A challenge in human genome research is how to describe the populations being studied. The use of improper and/or imprecise terms has the potential to both generate and reinforce prejudices and to diminish the clinical value of the research. The issue of population descriptors has not attracted enough academic attention outside North America and Europe. In January 2012, we held a two-day workshop, the first of its kind in Japan, to engage in interdisciplinary dialogue between scholars in the humanities, social (...) sciences, medical sciences, and genetics to begin an ongoing discussion of the social and ethical issues associated with population descriptors. (shrink)

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...) subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate. (shrink)

Truth is often considered to be a logico-linguistic tool for expressing indirect endorsements and infinite conjunctions. In this article, I will point out another logico-linguistic function of truth: to enable and validate what I call a blind argument, namely, an argument that involves indirectly endorsed statements. Admitting this function among the logico-linguistic functions of truth has some interesting consequences. In particular, it yields a new type of so-called conservativeness argument, which poses a new type of threat to deflationism about truth.

We discuss the work of Paul Cohen in set theory and its influence, especially the background, discovery, development of forcing.

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...) distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science. (shrink)

We introduce and analyze a new axiomatic theory$\mathsf {CD}$of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that$\mathsf {CD}$is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are (...) restricted todeterminatesentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of$\mathsf {CD}$are analyzed. (shrink)

The Sustainable Development Goal of the United Nations related to reduced inequalities calls for greater economic inclusion of the poor. Yet, how business leaders grant economic opportunities and development to the poor is significantly under-researched. Extending burgeoning responsible leadership theory that promotes paradox-savvy leadership for building inclusive ventures through various actors, this study introduces new concepts of inclusive leadership that foster the economic inclusion of the poor from Amartya Sen’s capability approach perspective. By studying how leaders include the poor in (...) social businesses, we provide a fresh perspective of inclusive leadership as a personalized empowering cycle of economic–social–economic inclusion to close the gaps between the rich and poor in business and society. This perspective provides new territories of diversity and inclusion research for reduced inequality. (shrink)

This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.

Azriel Levy did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcing and definability will continue to be basic to the subject. What follows is a detailed account and analysis of Levy’s work and contributions (...) to set theory. (shrink)

This paper studies several systems of the transfinite iteration and autonomous progression of self-applicable truth and determines their proof-theoretic strength.

This is the softcover reprint of the very popular hardcover edition. The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research. (...) A a oegenetica approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections. (shrink)

After publishing his first collection of poems entitled Interrogation (1917), Pierre Drieu La Rochelle returned to writing on the First World War in La Comédie de Charleroi (1934). The writer examined the moral and political significance of the “last war” in a retrospective manner in this collection of autobiographical short stories that he published just before his conversion to Fascism. However, Drieu did not treat his experience of the war as a distant memory. On the contrary, his texts are characterised (...) by emotivity, as if he was attempting to relive the very moment of his war. From this point of view, we examine the style and narrative structure of “La Comédie de Charleroi”. In this short story which opens the book, Drieu created a poetic narrative by mixing narrative prose and lyricism, and thus undermined realistic chronology. By means of this poetic narrative, he wrote his memory of the “last war” and, at the same time, expressed his “cry” which was the leitmotiv of his first collection of poems. This literary experience seems to have had an ideological consequence, as shown in Socialisme fasciste (1934). (shrink)

This study provides much-needed empirical study of workplace inclusion of underresourced employees of low socioeconomic status. Based upon a conservation of resources perspective, we have examined the centrality of resources as a key inclusion process for well-being outcomes for employees with insufficient resources. In the context of misuse of institutional power over operative workers within highly segmented and hierarchical work settings, this study validates the importance of economic inclusion for fostering workers’ well-being via fair employment practices. This study also offers (...) new knowledge of the integrative resource model of workplace inclusion research by validating workers’ personal resources of learning orientation as an internal condition for strengthening the positive effect of economic inclusion on well-being. (shrink)

メタ倫理学、規範倫理学、応用倫理学を体系的に概説した入門書。大学における倫理学教育のミニマム・エッセンスを体系的に学べるユニークなテキスト。.

The author reflects on his long career as an educational psychologist and on the role of literature in his vision of psychological science. The author followed with great interest the major developments in psychology around the world, but he felt himself progressively alienated from the revealing power of art and literature. At one moment, he realized that a simple narrative constitutes the most profound and also the most effective means of transmitting genuine insights about teaching from one generation to another. (...) This narrative reveals a career guided by high ideals and compromised by the harsh realities of the discipline of psychology. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, (...) are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...) set theory has proceeded in the opposite direction, from a web of intensions to a theory of extensionpar excellence, and like other fields of mathematics its vitality and progress have depended on a steadily growing core of mathematical structures and methods, problems and results. There is also the stronger contention that from the beginning set theory actually developed through a progression ofmathematicalmoves, whatever and sometimes in spite of what has been claimed on its behalf.What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory. The whole transfinite landscape can be viewed as the result of Cantor's attempt to articulate and solve the Continuum Problem. (shrink)

コンピュータの歴史、アルゴリズムの理論の解説を経て、未解決であるミレニアム問題のひとつ、「P≠NP問題」に迫ります!

