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)

Exploring Renaissance humanists’ debates on matter, life and the soul, this volume addresses the contribution of humanist culture to the evolution of early modern natural philosophy so as to shed light on the medical context of the ...

This volume brings Bergson's key ideas from Matter and Memory into dialogue with contemporary themes on memory and time in science, across analytic and continental philosophy. Focusing specifically on the application of Bergson's ideas to cognitive science, the circuit between perception and memory receives full explication in 15 different essays. By re-reading Bergson through a cognitive lens, the essays provide a series of alternative analytic interpretations to the standard continental approach to Bergson's oeuvre, without fully discounting either approach. The relevance (...) of philosophies of mind and memory sit alongside the role of a metaphysics of time in exploring connections to psychology, biology, and physics. This eclecticism includes an exciting focus on numerous topics that are not given sufficient attention in extant studies of Bergson, including the precise nature of his ideas on dualism, memory, and ecological theories of perception, especially in relation to his contemporaries. Led by leading Bergson scholars from France and Japan, this book maps the rich terrain of Bergson's contemporary relevance alongside the historical context of his ideas. (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 (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)

The neuromodulatory effects of brain stimulation therapies notably involving repetitive transcranial magnetic stimulation on nocturnal sleep, which is critically disturbed in major depression and other neuropsychiatric disorders, remain largely undetermined. We have previously reported in major depression patients that prefrontal rTMS sessions enhanced their slow wave activity power, but not their sigma power which is related to sleep spindle activity, for electrodes located nearby the stimulation site. In the present study, we focused on measuring the spindle density to investigate cumulative (...) effects of prefrontal rTMS sessions on the sleep spindle activity. Fourteen male inpatients diagnosed with medication-resistant unipolar or bipolar depression were recruited and subjected to 10 daily rTMS sessions targeting the left dorsolateral prefrontal cortex. All-night polysomnography data was acquired at four time points: Adaptation, Baseline, Post-1, and Post-2. Clinical and cognitive evaluations were longitudinally performed at Baseline, Post-1, and Post-2 time points to explore associations with the spindle density changes. The PSG data from 12 of 14 patients was analyzed to identify sleep spindles across the sleep stages II–IV at four electrode sites: F3, F4, P3, and P4. Statistical analysis by two-way ANOVA revealed that spindle density at F3 increased at Post-1 but decreased at Post-2 time points. Moreover, the local and transient increase of spindle density at F3 was associated with the previously reported SWA power increase at F3, possibly reflecting a shared mechanism of thalamocortical synchronization locally enhanced by diurnal prefrontal rTMS sessions. Clinical and cognitive correlations were not observed in this dataset. These findings suggest that diurnal rTMS sessions transiently modulate nocturnal sleep spindle activity at the stimulation site, although clinical and cognitive effects of the local changes warrant further investigation. (shrink)

In his embryological treatise De plastica seminis facultate , Jacob Schegk , professor of philosophy and medicine at the University of Tübingen, developed, through a unique interpretation of the Aristotelian embryology, a theory of the "plastic faculty" , whose origin lay in the Galenic idea of the formative power. The present study analyses the precise nature of Schegk's theory, by setting it in its historical and intellectual context. It will also discuss the hitherto unappreciated Neoplatonic dimension of Schegk's notion of (...) the soul's vehicle. (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)

Inspired by Christian Platonism as developed in the late fifteenth-century Florentine milieu, the French physician Jean Fernel proposed a particular interpretation of Galen in a medico-philosophical work entitled On the Hidden Causes of Things . With this interpretation, he responded to the serious and urgent need for a reconciliation of the newly reconstituted Galen of Renaissance humanism with Christian faith. The present study examines Fernel's strategy and method in constructing this singular Galenic body of doctrine, special attention being given to (...) the roles attributed to the Creator, the formative force, and the soul. Subsequently, an analysis of the notions of spirit and of its innate heat as indispensable instruments of Fernel's physiology will uncover the very target of his criticism of materialism. (shrink)

