Children often personify non-living objects, such as puppets and stars. This attribution is considered a healthy phenomenon, which can simulate social exchange and enhance children's understanding of social relationships. In this study, we considered that the tendency of children to engage in personification could potentially be observed in abstract entities, such as numbers. We hypothesized that children tend to attribute personalities to numbers, which diminishes during the course of development. By consulting the methodology to measure ordinal linguistic personification (OLP), which (...) is a type of synesthesia, we quantified the frequency with which child and adult populations engage in number personification. Questionnaires were completed by 151 non-synesthetic children (9--12 years old) and 55 non-synesthetic adults. Children showed a higher tendency than adults to engage in number personification, with respect to temporal consistency and the frequency of choosing meaningful answers. Additionally, children tended to assign unique and exclusive descriptions to each number from zero to nine. By synthesizing the series of analyses, we revealed the process in which number personification diminishes throughout development. In the discussion, we examined the possibility that number personification serves as a discrimination clue to aid children's comprehension of the relationships between numbers. (shrink)

There are still on-going debates on what exactly is wrong with Prior’s pathological “tonk.” In this article I argue, on the basis of categorical inferentialism, that two notions of inconsistency ought to be distinguished in an appropriate account of tonk; logic with tonk is inconsistent as the theory of propositions, and it is due to the fallacy of equivocation; in contrast to this diagnosis of the Prior’s tonk problem, nothing is actually wrong with tonk if logic is viewed as the (...) theory of proofs rather than propositions, and tonk perfectly makes sense in terms of the identity of proofs. Indeed, there is fully complete semantics of proofs for tonk, which allows us to link the Prior’s old philosophical idea with contemporary issues at the interface of categorical logic, computer science, and quantum physics, and thereby to expose commonalities between the laws of Reason and the laws of Nature, which are what logic and physics are respectively about. I conclude the article by articulating the ideas of categorical logical positivism and pluralistic unified science as its goal, including the unification of realist and antirealist conceptions of meaning by virtue of the categorical logical basis of metaphysics. (shrink)

In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 1-3 [Access article in PDF] Symposium:Aesthetic Education in Japan TodayThe purpose of this symposium is to provide readers with a general understanding of Japanese art and aesthetics education and its interaction with other cultures. The essays cover a variety of topics, including historical, cross-cultural, theoretical, and practical perspectives.First, the development and establishment of art education in the Japanese education system is introduced. (...) Kingo Masuda's essay provides a brief history of art education policy and how a formal system of art education has been organized from the modern era to the present. Takuya Kaneda examines the foundation for the historical evolution of the major reform movements in Japanese art education. He focuses on the philosophies of three pioneers who guided the movements and sheds light on to the role that "freedom" has played in the context of aesthetic education. Their historical studies show how the modern Japanese educational system incorporated the Western notion of art education into its foundation. Western art educators have given Japanese art educators the impetus to modernize the theory and practice of art education.The attempt to go beyond the modern framework of arts and aesthetic education is discussed in some authors' essays. Yoko Hino examines a key educational term, "Creative Play (Zokei Asobi)," and points out the dilemma educators face working within the modern framework that divides subject matter completely from individuality. Yasuaki Okamoto, in his philosophical essay, discusses the change in the nature of self-understanding in theage of media expansion. His point is that our sense of reality is no longer confined to physical existence, and that media provides us with a new kind of experience of self and reality. Kinichi Fukumoto illustrates the essential structure of art education with the metaphor of Disneyland, and emphasizes art education as an incomplete, further evolving project. Motoki Nagamori discusses Rousseau's concept of nature as a foundation for modern theory and practice of art education and suggests an alternative concept that incorporates cultural, linguistic, and media aspects. Based on a historical study on evaluation methods, Kazumi Yamada suggests that qualitative factors should play a significant role for improving art education.Some authors emphasize the current concern for integrating art with other disciplines in order to alter our understanding about aesthetic education. [End Page 1] Advocating for the integration of art and media literacy based on the educational principles of the Bauhaus, Kenta Motomura explores the possibility of media technology for a new type of expression. Kazuhiro Ishizaki and Wenchun Wang describe their cross-cultural study on children's aesthetic development to stress the importance of the communal, cultural, and linguistic considerations of integrated study, historically overlooked in traditional aesthetic education. Focusing on blending music and visual arts, Masashi Okada introduces his theory and practice of integrated study developed over many years.In addition, globalization and its effect on art education has become an important topic. Engaging in a cross-cultural dialogue is a critical part of this issue. Akio Okazaki discusses what Arthur Wesley Dow, an Americanart educator, recognized and learned by encountering the otherness of Japanese art. Yoshimasa Kaneko's study shows how Japanese aesthetics and Johannes Itten (the founder of Ittenschule in Germany) had a significant philosophical influence on each other. Toshio Naoe's comparativestudy between Japanese and British educational systems highlights somecrucial differences and similarities and points out overarching themes across the two countries. Mitsuru Fujie compares and contrasts the different educational meanings of "play" between Japan and the United States, and articulates the nature of play in the context of Japanese art education. Masako Iwano's study describes a case of cross-cultural aesthetic education in a small Japanese community and how this cultural interaction through art impacts that community.The perspectives of all of these authors are decidedly international. They are not only committed to, and engaged directly in, the current practice of Japanese education but have developed an international viewpoint through experiences overseas. Some have conducted research at educational institutions in other countries, and others have participated in the activities of international professional... (shrink)

