In his previous work, the author has introduced the axiom schema of inductive dichotomy, a weak variant of the axiom schema of inductive definition, and used this schema for elementary ) positive operators to separate open and clopen determinacies for those games in which two players make choices from infinitely many alternatives in various circumstances. Among the studies on variants of inductive definitions for bounded ) positive operators, the present article investigates inductive dichotomy for these operators, and applies it to (...) constructive investigations of variants of determinacy statements for those games in which the players make choices from only finitely many alternatives. As a result, three formulations of open determinacy, that are all classically equivalent with each other, are equivalent to three different semi-classical principles, namely Markov’s Principle, Lesser Limited Principle of Omniscience and Limited Principle of Omniscience, over a suitable constructive base theory that proves clopen determinacy. Open and clopen determinacies for these games are thus separated. Some basic results on variants of inductive definitions for \ positive operators will also be given. (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)

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA0, those in second order set theory extending NBG are. In this article, we establish the equivalence between Δ01-LFP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-LFP}}$$\end{document} and Δ01-FP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-FP}}$$\end{document}, which assert the existence of a least and of a fixed point, respectively, for positive elementary operators. Our proof also shows (...) the equivalence between ID1 and ID^1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widehat{\it ID}_1}$$\end{document}, both of which are defined in the standard way but with the starting theory PA replaced by ZFC. (shrink)

Given the growing centrality of interdisciplinarity to scientific research, gaining a better understanding of successful interdisciplinary collaborations has become imperative. Drawing on extensive case studies of nine research networks in the social, natural, and computational sciences, we propose a construct that captures the multidimensional character of such collaborations, that of a shared cognitive–emotional–interactional platform. We demonstrate its value as an integrative lens to examine markers of and conditions for successful interdisciplinary collaborations as defined by researchers involved in these groups. We (...) show that markers and conditions embody three different dimensions: cognitive, emotional, and interactional; these dimensions are present in all networks, albeit to different degrees; the dimensions are intertwined and mutually constitutive; and they operate in conjunction with institutional conditions created by funders. We compare the SCEI platforms to available frameworks for successful interdisciplinary work. (shrink)

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies have been extensively studied, we point out that well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting α⊢wfwhereα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_\alpha \vdash \mathsf{wf}\, {\rm where}\, _\alpha}$$\end{document} stands for the iteration of Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} comprehension along some ordinal α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document} and wf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{wf}}$$\end{document} stands for the well-foundedness of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document}. (shrink)

We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for \ formulae are provable in \. It is shown to be larger than the proof-theoretic ordinal \ by power of base 2. (...) We also show a similar result for the structural transfinite induction, defined with fundamental sequences. (shrink)

This study explores a liberatory epistemic virtue that is suitable for good learning as a form of liberating socially situated epistemic agents toward ideal virtuousness. First, I demonstrate that the weak neutralization of epistemically bad stereotypes is an end of good learning. Second, I argue that weak neutralization represents a liberatory epistemic virtue, the value of which derives from liberating us as socially situated learners from epistemic blindness to epistemic freedom. Third, I explicate two distinct forms of epistemic transformation: constitutive (...) and causal epistemic transformation. I argue that compared with the ideal conception of epistemic virtue, constitutive epistemic transformation that involves good learning has a transcendent value in light of agents constantly renewing their default epistemic status toward ideal virtuousness. (shrink)

We measure, in the presence of the axiom of infinity, the proof-theoretic strength of the axioms of set theory which make the theory look really like a “theory of sets”, namely, the axiom of extensionality Ext, separation axioms and the axiom of regularity Reg . We first introduce a weak weak set theory as a base over which to clarify the strength of these axioms. We then prove the following results about proof-theoretic ordinals:1. and ,2. and . We also show (...) that neither Reg nor affects the proof-theoretic strength, i.e., where T is Basic plus any combination of Ext and. (shrink)

By obtaining several new results on Cook-style two-sorted bounded arithmetic, this paper measures the strengths of the axiom of extensionality and of other weak fundamental set-theoretic axioms in the absence of the axiom of infinity, following the author’s previous work [K. Sato, The strength of extensionality I — weak weak set theories with infinity, Annals of Pure and Applied Logic 157 234–268] which measures them in the presence. These investigations provide a uniform framework in which three different kinds of reverse (...) mathematics–Friedman–Simpson’s “orthodox” reverse mathematics, Cook’s bounded reverse mathematics and large cardinal theory–can be reformulated within one language so that we can compare them more directly. (shrink)

This paper argues for a virtue-based account of questioning. First, it delineates the unreflective yet rational aspects of questioning and demonstrates that 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)

By forcing, we give a direct interpretation of into Avigad's. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

