This paper argues for a virtue-based account of questioning. First, it delineates the unreflective yet rational aspects of questioning and demonstrates that “good” questions – that is, properly focused, pertinent questions – can be obtained not only in reflective but also in unreflective processes. This paper then argues that the unreflective yet rational mode of inquirers in questioning can be characterized by an automatic response to good questions and cues for relevant doubt and further questions, the active and standby modes (...) of responsiveness, and emotional stress on cues for relevant doubt and further questions. Finally, this article outlines how these features can fully be explicated in terms of exercising a sensitivity to good questions as a virtue. (shrink)

Emotional processing without conscious awareness plays an important role in human social interaction. Several behavioral studies reported that subliminal presentation of photographs of emotional facial expressions induces unconscious emotional processing. However, it was difficult to elicit strong and robust effects using this method. We hypothesized that dynamic presentations of facial expressions would enhance subliminal emotional effects and tested this hypothesis with two experiments. Fearful or happy facial expressions were presented dynamically or statically in either the left or the right visual (...) field for 20 (Experiment 1) and 30 (Experiment 2) ms. Nonsense target ideographs were then presented, and participants reported their preference for them. The results consistently showed that dynamic presentations of emotional facial expressions induced more evident emotional biases toward subsequent targets than did static ones. These results indicate that dynamic presentations of emotional facial expressions induce more evident unconscious emotional processing. (shrink)

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)

Le présent essai soutient une position qui s’inscrit dans le courant dit « libertarien » tout en explorant les implications de la politique qui prône un revenu de base et suscite présentement un débat vivace à travers le monde, y compris au Japon. Il existe diverses formes d’éthique libertarienne. Ici, dans la lignée de Nozick, la « propriété de soi » et la clause lockéenne sont reconnus comme deux rouages essentiels de l’argumentation qui conduit à leur ajustement en vue d’une (...) éthique spécifique. Nous examinons comment Nozick défend la « propriété de soi » : son argumentation respecte la séparabilité des personnalités et elle accorde une grande importance à l’élaboration libre par chacun d’un mode de vie lui convenant. Une fois révisées la nature du droit dit « d’appropriation » et de la clause dite « lockéenne », nous réinterprétons cette position centrale des libertariens en considérant la position fondamentale de Nozick comme prenant appui sur une conception égalitariste de la notion de dispositions suffisantes. Les avantages de cette position sont dus non seulement à l’adéquation entre la théorie et un principe de distribution, mais encore à l’image de l’individu doté d’une propriété de soi réaffirmée, dans la vision libertarienne que Nozick déploie. Cette approche fournit les bases de la morale d’une activité libre exercée sur les marchés : ce point est essentiel pour les auteurs libertariens, qui refusent toute aliénation de la propriété privée et toute redistribution. Une version simplifiée du revenu de base une fois définie en l’adaptant à des cadres variés, dont le cadre japonais nous mène à conclure que le revenu de base, quoique séduisant, est partiellement conforme aux thèses libertariennes et qu’une version minimale serait à retenir. (shrink)

40億年に及ぶとされる、地球における生命の歴史。共通の祖先から進化した生きものたちは、多様でありながら共通点もあわせ持っています。いのちとは何か?いのちはどのようにして生まれたのか?どのように考えられ てきたのか?その歴史をひもときながら、私たちの来た道と、これから行く道を、探ってみましょう。.

「正義」の名で取り戻されなければならないものがあるとすれば、それは、「平等と教育」、「公共性と教育」、「統合と教育」をめぐる討議に、さまざまな考え方、さまざまな立場からの参加を人びとに保障する公論の場 である。教育論議に規範的視点を取り戻す!経済の成長路線に抗して、教育の制度設計をいかに進めるか。正義の原理に遡って問い直す。.