We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, yielding (...) vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 84-93 [Access article in PDF] Arthur Wesley Dow's Address in Kyoto, Japan (1903) Researchers concerned with the historical development of American art education cannot help but acknowledge Arthur Wesley Dow's significant contribution to the field. Although many writers have recognized him as one of greatest figures in art education, 1 it was not until the end of the twentieth century that art (...) historians discovered his impact on the early development of modernist American art.Several exhibitions of Dow's work have been shown recently, most notably: "Arthur Wesley Dow and American Art and Crafts," in Stanford, Chicago, and Fort Dodge, Iowa (1999 and 2000) and "Harmony of Reflected Light: The Photographs of Arthur Wesley Dow," at the New Mexico Museum of Fine Arts (2001). 2 In addition, two galleries in New York showed exhibitions of Dow's work in 1999 and 2000, respectively. These exhibitions indicate a rediscovery of Dow's work and his role, as well as a wider interest in the integral aspects of modernism in American artworks.Joseph Masheck recognized Dow's post-impressionistic aesthetic of flat surface design as influential on modernism in painting and the graphic arts. 3 Nancy Green sees Dow as "one of the first Western artists who did not simply imitate Japanese art, but who actually used the traditional Japanese woodcut techniques to create modernist prints." 4 Leah Ollman writes, "Those who credit Dow as a conduit to American modernism see his traces everywhere" because "Dow is revealed at the end of the rainbow, as the common ancestor" who spread his theory and practice of art and art education. 5 James Enyeart states that Dow can now receive appropriate critical assessment of his work as a photographer and his impact on pictorial and modernist photography. 6 [End Page 84]Dow is one of the few Americans whose work in the field of art and art education was influenced by Japanese traditional art. He came to Japan in October 1903 and spent three months in Japan, including six weeks in Tokyo and a month in Kyoto. His address in Kyoto in mid-December of that year has been mentioned in biographical studies. 7 However, a detailed account of what Dow said to the Japanese public has previously been unknown due to lack of a historical source.Contemporary Japanese newspaper articles are the primary source for the contents of this address. The purpose of this essay is to translate these source materials into English, providing a definitive description to encourage further research on Dow as an outstanding artist and educator. This essay describes his activity in Japan, provides useful primary sources about his address, and discusses the content of the address. Implications for a cross-cultural interpretation are discussed in the concluding remarks. Dow in Japan Dow was born in Ipswich, Massachusetts on April 6, 1857. He studied art in Boston and Paris, and exhibited his paintings at Salon, in Paris from 1886-1887. He established his summer school of art in Ipswich (1891-1907) and became the curator of Japanese art at the Boston Museum of Fine Arts in1897. He was an instructor of art at the Pratt Institute in Brooklyn from 1895-1904; taught composition at the Art Student's League in New York from 1897-1903; and served as a professor and the director of fine arts at Teachers College, Columbia University from 1904-1922. 8 Dow first studied Japanese art at the Boston Museum of Fine Arts under the direction of Ernest Fenollosa, and then during his residence in Japan.Arthur Johnson's 1934 biography provides the most detailed description of Dow's life and works. 9 In fact, "every subsequent publication about Dow has relied on this biographical information, and in some cases Dow's aesthetic sources, contained in Johnson's short text of about one hundred pages." 10 According to Johnson, Dow kept a careful day-by-day record during these months, and to read these notebooks, some six in number, is to see the world through the eyes... (shrink)