We consider iterations of general elementary embeddings and, using this notion, point out helices of consistency-wise implications between large large cardinals.Up to now, large cardinal properties have been considered as properties which cannot be accessed by any weaker properties and it has been known that, with respect to this relation, they form a proper hierarchy. The helices we point out significantly change this situation: the same sequence of large cardinal properties occurs repeatedly, changing only the parameters.As results of our investigation (...) of this helical structure, we have new characterizations of extendible cardinals and of Vopěnkan cardinals in terms of elementary embeddings from the universe V, a new large large cardinal property which looks like Shelahness properly between Vopěnkaness and almost hugeness, and a more direct relation between Vopěnkaness and Woodinness than already known.We also consider limits of the helices and relations with the axioms I1–I3. (shrink)

ABSTRACT This paper examines the ‘voluntarism’ challenge for achieving testimonial justice and advocates the virtue of just acceptance of testimony as the right target for efforts to alleviate testimonial injustice. First, we review the credibility deficit case of interpersonal testimonial injustice and explain how the doxastic voluntarism problem poses a challenge to redressing such testimonial injustice. Specifically, the voluntarism problem seems to rule out straightforward control over what and whom people believe; thus, the solution to the problem of testimonial injustice (...) cannot lie in voluntarily self-correcting unjust credibility judgements and replacing them with just testimonial beliefs. Second, we identify three distinctive characteristics of acceptance of testimony, as distinct from belief, and argue that, while it might be difficult to form credibility judgements completely voluntarily, it is easier to control one’s attitude of acceptance towards a speaker’s testimony. We hold that shifting focus from testimonial belief to acceptance can overcome the problem of (synchronic) involuntarism about testimonial belief. Third, we articulate a vision of a virtue of just acceptance of testimony that can move a hearer to collect the right evidence to reliably find the answer to whether a speaker’s testimony is true. Finally, we demonstrate that encouraging people to take a virtuous attitude of just acceptance towards a speaker’s testimony forms the basis of a remedial vision of education that can play a distinctive role in fostering the virtue of just acceptance aimed at testimonial justice. (shrink)

The nature and value of autonomy has long been debated in diverse philosophical traditions, including moral and political philosophy. Although the notion dates back to ancient Greek philosophy, it was during the Age of Enlightenment that autonomy drew much attention. Thus, as may be known, moral philosophers tended to emphasize self-regulation, particularly one’s own will to abide by universal moral laws, as the term “autonomy” originates from the Greek words “self” (auto) and “rule” (nomos). In parallel, modern epistemologists supposedly espoused (...) the idea of intellectual autonomy as self-reliance. In this classical view, an intellectually autonomous explorer of knowledge must not depend on a belief that is obtained from another’s testimony, until one can justify it to oneself. However, accompanying the growing focus on the importance of social dimensions of acquiring knowledge and understanding, recent epistemologists have doubted the classical view and have since reconsidered intellectual autonomy from distinct approaches such as social and virtue epistemology. This paper propounds an interpersonal-epistemic approach to intellectual autonomy. First, it is argued that thinking through questioning both individually and with other epistemic peers is an interpersonal-epistemic practice. Second, it is demonstrated that with particular cognitive features inherent within us, an intellectually autonomous person must think through questioning in necessary situations. This interpersonal account of intellectual autonomy can conceptually enrich intellectual autonomy by considering its relationship with not only responsibility but also with vulnerability. Specifically, regarding responsibility, an intellectually autonomous person must be responsible for his or her own actions throughout questioning processes. Regarding vulnerability, our intellectual autonomy lies in retaining autonomy with vulnerability in the plastic control of the questioning processes. (shrink)

Background: Dementia is one the major problems of aging societies, and, novel and effective non-drug therapies are required as interventions in the oldest-old to prevent cognitive decline.Objective: This study aims to examine the efficacy and safety of reminiscence using immersive virtual reality focusing on anxiety that often appears with cognitive decline. The secondary objective is to reveal the preference for VR image types for reminiscence: live-action or computer graphics.Methods: This was a pilot, open-label, and randomized crossover study which was conducted (...) on January 2020 at a single nursing home. The subjects were randomly divided into two groups in equal numbers, and they alternately viewed two types of VR images themed on the mid- to late Showa era in Japan. In group A, the CG images were viewed first, and then the LA images were viewed. In group B, the images were viewed in the opposite order. Before VR viewing, subjects responded to Mini-Mental State Examination Japanese version and State-Trait Anxiety Inventory Japanese version. After viewing the first and second VR, subjects responded to STAI and the numerical rating scale for satisfaction and side effects.Results: Ten subjects participated in this study. The values of analyses are presented in the mean. The age was 87.1 years, and the MMSE was 28.5. The total STAI score before VR viewing was 36.1, but it significantly decreased to 26.8 after the first VR viewing, and further decreased to 23.4 after the second VR viewing. The NRS score for satisfaction tended to be higher after viewing LA in group A vs. 8.6, P = 0.0993), while in group B, the score after CG was slightly lower than that after LA. There were no serious side effects.Conclusions: This study suggests that iVR reminiscence can reduce anxiety in the oldest-old without causing serious side effects. Furthermore, the impacts might be better with LA images. (shrink)

