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)

In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular (...) lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory. (shrink)

Grodzinsky's general approach to the neuroscience of language is interesting, but the evidence currently available has problems with pragmatic infelicity in experiments involving Japanese scrambling and the interpretation of experimental results on Japanese indirect passives. I will suggest a more direct way of testing the Trace-Deletion Hypothesis (TDH).

The famous Japanese novelist offers his personal interpretation of a classic work on samurai ethics, everyday life, and spiritual salvation.

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 59-69 [Access article in PDF] Buddhist Views on Ritual Pactice Protestant Character of Modern Buddhist Movements Yukio MatsudoUniversity of HeidelbergWhat is the relationship between ritual and ethical activities in Nichiren Buddhism, as practiced in the Soka Gakkai (SG)? SG is a lay Buddhist organization which is, as such, involved extensively in secular affairs, specifically in the field of educational, cultural, social, and peace-promoting programs. (...) The question is, therefore, not at all whether there is a connection of religious practice and ethical activities. Rather it begs an explanation regarding its ideological background. In this respect a further reflection on a metareflection level would be useful to clarify the "modern" character of SG, which may be discussed in relation to Christian Protestantism since it has been regarded as a spiritual background for the formation of modern ethos such as individualism, egalitarianism, and social engagement. Thus, I will depict the fundamental feature of Nichiren Buddhism as "reformative Buddhism," which makes the practice of Buddhism congruent with "modern" understanding of religious roles in daily life as well as social engagement. On the other hand, I will also discuss some problems being inherent to the Western acculturation of the reformed and "engaged Buddhism." 1 The Ethical Activities of the SG in the World Ethical and Social Aspects of the Movement It is generally well known that the lay Buddhist organization, SG, as a whole has initiated wide and multifaceted activities even in an international level in order to transform its religious ideals into social reality, specifically in the field of educational, cultural, social, and peace-promoting programs. For this purpose it established educational institutes ranging from kindergartens to universities as well as research [End Page 59] institutes such as the Institute of Oriental Philosophy (founded 1961), the Boston Research Center for the 21st Century (founded 1993), the Toda Institute for Global Peace and Policy Research (founded 1996), and other centers for ecological researches. For promoting mutual respect and understanding through cultural expressions and exchanges several institutes have been established, like the Min-On Concert Association (founded 1963), the Tokyo Fuji Art Museum (founded 1991), and La Maison Littéraire de Victor Hugo in Bièvre, France (founded 1992). On a global level, its political involvement is, for a large part, situated as a NGO in the frame of the UNO and the UNESCO. With the help of the UNO, SG has organized all over the world expositions translating its concerns for peace, e.g., "Nuclear War: Threat to our World" and "War and Peace." With the Simon Wiesenthal Center it organized an exhibition "The Courage to Remember: Anne Frank and the Holocaust Exhibition." The issue of human rights is another of its major concerns. Commemorating the forty-fifth anniversary of the United Nations' adoption of the Universal Declaration of Human Rights, SG held an exhibition entitled "Toward the Century of Humanity: An Overview of Human Rights in Today's World" at the UN office in Geneva. Also, money received from fund-raising activities has been donated to the Office of the United Nations High Commissioner for Refugees and related agencies to provide medical supplies and food, and to support educational programs in the areas concerned. To expose the horrors of war, SG has also published life histories written by members about their sufferings in war: "Women against War," "Cries for Peace," and "Peace is our Duty." Segmental Differentiation of Organizational Structure To meet the requirements of functional differentiation of today's modern societal life SG is organized in a segmental and hierarchical structure. The basic structure is the regional units, organized in a hierarchical model, and all members are integrated "in each group" in their residence area. At the same time each member belongs to a specific "division" which is organized according to gender, age, and occupation. There are the four divisions of men, women, young men, and young women. Additionally there are divisions for school boys and girls, university students, as well as divisions according to occupation such as artists, lawyers, medical doctors, academics, and so on. These divisional differentiations reflect the need... (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)