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, yielding (...) vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)

Science does not exist in vacuum; it arises and works in context. Ground-breaking achievements transforming the scientific landscape often stem from philosophical thought, just as symbolic logic and computer science were born from the early analytic philosophy, and for the very reason they impact our global worldview as a coherent whole as well as local knowledge production in different specialised domains. Here we take first steps in elucidating rich philosophical contexts in which Samson Abramsky’s far-reaching work centring around categorical science (...) as a new kind of science may be placed, explicated, and articulated. We argue, inter alia, that Abramsky’s work, as a whole, may be construed as demonstrating the categorical unity of science, or rather the sciences, in a mathematically rigorous, down-to-earth manner, which has been a salient feature of his work. At the same time we trace his intellectual history, leading from duality, to intensionality, and to contextuality, and place it in a broader context of philosophy beyond the analytic-continental divide, namely towards the reintegration of them as in the post-analytic tradition. Besides, we address issues in philosophy of category theory, such as the foundational autonomy of category theory and the (presumably two) dogmas of set-theoretical foundationalism, which Abramsky actually touch upon in one of his few philosophically inclined works. As to philosophy of category theory, we also address categorical structuralism as higher-order structuralism, categorical epistemology as elucidating higher-order meta-laws, and categorical ontology as allowing for reduction of ontological commitment via structural realism, the structuralist resolution of Benaceraff’s dilemma, and the pluralistic multiverse view of science as opposed to the set-theoretical reductionist ‘universe’ view. We conclude by speculating about the existence of the Oxford School of (Pluralistic) Unified Science as opposed to the Vienna Circle of (Monistic) Unified Science and to the Stanford School of (Pluralistic) Disunified Science; Categorical Unified Science may potentially allow us to reconcile the two camps on the unity and disunity of science whilst doing justice to both of them. Categorical unity arguably allows for unification via epistemological and ontological networking, and via knowledge transfer thus enabled, rather than unification via the reduction of everything and every truth to a single foundationalist framework, whilst taking at face value disunity, plurality, and diversity, and their significance in science and in human civilisation as a whole. (shrink)

The frame problem is a fundamental challenge in AI, and the Lucas-Penrose argument is supposed to show a limitation of AI if it is successful at all. Here we discuss both of them from a unified Gödelian point of view. We give an informational reformulation of the frame problem, which turns out to be tightly intertwined with the nature of Gödelian incompleteness in the sense that they both hinge upon the finitarity condition of agents or systems, without which their alleged (...) limitations can readily be overcome, and that they can both be seen as instances of the fundamental discrepancy between finitary beings and infinitary reality. We then revisit the Lucas-Penrose argument, elaborating a version of it which indicates the impossibility of information physics or the computational theory of the universe. It turns out through a finer analysis that if the Lucas-Penrose argument is accepted then information physics is impossible too; the possibility of AI or the computational theory of the mind is thus linked with the possibility of information physics or the computational theory of the universe. We finally reconsider the Penrose’s Quantum Mind Thesis in light of recent advances in quantum modelling of cognition, giving a structural reformulation of it and thereby shedding new light on what is problematic in the Quantum Mind Thesis. Overall, we consider it promising to link the computational theory of the mind with the computational theory of the universe; their integration would allow us to go beyond the Cartesian dualism, giving, in particular, an incarnation of Chalmers’ double-aspect theory of information. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality and physical (...) contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality and physical (...) contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

