Gentzen's three consistency proofs for elementary number theory have a common aim that originates from Hilbert's Program, namely, the aim to justify the application of classical reasoning to quantified propositions in elementary number theory. In addition to this common aim, Gentzen gave a “finitist” interpretation to every number-theoretic proposition with his 1935 and 1936 consistency proofs. In the present paper, we investigate the relationship of this interpretation with intuitionism in terms of the debate between the Hilbert School and the Brouwer (...) School over the significance of consistency proofs. First, we argue that the interpretation had the role of responding to a Brouwer-style objection against the significance of consistency proofs. Second, we propose a way of understanding Gentzen's response to this objection from an intuitionist perspective. (shrink)
Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard’s phase semantics so that it became phase semantics for proof-terms, i.e., lambda-terms. They formulated phase semantics for proof-terms of Laird’s dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird’s calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this paper, (...) we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying Tait-Girard’s saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. (shrink)
The scientific, ethical, and policy issues raised by research involving the engraftment of human neural stem cells into the brains of nonhuman primates are explored by an interdisciplinary working group in this Policy Forum. The authors consider the possibility that this research might alter the cognitive capacities of recipient great apes and monkeys, with potential significance for their moral status.
The Dominican theologian Albert the Great was one of the first to investigate into the system of the world on the basis of an acquaintance with the entire Aristotelian corpus, which he read under the influence of Islamic philosophers. The present study aims to understand the core of Albert's natural philosophy. Albert's emblematic phrase, “every work of nature is the work of intelligence” , expresses the conviction that natural things are produced by the intellects that move the celestial bodies, just (...) as houses are made by architects moving their instruments. Albert tried to fathom the secret of generation of natural things with his novel notion of “formative power” , which flows from the celestial intellects into the sublunary elements. His conception of the natural world represents an alternative to the dominant medieval view on the relationship between the artificial and the natural. (shrink)
Comparative quantifiers, such as more than three books, cannot take scope over any quantifier in subject position if they occupy object position. This is clearly different from the behavior of other quantifiers (e.g., universal quantifiers). This paper argues that this scope puzzle is due to a more complex internal structure of comparative quantifiers than other quantifiers. In the decompositional approach that I pursue, comparative quantifiers are decomposed into two generalized quantifiers (i.e., in the case above, the comparative operator er than (...) three and the DP many books). In this approach, obligatory narrow scope of comparative quantifiers in object position is a consequence of the interplay of the independently motivated principles of grammar that also constrain other quantifiers. On the basis of the scope puzzle, I specifically argue for two constraints on Scope Shifting Operations (SSOs) a locality condition on SSOs and Scope Economy, proposed by Fox (2000), which prohibits SSOs that have no effect on semantic interpretation. Thus, I argue that the apparently peculiar facts of comparative quantifiers are, in fact, additional evidence for the core properties of SSOs. (shrink)
In this thesis, we study the least fixed point principle in a constructive setting. A constructive theory of functions and sets has been developed by Feferman. This theory deals both with sets and with functions over sets as independent notions. In the language of Feferman's theory, we are able to formulate the least fixed point principle for monotone inductive definitions as: every operation on classes to classes which satisfies the monotonicity condition has a least fixed point. This is called the (...) principle of monotone inductive definition. Furthermore, we may formulate this principle in a uniform way as: there is an operation which maps a monotone operation to its least fixed point. This is called the principle of uniform monotone inductive definition. Feferman raised the question of the strength of the principle of monotone inductive definition when adjoined to his theory . This question is our primary concern in this thesis. ;Our main results are the consistency of both the principle of monotone inductive definition and the principle of uniform monotone inductive definition adjoined to his theory, and the proof theoretical equivalence between the principle of monotone inductive definition with Feferman's system without the inductive generation axiom and the system of the Pi-one-one Comprehension Axiom. Determination of the proof-theoretical strength of the principle of monotone inductive definition adjoined to Feferman's theory still remains open. ;The consistency of both the principle of monotone inductive definition and the principle of uniform monotone inductive definition with Feferman's theory will be achieved by constructing their models in set theoretical sense. The proof theoretical equivalence between the principle of monotone inductive definition with Feferman's system without the inductive generation axiom and the system of the Pi-one-one Comprehension Axiom can be obtained by a careful examination of the model construction for the principle of monotone inductive definition with Feferman's system without the inductive generation axiom, which is parallel to the model construction for the principle of monotone inductive definition with his theory. (shrink)