One of the most striking features of Giordano Bruno’s philosophy is the marriage of universal animation with atomism. This unusual combination produced an extraordinary image of the universe, which was governed by the World-Soul and its universal intellect along with an infinite number of living atoms or corpuscles, animated by their internal spiritual principle. After examining Bruno’s principal arguments on the World-Soul, universal animation and living atoms or corpuscles, this article explores two possible sources among the works of his near-contemporaries. (...) The first author, Agostino Steuco, tried to reconcile the doctrine of the World-Soul with Christianity, integrating the idea of Anaxagoras on the cosmic mind as the demiurgic agent of the universe. The second figure, Jacob Schegk, further elaborated his unusual atomistic or corpuscular reinterpretation of this Presocratic philosopher’s ideas. (shrink)

Inspired by Christian Platonism as developed in the late fifteenth-century Florentine milieu, the French physician Jean Fernel proposed a particular interpretation of Galen in a medico-philosophical work entitled On the Hidden Causes of Things. With this interpretation, he responded to the serious and urgent need for a reconciliation of the newly reconstituted Galen of Renaissance humanism with Christian faith. The present study examines Fernel's strategy and method in constructing this singular Galenic body of doctrine, special attention being given to the (...) roles attributed to the Creator, the formative force, and the soul. Subsequently, an analysis of the notions of spirit and of its innate heat as indispensable instruments of Fernel's physiology will uncover the very target of his criticism of materialism. (shrink)

The treatise On Formative Power of Ferrara's emblematic medical humanist, Nicolò Leoniceno, is the one of the first embryological monographs of the Renaissance. It shows, at the same time, the continuity of medieval Arabo-Latin tradition and the new elements brought by Renaissance medical humanism, namely through the use of the ancient Greek commentators of Aristotle like Simplicius. Thus this treatise stands at the crossroad of these two currents. The present study analyses the range of Leoniceno's philosophical discussion, determines its exact (...) sources and brings to light premises for the early modern development of the concept of formative force, which will end up in the theory of "plastic nature" at the heart of the Scientific Revolution. (shrink)

Organogenesis and metamorphosis require the intricate orchestration of multiple types of cellular interactions and signaling pathways. Glutamate (Glu) is an excitatory extracellular signaling molecule in the nervous system, while Ca2+ is a major intracellular signaling molecule. The first Glu receptors to be cloned are Ca2+‐permeable receptors in mammalian brains. Although recent studies have focused on Glu signaling in synaptic mechanisms of the mammalian central nervous system, it is unclear how this signaling functions in development. Our recent article demonstrated that Ca2+‐permeable (...) AMPA‐type Glu receptors (GluAs) are essential for formation of a photosensitive organ, development of some neurons, and metamorphosis, including tail absorption and body axis rotation, in ascidian embryos. Based on findings in these embryos and mammalian brains, we formed several hypotheses regarding the evolution of GluAs, the non‐synaptic function of Glu, the origin of GluA‐positive neurons, and the neuronal network that controls metamorphosis in ascidians. (shrink)

Summary The famous Jesuit father Athanasius Kircher (1602?1680) tried to interpret the Creation of the world and to explain the origin of life in the last book of his geocosmic encyclopedia, Mundus subterraneus (Amsterdam, 1664?1665). His interpretation largely depended on the ?concept of seeds? which was derived from the tradition of Renaissance ?chymical? (chemical and alchemical) philosophy. The impact of Paracelsianism on his vision of the world is also undeniable. Through this undertaking, Kircher namely developed a corpuscular theory for the (...) spontaneous generation of living beings. The present study examines this theory and its relationship with Kircher's chymical interpretation of the Creation in order to place it in its own intellectual and historical context and will uncover one of its most important sources. (shrink)

The treatise On Formative Power of Ferrara's emblematic medical humanist, Nicolò Leoniceno , is the one of the first embryological monographs of the Renaissance. It shows, at the same time, the continuity of medieval Arabo-Latin tradition and the new elements brought by Renaissance medical humanism, namely through the use of the ancient Greek commentators of Aristotle like Simplicius. Thus this treatise stands at the crossroad of these two currents. The present study analyses the range of Leoniceno's philosophical discussion, determines its (...) exact sources and brings to light premises for the early modern development of the concept of formative force, which will end up in the theory of "plastic nature" at the heart of the Scientific Revolution. (shrink)

福沢諭吉と並び立つ明治初期の大知識人中村正直。その生涯と思想を丹念に辿りつつ、日本の近代化に与えた影響を浮き彫りにする。.