This paper deals with two main topics: One is a semantical investigation for a bimodal language with a modal operator \blacksquare associated with the intersection of the accessibility relation R and the inequality ≠. The other is a generalization of some of the former results to general extended languages with modal operators. First, for our language L\sb{\square\blacksquare}, we prove that Segerberg's theorem (equivalence between finite frame property and finite model property) fails and establish both van Benthem-style and Goldblatt-Thomason-style characterizations. We (...) extract the notion of \blacksquare-realizer (a generalization of bulldozing) as an essence from the proofs of our results. Second, we generalize the notion of \blacksquare-realizer and prove quite general versions of these semantical characterization results. The known and previously unknown characterization results for almost all of the languages extended with modal operators already proposed will be immediate corollaries. (shrink)

Well-known critics of AI such as Hubert Dreyfus and Michael Polanyi tend to confuse cybernetics with AI. Such a confusion is quite misleading and should not be overlooked. In the first place, cybernetics is not vulnerable to criticism of AI as cognitivistic and behaviouristic. In the second place, AI researchers are recommended to consider the cybernetics approach as a way of overcoming the limitations of cognitivism and behaviourism.

We proposed the Standards of Conducts to provide a general framework that will serve as the basis for guiding each biostatistician and stem cell researcher to formulate their personal standards, rather than as rules with which they are required to comply. Given the responsibility and characteristics of their work, they are expected to maintain independence and work autonomously as professionals. Each of the Standards of Conducts comprises a preamble, mission and values to uphold, Standards of Conducts, and background. When one (...) internalizes “self-formulated” standards, to make excuses for oneself would be akin to a self-betrayal; responsible actions can be anticipated. If one begins and continues to consider “who I am and what do I work for,” this will become their inner energy, and a source of motivation and pride to inspire oneself. In addition, this aspirational style might help citizens to recognize the autonomous stance of the professional body and that they share the same values. (shrink)

The fostering of rationality has long been endorsed as an educational ideal by some philosophers; in recent years, whereas some have argued for this ideal, others have challenged it, particularly within debates relevant to the study of critical thinking. Harvey Siegel, who has spelled out the philosophical theory of educating for rationality, not only has defended his view from such challenges but also has been deepening his thoughts regarding how rationality can be fostered. This paper centers on the cultivating of (...) sensitivity to reasons in the fostering of rationality by critically examining and extending Siegel’s arguments concerning the notion of what he calls “felt reasons.” By clarifying the notion of felt reasons, I will argue for two ideas: first, teachers, parents, and fictional characters in media such as novels and films can be seen as exemplars that manifest rationality; second, the emotion of admiring exemplars may act as a motivating force for children—including small children who are still not sensitive to reasons and thus are not moved by reasons—to be critical thinkers. (shrink)

Very few attempts have been made to survey patient opinions, particularly regarding the use of residual biospecimens and health information in research, to clarify their values. We conducted a questionnaire survey that targeted outpatients of a university hospital to gauge their awareness levels and understand patient perspectives on research that uses these items. Few patients felt that obtaining individual consent for each research study was necessary. Most patients expressed the view that researchers should be obligated to inform them about the (...) research use of their items and be subject to self-directed rules. The research community should try to obtain “societal consent regarding an opt-out system” from the public. A salient value-sharing-based governance structure is necessary for obtaining public trust. (shrink)

A multilingual disaster information system (MLDI) has been developed to overcome the language barrier during times of natural disaster. MLDI is a web-based system that includes templates in nine languages so that translated texts can be made available immediately. Mobile phone e-mail with graphic text is a useful tool for delivering multilingual disaster information. The visibility of graphic text on mobile phones was measured and found to be equivalent to the built-in font. However, visibility deteriorates as the character size becomes (...) smaller, especially, on displays with poor resolution. This article also discusses the necessity of multilingual information and measures for a safe and barrier-free society. (shrink)

The priorities of French policy regarding genetically modified (GM) food shifted in the late 1990s from aggressive promotion to strict regulation based on precaution and separation of GM food. This paradigmatic policy change coincided with a rapid shift in the dominant meanings of GM food in larger French public discourses. Using data from media coverage, organizational documents, and in-depth interviews, the study examines the relationship between policy developments and GM food’s symbolic transformation. I argue that the interpretive dimension interacted with (...) and co-evolved incrementally with formal policy developments, and that it cannot be understood as epiphenomenal to political processes, or as preceding and propelling a policy change. I identify three mechanisms of symbolic transformation: (1) multiplication of meanings; (2) association with other salient issues; and (3) coupling with national identity (boundary work). Conversely, this symbolic transformation influenced the terms of political debates and viable strategies, influencing policy developments. The study also demonstrates how certain longstanding elements of French political culture shaped, and were changed or reproduced through, these processes. (shrink)