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)

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)

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)

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)

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)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...) of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of logic to be formal, (...) it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...) validity of inferences. In order to make sense of this claim, I will appeal to the Madhyamaka Buddhist philosopher Candrakīrti. I will then pose a problem for Priest’s anti-exceptionalism. Finally, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. (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)

Scientific progress in recent neurofeedback research may bring about a new type of moral neuroenhancement, namely, neurofeedback-based moral enhancement; however, this has yet to be examined thoroughly. This paper presents an ethical analysis of the possibility of neurofeedback-based moral enhancement and demonstrates that this type of moral enhancement sheds new light on the moral enhancement debate. First, I survey this debate and extract the typical structural flow of its arguments. Second, by applying structure to the case of neurofeedback-based moral enhancement, (...) I examine the ethical, legal, and social issues to show that this technique is unique and traditionalist, which makes it compatible with almost all our conservative notions, so that it, accordingly, can be seen as an ethically acceptable option. Third, by rejecting the premise in the moral enhancement debate that bio/neuro-enhancement has its unique ELSI that traditional methods would never create, I demonstrate that, by virtue of its traditional or conservative features, neurofeedback-based moral enhancement can be incorporated into the traditional moral education network. Finally, I conclude that, being a part of the traditional moral education network, neurofeedback-based moral enhancement can be a unique and ethically acceptable option of moral neuroenhancement. (shrink)

Neuroscientific claims have a significant impact on traditional philosophy. This essay, focusing on the field of moral neuroscience, discusses how and why philosophy can contribute to neuroscientific progress. First, viewing the interactions between moral neuroscience and moral philosophy, it becomes clear that moral philosophy can and does contribute to moral neuroscience in two ways: as explanandum and as explanans. Next, it is shown that moral philosophy is well suited to contribute to moral neuroscience in both of these two ways in (...) the context of the problem of ecological validity. Philosophy can play the role of an agent for ecological validity, since traditional philosophy shapes and reflects part of our social reality. Finally, based on these arguments, I tentatively sketch how a Kantian account of moral incentive can play this role. (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 1A:7 of the Mengzi, Mengzi tries to convince King Xuan of Qi that he is a “true” king. As a reading of Mengzi’s reasoning involved in his attempt at persuasion, David Nivison advances an inferential view, according to which Mengzi’s persuasion involves inferences. In this paper, I consider the assumptions underlying the objections raised against Nivison’s inferential view. I argue that these objections assume a contemporary Western view about the nature of logic and inferences. I propose an alternative characterisation (...) of the relevant sense of inference that, I believe, is more sensitive to the classical Chinese philosophical context and argue that certain insights can be derived from reading Mengzi in light of this alternative characterization of inferences. (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)

Feinberg and Mallatt, in their presentation of neurobiological naturalism, have suggested that visual consciousness was acquired by early vertebrates and inherited by a wide range of descendants, and that its neural basis has shifted to nonhomologous nervous structures during evolution. However, their evolutionary scenario of visual consciousness relies on the assumption that visual consciousness is closely linked with survival, which is not commonly accepted in current consciousness research. We suggest an alternative idea that visual consciousness is linked to a specific (...) class of agency, consequently justifying their phylogenetic claim. We also examine the implication of their phylogenetic claim: visual consciousness is homologous across vertebrates, but its neural basis is not. This apparent incongruence illustrates a general phenomenon of homology, and that the resulting hierarchical view of visual consciousness and its neural basis can be straightforwardly accommodated by neurobiological naturalism. Throughout these discussions, we aim to address the potential theoretical issues in neurobiological naturalism and refine the picture illustrated by Feinberg and Mallatt regarding phylogenetic distribution and trajectories of visual consciousness. (shrink)

Some skeptics question the very possibility of moral bioenhancement by arguing that if we lack a widely acceptable notion of morality, we will not be able to accept the use of a biotechnological technique as a tool for moral bioenhancement. I will examine this skepticism and argue that the assessment of moral bioenhancement does not require such a notion of morality. In particular, I will demonstrate that this skepticism can be neutralized in the case of recent neurofeedback techniques. This goal (...) will be accomplished in four steps. First, I will draw an outline of the skepticism against the possibility of moral bioenhancement and point out that a long-lasting dispute among moral philosophers nourishes this skepticism. Second, I will survey recent neurofeedback techniques and outline their three features: the variety of the target human faculties, such as emotion, cognition, and behavior; the flexibility or personalizability of the target brain state; and the nonclinical application of neurofeedback techniques. Third, I will argue that, by virtue of these three unique features, neurofeedback techniques can be a tool for moral bioenhancement without adopting any specific notion of morality. Fourth, I will examine the advantages and threats that neurofeedback-based moral enhancement may have. Finally, I will conclude that neurofeedback-based moral enhancement can become a new and promising tool for moral bioenhancement and requires further ethical investigations on its unique features. (shrink)

