if advocates know the culture in depth. (shrink)

This chapter purports to give empirical feedback on impartial reasoning to justice by using online survey experiments. More precisely, the study focuses on whether and how the different conceptions of the veil of ignorance and John Rawls’s method of reflective equilibrium affect real people’s impartial reasoning to justice. The findings show that, while ordinary people support impartial reasoning to the difference principle (maximin), their endorsement of it echoes neither John Harsanyi’s nor Rawls’s reasoning. The results illuminate that findings in human (...) psychology, such as the principles of loss aversion and “perceived luckiness,” cannot be dismissed for denoting the relevant impartial reasoning to justice. (shrink)

In this paper, we discuss uniform versions of some axioms of second order arithmetic in the context of higher order arithmetic. We prove that uniform versions of weak weak König's lemma WWKL and Σ01 separation are equivalent to over a suitable base theory of higher order arithmetic, where is the assertion that there exists Φ2 such that Φf1 = 0 if and only if ∃x0 for all f. We also prove that uniform versions of some well-known theorems are equivalent to (...) or the axiom of the existence of the Suslin operator. (shrink)

Self-determination is a central concept in the field of bioethics and the most critical decision among the myriad of decisions concerning medical care is the decision to choose to die; “self-determination of death.” The purpose of this paper is to clarify the basic positions on self-determination of death held by present Japanese people and we tentatively sorted these positions into 10 arguments. We discuss the problems and implications of these positions revealed within our present review and conclude that a society (...) needs to deny unnecessary intrusion and tolerance for different views might be a keyword in our oncoming society. (shrink)

Daily rhythms are a ubiquitous feature of living systems. Generally, these rhythms are not just passive consequences of cyclic fluctuations in the environment, but instead originate within the organism. In mammals, including humans, the master pacemaker controlling 24‐hour rhythms is localized in the suprachiasmatic nuclei of the hypothalamus. This circadian clock is responsible for the temporal organization of a wide variety of functions, ranging from sleep and food intake, to physiological measures such as body temperature, heart rate and hormone release. (...) The retinal circadian clock was the first extra‐SCN circadian oscillator to be discovered in mammals and several studies have now demonstrated that many of the physiological, cellular and molecular rhythms that are present within the retina are under the control of a retinal circadian clock, or more likely a network of hierarchically organized circadian clocks that are present within this tissue. BioEssays 30:624–633, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

The discipline of nursing has long maintained that is has a unique contribution to make within the health care arena. This assertion of uniqueness lies in great part in the discipline's claim to a distinct body of knowledge. Nursing knowledge is characterized by diverse and multiple forms of knowing and underpins the work of all nurses, regardless of field of practice. Unfortunately, it has been challenging for the discipline to take full ownership of its epistemological diversity, largely due to factors (...) such as competing worldviews, and ideological and binary positioning. A philosophical middle ground stance is proposed as a way for the discipline to contemplate, discuss and develop nursing knowledge; a middle space that provides the freedom to consider competing worldviews while still allowing for the discipline to fully express itself in all of its epistemological diversity. In being able to enact its multiple forms of knowledge in a creative and open space that is open to different ideas and worldviews, not only can nursing take full ownership of its practice and its unique knowledge, it can also demonstrate how best to navigate an increasingly polarized world. In a world that is increasingly fixated on binary solutions and dualistic points of view, it is time for nursing to celebrate its epistemological diversity. (shrink)

In this paper, we show within ${\mathsf{RCA}_0}$ that both the Jordan curve theorem and the Schönflies theorem are equivalent to weak König’s lemma. Within ${\mathsf {WKL}_0}$ , we prove the Jordan curve theorem using an argument of non-standard analysis based on the fact that every countable non-standard model of ${\mathsf {WKL}_0}$ has a proper initial part that is isomorphic to itself (Tanaka in Math Logic Q 43:396–400, 1997).