The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

In an earlier paper the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut (...) relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure , where I is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36 519–530]. (shrink)

We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...) [Formula: see text], proofs of [Formula: see text] sentences in [Formula: see text] can be translated into proofs in [Formula: see text] at a polynomial cost in size. Moreover, the [Formula: see text]-conservativity of [Formula: see text] over [Formula: see text] can be proved in [Formula: see text], a fragment of bounded arithmetic corresponding to polynomial-time computation. For [Formula: see text], this answers a question of Clote, Hájek and Paris. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

Throughout history, the generation, exercise, and dissemination of knowledge are fraught with dangers, the root causes of which are traceable to the definition of authority relations. The authors compare Greek myths and Chinese legends, setting the stage for a metarelational analysis of authority relations between teacher and students and between scholar-teachers and political rulers in Confucian-heritage cultures. These two relations are rooted in ideological conservatism. They are related in a higher-order relation or metarelation: Political control and the definition of the (...) teacher-student relationship reinforce each other in consolidating authoritarian values. Thus, ideological conservatism shapes educational philosophy and socialization. It conflicts with present demands for creativity in the service of knowledge-based economies. Hence, a major issue in cultural change to be addressed concerns the dilemma between maintaining authoritarian control and enhancing creativity. (shrink)

The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in $$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and 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}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1$$\end{document}-Foundation + V=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V=L$$\end{document} is enough to carry out finite injury arguments in 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}-recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. (shrink)

The progress of electronic health technologies and biobanks holds enormous promise for efficient research. Evidence shows that studies based on sharing and secondary use of data/samples have the potential to significantly advance medical knowledge. However, sharing of such resources for international collaboration is hampered by the lack of clarity about ethical and legal requirements for transfer of data and samples across international borders. Here, the International Clinical Trial Center Network reports the legal and ethical requirements governing data and sample exchange (...) across four continents. The most recurring requirement is ethical approval, whereas only in specific conditions approval of national health authorities is required. Informed consent is not required in all sharing situations. However, waiver of informed consent is only allowed in certain countries/regions and under certain circumstances. The current legal and ethical landscape appears to be very complex and under constant evolution. Regulations differ between countries/regions and are often incomplete, leading to uncertainty. With this work, ICN illuminates the unmet need for a single international collaborative framework to facilitate DSE. Harmonising requirements for global DSE will reduce inefficiency and waste in research. There are many challenges to realising this ambitious vision, including inconsistent terminology and definitions, and heterogeneous and dynamic legal constraints. Here, we identify areas of agreement and significant difference as a necessary first step towards facilitating international collaboration. We propose the establishment of a working group to continue the comparison across jurisdictions, create a standardised glossary and define a set of basic principles and fundamental requirements for DSE. (shrink)

ABSTRACT This study examined how lifestyle factors and gender affect kidney allocation to transplant patients by 99 British and Singaporean participants. Thirty hypothetical patients were generated from a combination of six factors and randomly paired four times. Participants saw 60 patient pairings and, in each pair, chose which patient would receive treatment priority. A Bradley-Terry model was used to derive coefficients for each factor per participant. A mean factor score was then calculated across all participants for each factor. Participants (...) gave lower priority to patients who drank more, were overweight, smoked more and exercised less. A patient’s diet and gender had no significant effect on allocation. There were no significant cross-cultural differences. There were moderate correlations between participants’ self-reported pre- and post-experiment ordering of decision criteria, and these measures and factor coefficients, suggesting a modest level of decision-making consistency. Between participants, moderate levels of concordance with respect to factor importance were observed for self-reported orderings of factors, and weaker agreement for model-derived coefficients. Very similar results were obtained for both British and Singaporean participants, and the implications of the findings are discussed. (shrink)

The Phenomenology of Spirit is both one of Hegel's most widely read books and one of his most obscure. The book is the most detailed commentary on Hegel's work available. It develops an independent philosophical account of the general theory of knowledge, culture, and history presented in the Phenomenology. In a clear and straightforward style, Terry Pinkard reconstructs Hegel's theoretical philosophy and shows its connection to ethical and political theory. He sets the work in a historical context and shows (...) the contemporary relevance of Hegel's thought for European and Anglo-American philosophers. The principal audience for the book is teachers and students of philosophy, but the great interest in Hegel's work and the clarity of Pinkard's exposition ensure that historians of ideas, political scientists, and literary theorists will also read it. (shrink)