The model of mind and body in Tibetan medical practice is based on Buddhist theory, and is neither dualistic in a Cartesian sense, nor monistic. Rather, it represents a genuine alternative to these positions by presenting mind/body interaction as a dynamic process that is situated within the context of the individual’s relationships with others and the environment. Due to the distinctiveness, yet interdependence, of mind and body, the physician’s task is to heal the patient’s mind (blo-gso) as well as body. (...) This in turn emphasizes the central importance of ‘compassion’ in the physician/patient relationship. This article investigates how Tibetan medical practitioners understand and enact the mind/ body and physician/patient relationships, and how this relates to theoretical explications of these relationships in Tibetan medical and Buddhist teachings. Furthermore, Tibetan medicine provides an interesting model for comparison with embodied theories of cognition, which see consciousness, the body and its environment as integral parts of a complex, dynamical cognitive system. (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)

Long time delay before lasing in a II-VI laser diode has been observed. Due to this delay, a nominal threshold current increases as the width of applied current pulse becomes shorter. This delay is attributed to the internal Q switching caused by the balance of injected carriers, temperature rise and gain-guiding. By fitting the calculated data to the experimental ones, rates of refractive index change with carrier concentration and with temperature have been estimated.

Involuntary eye movement during gaze fixation, referred to as fixational eye movement, consists of two types of components: a Brownian motion like component called drifts-tremor and a ballistic component called microsaccade with a mean saccadic amplitude of about 0.3° and a mean inter-MS interval of about 0.5 s. During GZ fixation in healthy people in an eccentric position, typically with an eccentricity more than 30°, eyes exhibit oscillatory movements alternating between centripetal drift and centrifugal saccade with a mean saccadic amplitude (...) of about 1° and a period in the range of 0.5–1.0 s, which has been known as the physiological gaze-evoked nystagmus. Here, we designed a simple experimental paradigm of GZ fixation on a target shifted horizontally from the front-facing position with fewer eccentricities. We found a clear tendency of centripetal DRT and centrifugal MS as in GEN, but with more stochasticity and with slower drift velocity compared to GEN, even during FEM at GZ positions with small eccentricities. Our results showed that the target shift-dependent balance between DRT and MS achieves the GZ bounded around each of the given targets. In other words, GZ relaxes slowly with the centripetal DRT toward the front-facing position during inter-MS intervals, as if there always exists a quasi-stable equilibrium posture in the front-facing position, and MS actions pull GZ intermittently back to the target position in the opposite direction to DRT. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...) and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

Buddhist philosophers have developed a rich tradition of logic. Buddhist material on logic that forms the Buddhist tradition of logic, however, is hardly discussed or even known. This article presents some of that material in a manner that is accessible to contemporary logicians and philosophers of logic and sets agendas for global philosophy of logic.

In one of his key texts, the Mūlamadhyamakakārikā, Nāgārjuna famously sets out to refute the ontology of essence.1 He presents numerous arguments to show that things don’t exist essentially—that is, that things are empty of essence or inherent existence. The doctrine of emptiness has been variously understood by traditional and contemporary commentators. Most radical is the recent interpretation presented by Garfield and Priest. They have rationally reconstructed Nāgārjuna’s doctrine of emptiness as an endorsement of the contradictory nature of reality. According (...) to them, Nāgārjuna can be seen to be arguing that the way in which things exist in reality and what we can truly say about them must be... (shrink)

Some philosophers of mind, cognitive scientists, phenomenologists as well as Buddhist philosophers have claimed that an awareness of an object is not just an experience of that object but also involves self-awareness. It is sometimes argued that being aware of an object without being aware of oneself is pathological. As anyone who has been involved in martial arts, as well as any sports requiring quick responses such as cricket and tennis, can testify, however, awareness of the self at the time (...) of acting becomes problematic: you would not be able to respond to the slight movement of your opponent if you were aware of yourself responding to it. This suggests that it must be possible for us to be aware without being aware of ourselves. The aim of this paper is to clarify the notion of self-awareness and its relation to the self by investigating the phenomenology of the martial artist who is ‘in the act’. I shall argue that we can make sense of self-awareness without invoking awareness of oneself. (shrink)