The number of competing-brands changes by new product's entry. The new product introduction is endemic among consumer packaged goods firm and is an integral component of their marketing strategy. As a new product's entry affects markets, there is a pressing need to develop market response model that can adapt to such changes. In this paper, we develop a dynamic model that capture the underlying evolution of the buying behavior associated with the new product. This extends an application of a dynamic (...) linear model, which is used by a number of time series analyses, by allowing the observed dimension to change at some point in time. Our model copes with a problem that dynamic environments entail: changes in parameter over time and changes in the observed dimension. We formulate the model with framework of a state space model. We realize an estimation of the model using modified Kalman filter/fixed interval smoother. We find that new product's entry (1) decreases brand differentiation for existing brands, as indicated by decreasing difference between cross-price elasticities; (2) decreases commodity power for existing brands, as indicated by decreasing trend; and (3) decreases the effect of discount for existing brands, as indicated by a decrease in the magnitude of own-brand price elasticities. The proposed framework is directly applicable to other fields in which the observed dimension might be change, such as economic, bioinformatics, and so forth. (shrink)

In the current model of visual transduction, the lifetime of active cGMP phosphodiesterase depends upon the period of its interaction with GTP-bound transducin. If recoverin regulates the lifetime of light-activated cGMP phosphodiesterase through inhibition of rhodopsin phosphorylation, rhodopsin should directly interact with cGMP phosphodiesterase and/or GTP-bound transducin complexed with cGMP phosphodiesterase. Is this true?

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)

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)

We can easily discriminate self-produced from externally generated sensory signals. Recent studies suggest that the prediction of the sensory consequences of one’s own actions made by forward model can be used to attenuate the sensory effects of self-produced movements, thereby enabling a differentiation of the self-produced sensation from the externally generated one. The present study showed that attenuation of sensation occurred both when participants themselves performed a goal-directed action and when they observed experimenter performing the same action, although they clearly (...) reported that the tones were produced by other during action observation and by themselves during their own action. These results suggest that sensory prediction of action modulates ongoing auditory processing irrespective of who produces the sounds and that the explicit judgment of agency does not necessarily rely on the same mechanisms on which implicit perceptual measures such as sensory attenuation rely. (shrink)

In the vision of the semantic web, agents are defined as the programs that collect information from diverse sources, process the information, and exchange the results with other programs. In order to extend application areas of the agents from the Internet to the real world, we propose CONSORTS, a multiagent architecture for content managements in ubiquitous computing. In this paper, we, first, describe two important concepts in order to realize the agent-based content managements in ubiquitous computing, ``physically grounding'' and ``cognitive (...) resources managements.'' Second, we describe the outline of the CONSORTS and its RDF-based spatial information representation. Finally, we show an application of the CONSORTS, context-aware information assist services in a museum. (shrink)

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; (...) this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy. (shrink)

... because the thing-in-itself has no abnormality. Anything unusual will appear, after I myself see it: Abnormality belongs not to the thing-in-itself, but to myself. Kuo P'u (276-324), Shan-hai ching (Scriptures of the Mountains and the Seas).

Today in Japan psychoactive drugs are widely prescribed for various psychiatric disorders including so-called ‘functional’ disorders. They are undoubtedly effective in relieving various psychological and behavioral symptoms. However, Japan has yet to address some basic questions: (1) uncertainty concerning the cause of various psychiatric functional disorders; (2) unknown factors that affect the function of psychotropic drugs in patients; (3) the difficulty in obtaining objective data concerning the effects of these medications * both on the brain and the psychological symptoms (behavior); (...) and most importantly, (4) due to both the behavioral and organic (brain and CNS) effects of psychoactive drugs, the difficulty in evaluating the risk/benefit ratio between the behavioral (primary) effect and the organic (side) effect. In addition, there are bioethical problems, since these uncertainties tend to permit too broad a range of intention and too many modes of intervention in (a) prescribing and (b) taking psychoactive drugs on the part of therapists and patients, respectively. Though the increased risk of the inappropriate use of these drugs – the non-therapeutic uses, and their over-prescription – has been indicated in other industrialized countries, it has not yet been fully recognized and adequately discussed in Japan. Moreover, it is necessary to establish a sound basis for the ‘somato-psychic’ evaluation of these effects in the context of the physician-patient relationship, including the patient's family and even the broader society. Keywords: bioethics, pharmacological treatment, primary and secondary effects, psychiatric-functional disorders, risk/benefit ratio CiteULike Connotea Del.icio.us What's this? (shrink)