Free will in intentional consciousness is exposed to skeptics since it was found that subconscious neural activities, what is called readiness potential, precedes the intention to an action. The question of whether free will is an authentic illusion has been argued not only in psychology but physics and philosophy. Most of scientists, however, think that the intentional consciousness who believes to have his/her own free will, is determined by readiness potential in advance, and that free will cannot coexist with determinism. (...) We here point out that knowing to be determined in advance cannot be verified till local event at a local site can be known from a different local site without disturbing the event. That is the assumption of locality. We here show that determinism, free will and locality are three essential elements in consciousness, and show that they constitute trilemma. The fact that one of three elements must be abandoned can lead to three types of consciousness. Absence of free will can constitute type I consciousness which is consistent with symptoms in autism spectrum disorder such as weakened theory of mind. Absence of determinism can constitute type II consciousness which is consistent with symptoms in schizophrenia such as thought insertion, self-other integration. Absence of locality can constitute type III consciousness which is consistent with typical people. We can find the entanglement of intentional consciousness with unconsciousness including readiness potential only in type III consciousness. Finally, we show that sense of agency and free will cannot be established until consciousness as an entanglement is implemented. (shrink)

Floridi’s infosphere consisting of informational reality is estimated and delineated by introducing the new notion of Typ-Ken, an undifferentiated amalgam of type and token that can be expressed as either type or token dependent on contingent ontological commitment. First, we elaborate Floridi’s system, level of abstraction (LoA), model, and structure scheme, which is proposed to reconcile ontic with epistemic structural reality, and obtain the duality of type and token inherited in the relationship between LoA and model. While we focus on (...) the ontological commitment that can negotiate and emphasize the discrepancy between type and token, we show that most research focusing on different hierarchical layers (type and token) has converged onto the flattened perspective of type and token to clarify the role of ontological commitment. We propose the idea of Typ-Ken to avoid this flattening. In addition, we elaborate Taddeo and Floridi’s criticism of approaches to the symbol grounding problem and show that their criticism based on the zero semantical commitment condition is specific to the agents affected by the flattening. We then take bird flocks as a metaphor for the living infosphere as if it had one mind. The knowledge recently yielded by image analysis indicates that it is difficult for previous flock models based on agents equipped with the flattening of local (token) and global (type) to show the special feature of a flock of the scale-free proportion (SFP). We show here that agents based on the Typ-Ken can reveal the SFP, which is the essential characteristic of the living infosphere. In other words, Typ-Ken is an expression for informational reality (LoA and model with ontological commitment) that can reveal seamless local and global interactions in the functioning of a flock or infosphere. (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)

Western sociology of the body, despite its attempt to create a somatic approach to human existence, inevitably shares many of the rationalistic and Cartesian assumptions of wider Western sociology. A contrasting, and in many ways radically different approach is that found in both classical and contemporary Japanese thought. In this article two major contemporary Japanese theorists of the body - Ichikawa Hiroshi and Yuasa Yasuo - are introduced and their work examined as distinctive, and in the West virtually unknown, contributions (...) to body analysis. Their views are briefly contrasted with some of the major themes of Western, and in particular British, sociology of the body and the implications of their work for future investigation of the human body are sketched out. (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)

The emotions that people experience in day-to-day social situations are often mixed emotions. Although autobiographical recall is useful as an emotion induction procedure, it often involves recalling memories associated with a specific discrete emotion. However, real-life emotions occur freely and spontaneously, without such constraints. To understand real-life emotions, the present study examined characteristics of emotions that were elicited by recalling “stressful interpersonal events in daily life” without the targeted evocation of a specific discrete emotion. Assuming generation of mixed and complex (...) emotions, emotional groups with relatively strong correlation of multiple emotions according to surprise, fear, anger, disgust, sadness, and happiness were expected. Seventy-two university students participated in the study. In the emotion induction procedure, participants freely recalled memories as per the instructions on a monitor, and then responded silently to a series of questions concerning any one recalled incident. Assessments of emotional states using emotion scales and another item indicated that validated emotional changes had occurred during the task. Inter-correlations between six emotions demonstrated an emotional group consisting of disgust and anger, which frequently occur as negative interpersonal feelings, and that of fear and sadness. This indicated generation of mixed and complex emotions as experienced in social life. Future studies concerning relationships between these emotions and other factors, including neurophysiological responses, may facilitate further understanding about relationships between mental and physiological processes occurring in daily life. (shrink)

A modified form of Mach's principle is proposed, and its consequences are discussed.