This study examined the relationships of perceived ethical leadership, workplace jealousy, and organizational citizenship behaviors directed at individuals and organizations. Survey responses were collected from 491 employee-coworker pairs from 33 hospitals in Taiwan. The employees provided assessments of their perceived ethical leadership and the workplace jealousy they experienced, while the coworkers provided information about the employees’ OCBI and OCBO. In the hypotheses testing, perceived ethical leadership was found to be negatively related to employees’ workplace jealousy and jealousy was negatively related (...) to their OCBI and OCBO. Workplace jealousy partially mediated the effect of ethical leadership on OCBI and OCBO. In addition, perceived ethical leadership was found to have a moderation effect on the jealousy-OCBI/ocbo relationship. This study contributes to the literature of ethical leadership as well as to the literature of OCB by relating workplace jealousy to OCB and by making sense of the effects of ethical leadership on OCB through the mediation of jealousy and through the moderation of ethical leadership on the jealousy-OCB relationship. (shrink)

The essence of the associated-proposition strategy is to distinguish the necessary proposition _expressed by_ a sentence.

I thought the paper by Kai-yee Wong and Chris Fraser was fascinating and insightful. Two things I especially appreciated are the clarity with which they summarize my views. I think they are quite fair and accurate. Second, I appreciate their suggestion that the way to deal with the practical problem of weakness of will has much to do with the role of the Background in shaping our actions. I think they are especially on the right track when they say (...) that the improvement of Background skills may actually narrow the range of real options for action, (p. 21) nonetheless, they do not decrease freedom. As they say, “It is a process of strengthening the self, and the agent is likely to experience the concomitant restriction of ‘live’ options not as a limitation but as strength of character.” (p. 21). That seems to me very much on the right track. What they are suggesting, and it is a powerful addition to my own writings, is that we should not just think of the Background as facilitating languages, games and social practices generally, but for morality as well (p. 23). (shrink)

There are a number of recent attempts to introduce Confucian values to the ethical analysis of technology. These works, however, have not attended sufficiently to one central aspect of Confucianism, namely Ritual (‘Li’). Li is central to Confucian ethics, and it has been suggested that the emphasis on Li in Confucian ethics is what distinguishes it from other ethical traditions. Any discussion of Confucian ethics for technology, therefore, remains incomplete without accounting for Li. This chapter aims to elaborate on the (...) concept of Confucian Li and discuss its relevance to ethics of technology. Particularly, by referring to Li’s communicative, formative, and aesthetic function, I formulate an approach to ethics of technology with an emphasis on community, performance, and the aesthetic and demonstrate how this approach proceeds with the ethical analysis of technology. In doing so, I attempt to answer the question: why Confucianism matters in ethics of technology. (shrink)

In the second half of the eighteenth century, German philosophy came for a while to dominate European philosophy. It changed the way in which not only Europeans, but people all over the world, conceived of themselves and thought about nature, religion, human history, politics, and the structure of the human mind. In this rich and wide-ranging book, Terry Pinkard interweaves the story of 'Germany' - changing during this period from a loose collection of principalities into a newly-emerged nation with (...) a distinctive culture - with an examination of the currents and complexities of its developing philosophical thought. He examines the dominant influence of Kant, with his revolutionary emphasis on 'self-determination', and traces this influence through the development of romanticism and idealism to the critiques of post-Kantian thinkers such as Schopenhauer and Kierkegaard. His book will interest a range of readers in the history of philosophy, cultural history and the history of ideas. (shrink)

By melodic landscape, this paper points to natural milieus such as mountains whose motifs are caught up in contrapuntal relations. With Merleau-Ponty, the structure of the world is a symphony, and the production of life which implicates both organism and environment as unfurling of Umwelt is ‘a melody that sings itself’. For the Chinese culture, mountains have been deemed virtuous in Confucianism, immortal by Daoists, and spiritual for a Buddhist to reach a substrate level of pure stream of a-subjective consciousness. (...) A Chinese painter-poet within the ‘mountain-water’ genre would consider mountains as performance of events, a concert of vibration of light, shape and sound, movement and rest. Insofar as art is to create energy transfer, Chinese artists of mountains aim at concerting with nature as organised by rhythms and conspecifics, unfolding contrapuntal melodies with all kinds of counterpoints. As Deleuze and Guattari's notion of refrains are the three forces or tempos of chaos, earth and world confronting/converging one another, this paper endeavours to find out, first, how Deleuze and Guattari's geological, organic and alloplastic stratifications can be put alongside mountains, animals, plants and arts, and second, how this notion can contribute to our new appreciation of the way Chinese mountains in arts can give out music. (shrink)

The Art of War application to education is about solving problems to improve student and school success. The Art of War describes the significance of a leader and his knowledge and prudent application of the strategies. At the core of theses strategies is the non-negotiable moral purpose of the leader to be reinforced by other fine qualities as wisdom, commitment, discipline, and courage.