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)

Crew Pairing is one of the most important and difficult problems for airline companies. Nets to fuel costs, the crew costs constitute the largest cost of airlines, and the crew costs depend on the quality of the solution to the pairing problem. Conventional systems have been used to solve a daily model, which handles only regular flights with many simplifications, so a lot of corrections are needed to get a feasible solution and the quality of the solution is not so (...) high. A fully dated model, which handles regular flights and irregular flights simultaneously, is extremely hard and has not been solved directly hitherto. The number of irregular flights tend to increase in Europe and Japan, hence the resolution of the practical fully dated pairing system is desired. This paper presents a new approach which solves directly the fully dated crew pairing by Genetic Algorithms. GA is improved with stochastic processes to attack the fully dated model, and many heuristics are included in the decoding mecanism of the GA. For several hundred flights per day for fully dated 2 months scheduling period, the system found better or equivalent solutions to the human scheduler’s without any simplification from 5 to 20 times faster. (shrink)

Schedule planning is one of the most crucial issues for any airline company, because the profit of the company directly depends on the efficiency of the schedule. This paper presents a novel scheduling method which solves problems related to time scheduling, fleet assignment and maintenance routing simultaneously by Genetic Algorithms. Every schedule constraint is embeded in the fitness function, which is described as an object oriented model and works as a simulater developing itself over time, and whose solution is executable (...) without human correction. The schedular is able to solve the problems involving several hundred flights in a few hours, and the solutions are superior or equivalent to those by human experts in terms of the estimated profit. (shrink)

We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman's method of defining the extensional membership relation ∈ by means of the intensional membership relation ε .Analogously to the usual forcing and the usual generic (...) extension for FA-models, we can justify the existence of generic filters and can obtain the Forcing Theorem and the Minimal Model Theorem with some modifications. These results are on the line of works to investigate whether model theory for AFA-set theory can be developed in a similar way to that for FA-set theory.Aczel pointed out that the quotient of transition systems by the largest bisimulation and transition relations have the essentially same theory as the set theory with AFA. Therefore, we could hope that, by using our new method, some open problems about transition systems turn out to be consistent or independent. (shrink)

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...) totality. (shrink)

Following the finitist’s rejection of the complete totality of the natural numbers, a finitist language allows only propositional connectives and bounded quantifiers in the formula-construction but not unbounded quantifiers. This is opposed to the currently standard framework, a first-order language. We conduct axiomatic studies on the notion of truth in the framework of finitist arithmetic in which at least smash function $\#$ is available. We propose finitist variants of Tarski ramified truth theories up to rank $\omega $, of Kripke–Feferman truth (...) theory and of Friedman–Sheard truth theory, and show that all of these have the same strength as the finitist arithmetic of one higher level along Grzegorczyk hierarchy. On the other hand, we also show that adding Burgess-style groundedness schema, adjusted to the finitist setting, makes Kripke–Feferman truth theory as strong as primitive recursive arithmetic. Meanwhile, we obtain some basic results on finitist theories of (full and hat) inductive definitions and on the second order axiom of hat inductive definitions for positive operators. (shrink)

We investigate which part of Brouwer’s Intuitionistic Mathematics is finitistically justifiable or guaranteed in Hilbert’s Finitism, in the same way as similar investigations on Classical Mathematics already done quite extensively in proof theory and reverse mathematics. While we already knew a contrast from the classical situation concerning the continuity principle, more contrasts turn out: we show that several principles are finitistically justifiable or guaranteed which are classically not. Among them are: fan theorem for decidable fans but arbitrary bars; continuity principle (...) and the axiom of choice both for arbitrary formulae; and $\Sigma _2$ induction and dependent choice. We also show that Markov’s principle MP does not change this situation; that neither does lesser limited principle of omniscience LLPO ; but that limited principle of omniscience LPO makes the situation completely classical. (shrink)