In one of his influential works ‘One the Very Idea of a Conceptual Scheme’, Donald Davidson argues against conceptual relativism. According to Davidson, ‘we could not be in a position to judge that others had concepts or beliefs radically different from our own’. Davidson’s thesis seems to have a consequence for comparative philosophy, particularly in a comparative study between Chinese and Western traditions of philosophy which are often considered to differ conceptually. If Davidson is correct, it is not clear whether (...) or not we can have insight into how and why concepts differ between these traditions. -/- In this paper, I philosophically reflect on Davidson’s argument against conceptual relativism. Though this paper retains the backbone of his argument, I reject Davidson’s thesis that different ways of conceptualisation cannot be compared. I do this through a discussion of the comparative studies conducted by David Hall and Roger Ames. In conclusion, I self-reflectively examine the nature of the demarcation between different traditions of philosophy and show how the activities of comparative philosophy can proceed. (shrink)

In his book review of Graham Priest's The Fifth Corner of Four, Mark Siderits, while criticising Priest's philology, suggests that Priest's work is 'of considerable interest' for two reasons. First, 'when two independent traditions use similar methods to work on similar issues, it is always possible that one may have hit on approaches that the other missed'. Second, 'the decentering that can be induced by looking at another tradition may trigger fresh insights, even if those insights are not ones that (...) were actually developed by the tradition marked 'other''. The main task of this paper is to unpack Siderits' thought. By analysing some of Priest's work, I will suggest a decentering that must have taken place in China when Buddhism was 'exported to China in Buddhist shipping containers'. For anyone familiar with the forms of Buddhist philosophy developed in India, various forms of Chinese Buddhism can often look strange. Some ideas that were debated and defended by Indian Buddhists do not appear anywhere in Chinese Buddhism and some assumptions have been quietly added to Buddhism by Chinese Buddhists. By showing that Priest's work brings out the 'innovation' that Chinese Buddhists gave to Buddhism, I will suggest that it is this decentering that Siderits suggests Priest makes use of. (shrink)

Nearly a decade has past since Grove gave a semantics for the AGM postulates. The semantics, called sphere semantics, provided a new perspective of the area of study, and has been widely used in the context of theory or belief change. However, the soundness proof that Grove gives in his paper contains an error. In this note, we will point this out and give two ways of repairing it.

CETTE THESE SE VEUT UNE CONTRIBUTION A LA COMPREHENSION DE LA DERNIERE PHILOSOPHIE DE MERLEAU-PONTY, EN PRENANT COMME FIL CONDUCTEUR LA NOTION D'INSTITUTION. NOUS ESSAYONS D'ABORD DE DELIMITER LE CHAMP D'INTERROGATION DE LA NOTION D'INSTITUTION, TELLE QU'ELLE EST PRESENTEE DANS SES DEUX PREMIERS OUVRAGES. DEUXIEMEMENT, LA DESCRIPTION DE QUATRE ORDRES DE L'INSTITUTION SYMBOLIQUE (ANIMALITE ET VIE; STYLE ARTISTIQUE; LANGUE ET IDEALITE; SYSTEME SOCIAL) QUE NOUS NOUS EFFORCONS DE RECONSTITUER A L'AIDE DES MANUSCRITS INEDITS CONDUIT A DEVOILER LES MOTIVATIONS DE LA (...) RADICALISATION DE LA QUESTION PHENOMENOLOGIQUE. ENFIN, NOTRE PROBLEMATIQUE SE PRESENTE DANS LE DERNIER OUVRAGE COMME UN PROJET DE L'INSTITUTION DE LA PHILOSOPHIE ELLE-MEME. CE PROJET A SA PORTEE HISTORIQUE, SE PROPOSANT DE METTRE EN EVIDENCE LES MOMENTS FECONDS DANS L'HISTOIRE DE LA PHILOSOPHIE, DE MANIERE A LEVER LES DIFFICULTES DE L'ONTOLOGIE ACTUELLE. (shrink)

The paper is concerned with John Searle’s famous Chinese room argument. Despite being objected to by some, Searle’s Chinese room argument appears very appealing. This is because Searle’s argument is based on an intuition about the mind that ‘we’ all seem to share. Ironically, however, Chinese philosophers don’t seem to share this same intuition. The paper begins by first analysing Searle’s Chinee room argument. It then introduces what can be seen as the (implicit) Chinese view of the mind. Lastly, it (...) demonstrates a conceptual difference between Chinese and Western philosophy with respect to the notion of mind. Thus, it is shown that one must carefully attend to the presuppositions underlying Chinese philosophising in interpreting Chinese philosophers. (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)