Some researchers have concluded that nonverbal recognition is generally superior to verbal recognition memory performance. The present study involved two experiments designed to assess claims of superior nonverbal memory. Experiment 1 compared performance for letter (common words) and nonletter (meaningful line drawings) items with matched high-imagery values. Experiment 2 compared performance for matched low-imagery items consisting of letters (pseudowords) and nonletter items (geometric matrices). Performance did not differ significantly between verbal and nonverbal items in either experiment, although the expected effects (...) of presentation rate and type of retrieval task were significant. It was concluded that recognition memory performance is not necessarily dependent upon the “verbalness ” or “non-verbalness ” of stimulus items. (shrink)

Several important physical implications left out in The Five Dimension Space-Time Universe: A creation and grand unified field theory model. Book, are presented under rigorous mathematical theorems. It was found that Temperature, a classical variable, must be added as an imaginary component to time, under the Quantum uncertainty dt∙dE = h/2π, so that the Gell-Mann Quark model can be verified, with gauge invariance, to form hadrons at the Bethe Fusion Temperature. Accordingly from the corresponding uncertainty dp∙dr = h/2π. Pairs of (...) Diagonal Long Range Ordered gravitons, with continuous frequency spectrum together with those represented by magnetic monopoles must be formed within the space r, of the homogenous 5D manifold, without the presents of photons, thus defines the 5D as a Black Hole. Then from which we can derive the classical Newtonian Law of attractive Gravity, as the 5D manifold is mapped by Perelmann Ricci-flow entropy mapping and the DLRO graviton pair symmetry is broken and converted into two masses, with motions satisfying Special Relativity in the doughnut shape Lorentz manifold, thus indirectly verifies the principle of Covariant Riemannian curvatures and General Relativity theory. (shrink)

One of the founders of modern philosophical thought Georg Wilhelm Friedrich Hegel has gained the reputation of being one of the most abstruse and impenetrable of thinkers. This major biography of Hegel offers not only a complete account of the life, but also a perspicuous overview of the key philosophical concepts in Hegel's work in a style that will be accessible to professionals and non-professionals alike. Terry Pinkard situates Hegel firmly in the historical context of his times. The story (...) of that life is of an ambitious, powerful thinker living in a period of great tumult dominated by the figure of Napoleon. The Hegel who emerges from this account is a complex, fascinating figure of European modernity, who offers us a still compelling examination of that new world born out of the political, industrial, social, and scientific revolutions of his period. (shrink)

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has only recently started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics (...) to artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

This is a fascinating study of the a-temporal nature of evil in the West. The international authors who have contributed to this text not only concentrate on political, social and legally sanctioned cruelty from the past and present, but also explore the nature of moral transgression in contemporary art, media and literature. Although many forms and practices of what might be called evil' are analysed, all are bound by violence and/or the sexually perverse.

In this book, David B. Wong defends an ambitious and important new version of moral relativism. He does not espouse the type of relativism that says anything goes, but he does start with a relativist stance against alternative theories such that there need not be only one universal truth. Wong proposes that there can be a plurality of true moralities existing across different traditions and cultures, all with one core human question as to how we can all live (...) together. (shrink)

The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...) is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF. (shrink)

Sobre la base de una línea interpretativa propiciada por la misma doctrina de Plotino, este trabajo pretende estudiar el problema que conlleva el fin último del alma humana en vista de su ascenso hacia el Uno-Bien. En varios pasajes de su obra, el filósofo sostiene que, conociendo el propio sí-mismo, se puede tomar contacto con un principio supremo, anterior incluso a la potencia intelectiva, en virtud de cuya visión es dable gozar de un amor sin medida. El remate en la (...) unificación no depende en última instancia del acierto racional, sino de concordar en el mismo centro con aquello de semejante al Uno-Bien que hay en el alma. Estas distinciones abonarían la posibilidad de una unión mística dentro del sistema plotiniano. Sin embargo, desde el punto de vista epistemológico, el estatuto místico es controvertido y plantea una serie dificultades teóricas que es necesario dilucidar. Para el análisis de los tópicos mentados se desarrolla una lectura a la vez hermenéutica y crítica tanto de las fuentes como de la bibliografía erudita. (shrink)