We pursue the idea that predicate logic is a “fibred algebra” while propositional logic is a single algebra; in the context of intuitionism, this algebraic understanding of predicate logic goes back to Lawvere, in particular his concept of hyperdoctrine. Here, we aim at demonstrating that the notion of monad-relativised hyperdoctrines, which are what we call fibred algebras, yields algebraisations of a wide variety of predicate logics. More specifically, we discuss a typed, first-order version of the non-commutative Full Lambek calculus, which (...) has extensively been studied in the past few decades, functioning as a unifying language for different sorts of logical systems (classical, intuitionistic, linear, fuzzy, relevant, etc.). Through the concept of Full Lambek hyperdoctrines, we establish both generic and set-theoretical completeness results for any extension of the base system; the latter arises from a dual adjunction, and is relevant to the tripos-to-topos construction and quantale-valued sets. Furthermore, we give a hyperdoctrinal account of Girard’s and Gödel’s translation. (shrink)

Lawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics. This yields uniform hyperdoctrinal completeness results for numerous logics such as different types of relevant predicate logics and beyond, which are new results on their own; i.e., we give uniform categorical semantics for a broad variety of non-classical predicate logics. And (...) we introduce an analogue of Lawvere–Tierney topology and cotopology in the hyperdoctrinal setting, which gives a unifying perspective on different logical translations, in particular allowing for a uniform treatment of Girard’s exponential translation between linear and intuitionistic logics and of Kolmogorov’s double negation translation between intuitionistic and classical logics. In the hyerdoctrinal conception, type theories are categories, logics over type theories are functors, and logical translations between them, then, are natural transformations, in particular Lawvere–Tierney topologies and cotopologies on hyperdoctrines. The view of logical translations as hyperdoctrinal Lawvere–Tierney topologies and cotopologies has not been elucidated before, and may be seen as a novel contribution of the present work. From a broader perspective, this work may be regarded as taking first steps towards interplay between algebraic and categorical logics; it is, technically, a combination of substructural algebraic logic and hyperdoctrinal categorical logic, as the hyperdoctrinal completeness theorem is shown via the integration of the Lindenbaum–Tarski algebra construction with the syntactic category construction. As such this work lays a foundation for further interactions between algebraic and categorical logics. (shrink)

It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercompact.

Specification acquisition in the system design process has been improved since the middle of the 1980s when the upper CASE tools appeared. On the contrary the quality of requirement acquisition in the upper processes of system design has not been enhanced as much as specification acquisition. Understanding the user's requirements is indispensable as one of the basic conditions for building systems that can really satisfy users.This article discusses obtaining requirement knowledge, in terms of human-centred design. The focus is on the (...) process of requirement acquisition, where there is room for one to make full use of human knowledge in a dynamic manner. (shrink)

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document} is a minimal essentially undecidable theory’. For the alternative theories WTC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}}$$\end{document} and TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}}$$\end{document} which have the empty string, we also prove that the each theory without the neutrality of ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} is to be such a theory too. (shrink)