BackgroundThis study aimed to ask a sample of the general population about their preferences regarding doctors holding discretionary powers in relation to disclosing cancer diagnosis and prognosis.MethodsThe researchers mailed 443 questionnaires to registered voters in a ward of Tokyo which had a socio-demographic profile similar to greater Tokyo's average and received 246 responses . We describe and analysed respondents' attitudes toward doctors and family members holding discretionary powers in relation to cancer diagnoses disclose.ResultsAmongst respondents who wanted full disclosure about the (...) diagnosis without delay, 117 respondents agreed to follow the doctor's discretion, whilst 111 respondents agreed to follow the family member's decision. For respondents who preferred to have the diagnosis and prognosis withheld, 59 agreed to follow the doctor's decision, and 79 of respondents agreed with following family member's wishes.ConclusionsThe greater proportion of respondents wants or permits disclosure of cancer diagnosis and prognosis. In patients who reveal negative attitudes toward being given a cancer disclosure directly, alternative options exist such as telling the family ahead of the patient or having a discussion of the cancer diagnosis with the patient together with the family. It is recommended that health professionals become more aware about the need to provide patients with their cancer diagnosis and prognosis in a variety of ways. (shrink)
In their examination of elementary science classrooms, Amerine and Bilmes (1988) found that following instructions requires students to understand the relationship between the projected outcome and the corresponding course of actions. One of the most important resources for instructions is the lesson plan, which prescribes the sequence of teaching. However, there is often a gap between what is planned and what actually happens in the classroom. This raises the question of how teachers come to terms with contingent variants and unexpected (...) outcomes that real-time interactions occasion and how lesson plans are configured into these processes. This study examines a teacher education program that uses lesson plans as a central resource for teaching mathematics. The results suggest that classroom teachers use lesson plans as communicative resources to identify problems, specify assumptions about their teaching and act on the evolving contingency of classroom interaction. The interactional contingency is the locus of teaching practices, not an obstacle to the application of procedures in lesson plans. (shrink)
This essay aims to deepen our comprehension of the economic ethics of different peoples in Asia, as well as realizing a degree of cultural relativism, in order to enhance amicable economic associations. It counterbalances the conventionally strong West-oriented views which regard exotic features of non-Western economies as backward and illogical elements that disturb smooth and orthodox development and, hence, should be eradicated. The author, first, recalls a number of facts which depict the eruptive economic transformation in Asia. He, then, criticizes (...) the imposition of Western-style development and exploitation without excluding Japan’s colonialism in Taiwan and Korea, and pleads for multiple forms of development and modernity. Economic transactions should be analysed in relation to sociocultural aspects, and, therefore, communities and ethics groups play a substantive role between the public and private sectors, the market, and individuals. For instance, small farmers in Southeast Asia, struggling with the weakness of tenant farmers and pressures of the market mechanism, developed ingenious and participatory forms of survival, increasingly supported by non-governmental organizations. Case studies from Thailand, Malaysia, and the Philippines give a vivid picture of these activities. Because the developing economies are composed of market and non-market sectors, reasonable attention should be given to theethics beyond market principles, with particular emphasis on community as foundation. (shrink)
We study L∞κ-freeness in the variety of Boolean algebras. It is shown that some of the theorems on L∞κ-free algebras which are known to hold in varieties such as groups, abelian groups etc. are also true for Boolean algebras. But we also investigate properties such as the ccc of L∞κ-free Boolean algebras which have no counterpart in the varieties above.
Causal induction in the real world often has to be quick and efficient as well as accurate. We propose that people use two different frames to achieve these goals. The A-frame consists of heuristic processes that presuppose rarity and can detect causally relevant factors quickly. The B-frame consists of analytic processes that can be highly accurate in detecting actual causes. Our dual frame theory implies that several factors affect whether people use the A-frame or the B-frame in causal induction: among (...) these are symmetrical negation, intervention and commitment. This theory is tested and sustained in two experiments. The results also provide broad support for dual process accounts of human thinking in general. (shrink)
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the (...) development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed. (shrink)
The paper reviews the current situation regarding a new theory of brain dynamics put forward by the authors in an earlier publication. Motivation for the theory is discussed in terms of two issues: the long-standing problem of accounting for the stability and nonlocal properties of memory, and the experimental and theoretical evidence against the classical theory of brain action. It is shown that the new theory provides an explanation and a conceptually unifying framework for phenomena of brain action that resist (...) classical explanation. Further independent experiments provide strong additional support for the theory. The fact that this theory incorporates quantum mechanisms in an essential way is considered to be of wide scientific interest in view of the unique status of the brain in relation to the physical, biological, and mental orders in nature. (shrink)
Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In a stronger (...) perturbation regime, the tunneling component of the wave-matrix exhibits a remarkable interference fringes, which is clarified by the semiclassical theory as an interference among multiple complex tunneling trajectories. It turns out that such a peculiar behavior is the manifestation of an intrinsic multi-dimensional effect closely related to a singular movement of singularities possessed by the complex classical trajectories. (shrink)
A psycho-historical framework for the science of art appreciation will be an experimental discipline that may shed new light on the highest capacities of the human brain, yielding new scientific ways to talk about the art appreciation. The recent findings of the contextual information processing in the human brain make the concept of the art-historical context clear for empirical experimentation.
El artículo señala la fascinación ejercida por la Matemática sobre algunos pensadores, antiguos y modernos, y sugiere una posible explicación basada en la utilidad de la Matemática, la certeza de sus afirmaciones y la elegancia de sus procedimientos.