The present study investigates the dynamics of emotional processing and awareness using an affective facial priming paradigm in conjunction with a multimodal assessment of awareness. Key facial primes are visually masked, and are presented for brief and extended durations. Using a preference measure, we examine whether the effects of the primes differ qualitatively . We show that: unconscious affective priming with faces emerges strongly in initial presentations and diminishes rapidly with repetition; conscious affective priming also emerges strongly in initial presentations, (...) however it persists in strength with repetition; and in contrast to other reports on the salience of negative stimuli, happy faces appear more salient than sad faces when presented outside awareness. We discuss the limits and extensions of unconscious affective priming with faces, and consider several methodological and conceptual questions concerning emotional processing out of awareness. (shrink)

Why do leaders fail ethically? In this book, Terry L. Price applies a multi-disciplinary approach to an understanding of immorality in the public, private, and non-profit sectors. He argues that leaders can know that a certain kind of behavior is generally required by morality but nonetheless be mistaken as to whether the relevant moral requirement applies to them in a particular situation and whether others are protected by this requirement. Price articulates how leaders make exceptions of themselves, explains how (...) the justificatory force of leadership gives rise to such exception-making, and develops normative prescriptions that leaders should adopt as a response to this feature of their moral psychology. (shrink)

This paper is to inform the recent situations of work by the foreign domestic workers (FDWs) in Hong Kong through the lens of Covid-19. Through the interviews with seven informants — two employers and five FDWs, stories describing the changes in their working conditions, rights and entitlement, and the contextual environment related to the impacts of Covid-19 were collected. They were analysed through three theoretical tools — visibility/invisibility, mobility/immobility, and work boundary. The findings show that under the Covid-19 crisis, the (...) FDWs experienced more hardships and struggles in both the home country and host country. The paradoxes of visibility/invisibility and mobility/immobility together with blurred work boundary were found in their experience of work, rights and entitlement, and the contextual environment. On one hand, the employers’ power of controlling FDWs has increased, but the agency to resist by the FDWs has decreased making them to turn to more passive means of resistance which could harm the FDWs’ physical and mental health and wellbeing. (shrink)

In Homelessness, Liberty and Property, Terry Skolnik establishes a novel theory about the government's duties to end homelessness, maintain public property's value, and legitimize laws that regulate public space. In doing so, Skolnik provides new insight into how the property law system and the regulation of public space limit unhoused persons' freedom and political equality. The book deepens our understanding of how various areas of law, such as constitutional law, legal philosophy, criminal law, and property law, approach the reality (...) of homelessness and advances original arguments to provide new justifications for the right to housing. Skolnik concludes by offering a set of concrete proposals for how the government can reduce the incidence of homelessness and treat unhoused persons with greater concern and respect. This title is part of the Flip it Open Programme and may also be available open access. Check our website Cambridge Core for details. (shrink)

Research concerning the relationship between psychological ethical climate and job satisfaction is popular in the literature. However, to date, no study in the literature has simultaneously investigated both the effects of individual-level and organization-level ethical climates on employees’ job satisfaction. On the basis of a multilevel analysis, the present study used a sample of 472 full-time employees from 31 organizations in Taiwan to examine the above two effects. Results from the analyses showed that within the organizations, individual employees’ instrumental climate (...) perceptions were negatively related to job satisfaction, whereas their caring climate perceptions and rules climate perceptions were positively related to job satisfaction. Also, the results indicated that between organizations, organizational instrumental climate was negatively related to job satisfaction, whereas organizational caring, independence, and rules climates were positively related to job satisfaction. Implications for research and managerial practices were derived from these findings. (shrink)

Serious thinking about the computational aspects of situation theory is just starting. There have been some recent proposals in this direction (viz. PROSIT and ASTL), with varying degrees of divergence from the ontology of the theory. We believe that a programming environment incorporating bona fide situation-theoretic constructs is needed and describe our very recent BABY-SIT implementation. A detailed critical account of PROSIT and ASTL is also offered in order to compare our system with these pioneering and influential frameworks.

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has just started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics to (...) artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)