This research was partially supported by Grant-in-Aid for Scientific Research (No. 06640178 and No. 06640336), Ministry of Education, Science and Culture of Japan Mathematics Subject Classification: 03E05 --> Abstract. Following Carr's study on diagonal operations and normal filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} in [2], several weakenings of normality have been investigated. One of them is to consider normal filters without \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness, for (...) example, see DiPrisco-Uzcategui [3]. The other is weakening normality itself while keeping \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness such as in Mignone [10] and Shioya [11]. We take the second one so that all filters are assumed to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-complete. In Sect. 1 a hierarchy of filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} is presented which corresponds to the length of diagonal intersections under which the filters are closed. It turns out that many ranks exist between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $FSF_{\kappa\lambda}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $CF_{\kappa\lambda}$\end{document}. We consider seminormal ideals in Sect. 2 and determine the minimal seminormal ideal extending Johnson's result in [6]. Its precise descripti on changes according to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $cf(\lambda )$\end{document} although we can write it in a single form as well. We also prove that a nonnormal seminormal ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $I\supset NS_{\kappa\lambda}$\end{document} exists if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\lambda$\end{document} is regular. (shrink)

Although many models of consciousness have been proposed from various viewpoints, they have not been based on learning activities in a whole system with the capabilities of autonomous adaptation. We have been investigating a simplified system using artificial neural nodes to clarify the functions and configuration needed for learning in a system that autonomously adapts to the environment. We demonstrated that phenomenal consciousness is explained using a method of "virtualization" in the information system and that learning activities in a whole (...) system adaptation are related to consciousness. However, we have not sufficiently clarified the learning activities of such a system. Consciousness is basically modeled as a system-level learning activity to modify both its own configuration and states in autonomous adaptation through investigating learning activities as a whole system. The model not only explains the time delay in Libet's experiment, but is also positioned as an improved model of Global Workspace Theory (GWT). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Artist as Professional in JapanKazuyo Nakamura and Akio OkazakiThe Artist as Professional in Japan, edited by Melinda Takeuchi. Stanford, Calif.: Stanford University Press, 2004, 262pp., $45.00 cloth.With the increase of cross-cultural academic exchange in our time, more accurate information on art from other cultures has become more easily available, and curriculum development of art education directed toward multiculturalism has been brought to realization. There is need emerging (...) among art educators for academic resources for teaching cross-cultural subject matters, and The Artist as Professional in Japan provides historical information helpful in gaining a critical understanding of the nature of Japanese art discourse. The volume is edited from a fresh sociocultural perspective by Melinda Takeuchi, professor of Japanese art at Stanford University.Takeuchi, noticing that few scholarly books on the profession of Japanese artists are available to students of art history in the United States, set about the volume in concerted efforts with her colleagues. The volume consists of individual case studies on different Japanese artists; they are well-known sculptors, painters, potters, printmakers, and architects and are recognized in Japan as representative in different eras from the seventh to the twentieth century. Running through the individual studies, there is a concern for political forces that shaped art discourse and the identity of the Japanese artist. The following questions are asked: What degree of control did the artists exercise over their métier? What were some of the dynamics operating in the production, consummation, and evaluation of art and artist? How was the image of the artist formed during various periods? Working with these questions, seven case studies address issues of canon formation of art by looking into the terrain of the meaning of a critical word, Shoku-nin; it literally means people (nin) with an occupation (shoku) and denotes the collective artisan class.Different art historians and art theorists take a unique approach for developing each case study in the volume. Donald F. McCallum's study in chapter 2 is on the Buddhist Icons of the Shaka Triad during the Asuka Period (ca.590-ca.650), and it is asked what were the political forces working on the production of the [End Page 118] icons. In contrary to orthodox view, it is argued that the icons were produced not by an individual sculptor named Tori-busshi but by the guilds of which the supervisor was Tori. Also, it is argued that the icons were produced with the patronage of soga clan, the dominant political force of the time, not by the imperial family, including Shotoku Taishi.Karen L. Brock in chapter 3 examines the case of E'nichibo Jonin (active ca.1211-ca.1243), the painter of Saint Myoe. The case shows that the ateliers of temples, such as Kozanji in Kyoto, played a central role in producing and distributing sacred images. This study makes clear that few individual painters, such as those named ebusshi, participated in the formation of the canon of Japanese painting, but collective political forces, such as Kozanji ateliers, exercised power in bringing out sacred objects.In chapter 4 Melinda Takeuchi takes up the case of Tosa Mitsunobu (1434-ca.1523), an artisan painter active in Kyoto court circles. It shows a historical fact particular to Japanese art discourse—that later artists manipulated the names of earlier ones for professional or cultural merits. Taking notice of the fact that Mitsunobu's name late became synonymous with a production unit that shares secret techniques of products, Takeuchi concludes, "In the end, the name of an artist transcends time, space, materiality, and ultimately discourse itself" (101).The study of Louise Allison Cort in chapter 5 is on the case of Morita Kyuemon in the seventeenth century, a warrior trained as a potter and running the Odo pottery in the Tosa domain. By exploring the motivations of the Tosa domain in trying to transform local products into refined and stylish pottery worthy of formal presentation to other domain rulers (daimyo), to government officials, and to the shogun in Edo, this chapter demonstrates how both the potter and the ruler actively sought to join the aesthetic mainstream of their own day.In... (shrink)