RésuméDans la partie duŠifāʾqui porte “sur les plantes”, Avicenne aboutit à cette conclusion inattendue que celles-ci ne seraient pas vivantes. Cette thèse surprend étant donné l'opinion d'Aristote voulant que tout ce qui a une âme est vivant. Cet article montre qu'Avicenne a évolué quant à la question de la vie des plantes. Il commence par adopter la conception aristotélicienne selon laquelle les plantes sont vivantes dans la mesure où elles sont dotées d'une âme, comme il ressort de son œuvre précoce (...) qu'est leCompendium sur l'âme.Ensuite cependant, une fois qu'Avicenne a analysé les facultés de l'âme comme il le fait principalement dans sonCanon de Médecine, il est conduit à conclure que les plantes ne pouvaient pas être dites vivantes. Cet article illustre ainsi l'intérêt qu'il y a, lorsqu'on étudie le développement de la pensée d'Avicenne, à prendre en compte l'impact de ses découvertes médicales sur ses réflexions philosophiques. (shrink)

Web-based learning resources provide learners with hyperspace where they can navigate in a self-directed way to learn the contents included in the Web pages. The navigation involves making a sequence of the pages visited, which is called navigation path. However, learners often fail in making the navigation path due to a cognitive overload, which is caused by diverse cognitive efforts at comprehending the contents in Web pages, and monitoring the navigation process such as planning and reflection of navigation path. In (...) the self-directed learning, in particular, it is difficult for learners to maintain the navigation monitoring. Focusing on navigation planning, this paper addresses the issue of how to facilitate learners' navigation monitoring to promote their learning in hyperspace provided by Web-based learning resources. Our approach to this issue is to provide learners with a space, in which they can see through the learning resources to plan a navigation path, apart from hyperspace. In this paper, we also demonstrate an assistant system for the navigation planning, which is composed of hyperspace map, page previewer, and path previewer. These facilities give learners an overview of Web pages and navigation path to help them make a navigation path plan without visiting Web pages in hyperspace. This paper also describes a case study with the assistant system. The results indicate that the system facilitates navigation particularly in a more complicated hyperspace. (shrink)

For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Choice (...) are broached in the formal elaboration of the ‘set of’f {} operation. So it is surprising that, while these notions are unproblematic today, they were once sources of considerable concern and confusion among leading pioneers of mathematical logic like Frege, Russell, Dedekind, and Peano. In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic: the shift from the intensional to the extensional viewpoint, the development of type distinctions, the logical vs. the iterative conception of set, and the emergence of various concepts and principles as distinctively set-theoretic rather than purely logical. Here there is a loose analogy with Tarski's recursive definition of truth for formal languages: The mathematical interest lies mainly in the procedure of recursion and the attendant formal semantics in model theory, whereas the philosophical interest lies mainly in the basis of the recursion, truth and meaning at the level of basic predication. Circling back to the beginning, we shall see how central the empty set, the singleton, and the ordered pair were, after all. (shrink)

Kurt Gödel with his work on the constructible universeLestablished the relative consistency of the Axiom of Choice and the Continuum Hypothesis. More broadly, he ensured the ascendancy of first-order logic as the framework and a matter of method for set theory and secured the cumulative hierarchy view of the universe of sets. Gödel thereby transformed set theory and launched it with structured subject matter and specific methods of proof. In later years Gödel worked on a variety of set theoretic constructions (...) and speculated about how problems might be settled with new axioms. We here chronicle this development from the point of view of the evolution of set theory as a field of mathematics. Much has been written, of course, about Gödel's work in set theory, from textbook expositions to the introductory notes to his collected papers. The present account presents an integrated view of the historical and mathematical development as supported by his recently published lectures and correspondence. Beyond the surface of things we delve deeper into the mathematics. What emerges are the roots and anticipations in work of Russell and Hilbert, and most prominently the sustained motif of truth as formalizable in the “next higher system”. We especially work at bringing out how transforming Gödel's work was for set theory. It is difficult now to see what conceptual and technical distance Gödel had to cover and how dramatic his re-orientation of set theory was. (shrink)

In this article we study the systems KF and VF of truth over set theory as well as related systems and compare them with the corresponding systems over arithmetic.

On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.

Deflationism about truth describes truth as a logical notion. In the present paper, I explore the implication of the alleged logicality of truth from the perspective of axiomatic theories of truth, and argue that the deflationist doctrine of the logicality of truth gives rise to two types of self-undermining arguments against deflationism, which I call the conservativeness argument from logicality and the topic-neutrality argument.

Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets. Then, what are classes? Predicativism about classes suggests that classes are predicates of sets, and this article investigates the question from the predicativist point of view in light of recent developments in the use of classes in set theory. Predicativism has been considered too restrictive and unable to accommodate (...) the use of classes in set theory. This diagnosis, however, is only true of a certain specific type of predicativism. In this article, we propose a new type of predicativism, which we call liberal predicativism, and argue that predicativism is still a highly viable option, and our liberal version provides a sufficiently versatile and workable nominalist concept of classes for set theory. (shrink)

Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. Two (...) decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory and championed the use of infinitary logic, anticipating broad modern developments. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the awareness of what has endured in the subsequent development of set theory. Elaborating formulations and results are provided, and special emphasis is placed on the to and fro surrounding the Schröder-Bernstein Theorem and the correspondence and comparative approaches of Zermelo and Gödel. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details. (shrink)

This paper describes availability of personal Web-pages and a prototype development for Decision Support for Internet Users, called DSIU, which is an area of research for decision support by using information on the Internet. The availability of Web-pages concerns usage of formal pages, which are provided by companies and so on, and personal pages, which are provided by private persons. Web-pages are gathered by using an Internet search engine to determine destinations for travel and personal pages are confirmed to provide (...) much subjective information than formal pages. The prototype development concerns a travel recommendation system, which is a kind of decision support systems. The prototype uses subjective and objective information on the Internet to select several destinations for users and to provide explanations the reason why the destinations are recommended. This paper also describes our perspective of DSIU researches. (shrink)

Audrito and Viale introduced the new large cardinal notion of an (α)‐uplifting cardinal (for an ordinal α). We shall show that this notion cannot be defined (or expressed) in the standard first‐order language of set theory for every tranfinite α.