“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all (...) sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand. (shrink)

Cet article s’intéresse aux mutations de la famille japonaise au XXe siècle à travers les manga de Machiko Hasegawa (Sazae-san), première dessinatrice de bande dessinée au Japon, et de Kyoko Okazaki (La maison du bonheur et Au bord de la rivière), qui appartient à la génération actuelle. L’analyse comparée de plusieurs de leurs albums montre, notamment à travers les scènes de repas, la déstructuration de la famille japonaise d’après-guerre, dans un contexte d’industrialisation qui a poussé les Japonaises à délaisser (...) en partie le foyer familial pour travailler. (shrink)

Unlike the most well‐characterized prokaryotic polymerase, E. Coli DNA pol I, none of the eukaryotic polymerases have their own 5′ to 3′ exonuclease domain for nick translation and Okazaki fragment processing. In eukaryotes, FEN‐1 is an endo‐and exonuclease that carries out this function independently of the polymerase molecules. Only seven nucleases have been cloned from multicellular eukaryotic cells. Among these, FEN‐1 is intriguing because it has complex structural preferences; specifically, it cleaves at branched DNA structures. The cloning of FEN‐1 (...) permitted establishment of the first eukaryotic nuclease family, predicting that S. cerevisiae RAD2 (S. pombe Rad13) and its mammalian homolog, XPG, would have similar structural specficity. The FEN‐1 nuclease family includes several similar enzymes encoded by bacteriophages. The crystal structures of two enzymes in the FEN‐1 nuclease family have been solved and they provide a structural basis for the interesting steric requirements of FEN‐1 substrates. Because of their unique structural specificities, FEN‐1 and its family members have important roles in DNA replication, repair and, potentially, recombination. Recently, FEN‐1 was found to specifically associate with PCNA, explaining some aspects of FEN‐1 function during DNA replication and potentially in DNA repair. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 12-19 [Access article in PDF] The Concept of Freedom in Art Education in Japan The concept of freedom has played a very important role in art education in Japan. Needless to say, freedom has been regarded as an essential principle of education in the West. Writers from Jean Jacques Rousseau to John Dewey stressed the significance of freedom in education. Especially, in (...) the field of art education, Frantz Cizek, Viktor Lowenfeld, and Herbert Read emphasized the importance of children's free expression in relation to creativity. This article examines the concept of freedom in art education in Japan, focusing on the ideas of two major non-governmental movements in art education; the Free-Expression Movement in the 1920s and the Creative Aesthetic Education Movement in the 1950s-1960s. Although both movements have already declined, their impacts are still felt in Japanese art education. The Beginning of Art Education in Japan In the early Meiji Era (1868-1912), art education was introduced to Japan when the modern school system was imported from the West. In 1872, the first government drawing textbook; Seiga Shinan [Guide to Western Pictures] was published based on a Japanese translation of British drawing manuals. 1 In this period, the purpose of art class was to teach the basic skill of mechanical drawing for industrial development; the method consisted of merely copying model pictures in the drawing textbook. In 1910, Akira Shirahama, who spent three years in Europe and the United States surveying art education, edited Shintei Gacho [New Textbook of Drawing]. As Okazaki points out, Shirahama, who was impressed by the art curriculum in the public schools of the United States, referred to the importance of children's creative imagination; however, the new textbook did not fully reflect the idea. 2 Thus, the practice of art class was limited to copying textbooks, and children's free expression was not considered important in art class. Until this period, the issue of freedom did not correlate to art education. The Free Expression Movement in the Taisho Era After the World War I, a democratic movement prevailed during the Taisho Era (1912-1926) in Japan. This movement, called Taisho Democracy, influenced various parts of Japanese life including politics. In the field of education, many democratic ideas of education were introduced from the West and books on progressive educational thought such as John Dewey's Democracy and Education were translated into Japanese. Child-centered education also became popular among progressive teachers. During this period, Jiyuga KyouikuUndo, the Free-Drawing Education movement, was started by Kanae Yamamoto. Okazaki describes this epoch-making movement as "the remarkable movement of art education in 1919 which began to change art education philosophy." 3 It was the first time the issue of freedom was raised in art education in Japan. [End Page 13] Yamamoto's Concept of Freedom Kanae Yamamoto, born in 1882, studied Western painting at the Tokyo Fine Arts School. After graduation, he started his career as a print artist and set off for Europe in 1912. He stayed in France to study art and experienced the much freer atmosphere in Europe compared to Japan. When he returned to Japan via Russia in 1916, he encountered an exhibition of children's paintings in Moscow. The free expression of the Russian children's paintings deeply impressed him.After Yamamoto's return from Europe, he organized the first exhibition of children's free painting in Japan and established Japan Children's Free Drawing Association in 1919. The exhibition was given great attention by the public, who, influenced by the Taisho democratic movement, was becoming very interested in democratic education. Yamamoto's book; Free Drawing Education was published in 1921. In his usage, the term "freedom" is sometimes synonymous with creativity. 4 He explained the meaning of freedom in his education theory: Our education of freedom is not to educate as teachers like. It is not a worship of freedom showing the model of freedom but to teach freedom itself....In my belief, the essence of human beings will never... (shrink)

in a recent article entitled “Hume on the Passions,” Stephen Buckle opens with the claim that Hume’s theory of the passions has largely been neglected. “Apart from a couple of famous sections in the Treatise concerning the sources of action,” he writes, “the subject matter has rarely excited interest.”1 His analysis of why the subject of the passions in Hume has been uninspiring points to the fact that readers have largely misunderstood the point of Hume’s theory. They usually regard the (...) account as yet another mechanistic analysis of the passions in the vein of seventeenth-century science, alongside the offerings of Malebranche, Hobbes, and Spinoza. Buckle is right to point out that there is a.. (shrink)

The period from Kant to Hegel is one of the most intense and rigorous in modern philosophy. The central problem at the heart of it was the development of a new standard of theoretical reflection and of the principle of rationality itself. The essays in this volume, published in 2000, consider both the development of Kant's system of transcendental idealism in the three Critiques, the Metaphysical Foundations of Natural Science, and the Opus Postumum, as well as the reception and transformation (...) of that idealism in the work of Fichte, Schelling and Hegel. (shrink)

Health professionals do not always have the luxury of making “right” choices. This article introduces the “devil's choice” as a metaphor to describe medical choices that arise in circumstances where all the available options are both unwanted and perverse. Using the devil's choice, the paper criticizes the principle of double effect and provides a re-interpretation of the conventional legal and ethical account of symptom relief in palliative care.