(1976). PROBABILITY, LIKELIHOOD AND SUPPORT: A METAMATHEMATICAL APPROACH TO A SYSTEM OF AXIOMS FOR UPPER AND LOWER DEGREES OF BELIEF. Philosophical Papers: Vol. 5, No. 2, pp. 153-161.

There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws. We focus on Marc Lange’s account of distinctively mathematical explanations to argue that purported mathematical explanations are essentially causal explanations in disguise and are no different from ordinary applications of mathematics. This is because these explanations work not by appealing to what the (...) world must be like as a matter of mathematical necessity but by appealing to various contingent causal facts. (shrink)

In this book, I will discuss three main topics: the roots and aims of scientific knowledge, scientific knowledge in society, and science and values I understand scientific knowledge as being a planned and continuous production of the general and common knowledge of scientific communities. I begin my discussion with a brief analysis of the main differences between sciences, on the one hand, and everyday experience, philosophies, religions, and ideologies, on the other. I define the concept of science as a set (...) of family resemblances (in Wittgenstein's sense). The sciences can be distinguished along three lines, in terms of the difference between empirical and non-empirical sciences, differences in degrees of theoretical and methodological structure among individual sciences and scientific disciplines. Scientific knowledge is based upon some grounds, paradigmatic knowledge bases. Scientific knowledge is founded on a unified paradigmatic knowledge base. The latter includes fundamental theories, basic facts, generally accepted empirical regularities (laws), scientific research methods, scientific explanations, and established relations to other sciences. Scientific knowledge in general is defined well in classical terms by the definition that knowledge is a true and rationally-justified belief. In this connection, scientific truth is relative, depending on the given paradigmatic knowledge base and on the precision and accessibility of the measurements and observations involved. In the book's first part, I consider the production and testing of scientific hypotheses, scientific explanations, the structure of scientific theories, and the problem of scientific realism. I consider explanation an integral part of a wider nexus of heuristic and theoretical activities in science like giving reasons, understanding, clarification, and founding. Continuous production of scientific explanations is a necessary condition for the systematic reproduction of scientific knowledge. Accordingly, it does not suffice to describe them in terms of the logical structure of the arguments on which they are based, but rather, scientific explanations ought to be given complete with an epistemic and pragmatic context of the explanation. I consider especially deductive-nomological, inductive-statistical, dispositional, teleological-functional, and genetic explanations. I emphasize the ever-increasing importance of explanations by analogy and by model. Orthogonal to these distinctions lies the distinction between causal and epistemic explanation. Epistemic explanations relate scientific discoveries to epistemic progress, and causal explanations are these epistemic explanations that relate scientific discoveries to reality too. Causal explanations inform us that certain changes occur in the world as agents of other changes, or rather, that certain changes are real consequences of other changes. Thus, by having explanations of causes, we can intervene in the world to induce by design certain changes in some course of phenomena. I consider scientific theories as logically and epistemically ordered wholeness of scientific knowledge in a realm of research that enables us to construct useful models of reality. After the discussion of different 'statement' views on theories and different interpretations of the theory-experience relation, I introduce the 'model' theoretical (non-statement) views on theories, especially the structural theory of science. The model views on theories transcend the realism-antirealism dualism by introducing models between theory and reality. Therefore, the question of scientific realism is not merely whether and, if so, which element(s), of scientific theories represent reality, but rather which conditions suffice to infer from a theory that one of its models truly expresses reality. In other words, under which conditions do models of a theory represent models of reality? Generally, models are just as much images of reality in a theory as they are images of a theory in reality. The actual problem of scientific realism doesn't originate in the observable-unobservable distinction (even if this distinction is otherwise theoretically loaded), but rather in ontological quandaries, of the sort especially encountered in modern physical theories such as quantum mechanics, relativity theory, and cosmological theories, although they are known to arise in other sciences as well. Scientific theories may be real, even if they describe nothing about the world. However, such theories can be given this status only if their formal, mathematical postulates exhibit some formal homology between reality and mathematical forms. The very fact that it is possible to describe reality with the help of mathematics even in cases, where every (representational, conceptual) language and thought fall short, would indicate that even mathematics itself is, in some sense, a part of reality, although 'outside' of the empirical world. It follows we have to distinguish the non-empirical reality and the empirical world. Formal objectivity and non-arbitrariness of theories do not emerge from either our language or thoughts, or from the world of facts, causes, and effects, but rather from non-empirical reality, which frames the world as some kind of objective transcendental condition for the possibility of the existence of the world, thoughts, and language. In the second part of the book, I consider the incorporation of scientific work and scientific knowledge into modern society and its relations to values and ethics. Production of scientific knowledge goes on as a parallel distributed process of a special kind of social (shared) cognition. The central part of this cognition is the presentation of parts of the world by scientific (theoretical) models which are warranted by the shared and public practice of justification, and in reflective acting in the world as it would. I consider various formal concepts of collective propositional knowledge (distributed, mutual, common knowledge). Scientific knowledge is an achievement to be ascribed to a scientific community or, indirectly, to all those who apply or expand it, rather than to individuals per se. It presents the continuous and partially planned production of non-trivial common knowledge of the research communities in modern societies. However, besides common knowledge, shared dispositional knowledge (knowledge how of scientific teams) and shared knowledge by acquiring (knowledge of fundamental similarities and differences in scientific teams) are parts of the real body of scientific knowledge. Scientific common knowledge implies the projection into idealized universal knowledge of all real or potentially rational and well-informed individuals. The respect of scientific knowledge thus presents the norm of rationality. Science as the intensively shared and socially distributed kind of cognition enters into modern society as a special kind of work (general work), as a productive force (social invention drive), and as a form of capital (human, social, cultural, informational, etc.). However any of these categories can adequately represent the socio-economical role of science in modern societies, and we are still waiting for a more adequate general concept that would theoretically cover the 'scientification' of modern societies. My thesis is that the most important general effect of scientification is (and will be) the growth of social processes that structurally resemble parallel distributed shared social cognition of science, and not so much the rise of the use of scientific knowledge and scientifically based information in all kinds of production. Scientification of modern societies inevitably includes a much stronger need for moral and social responsibility of scientists for their work and its effects in their local society and the global world. This need comes in contradiction with the quite large accepted idea (and even the 'norm') on value-free research. I discuss to some degree different arguments for the absence of non-epistemic values and ethical reasoning from science and find them non-convincing. The sound idea of value-free research lies in the need for the absence of categorical value statements from scientific explanations and theoretical deductions. Values and ethical judgment have, and sometimes they even have to play an important role in another part of research and its application in science or outside it. Not the value-loudness of research is a danger for science but its blind, non-reflective use. It leads to the ideologization and politicization of science. A similar danger lies in the purely value-neutrality of research. It leads to the instrumentalization of science to the technical or bureaucratic means for 'any' aims. (shrink)

The key concept in Kant’s aesthetics is “aesthetic reflective judgment,” a critique of which is found in Part 1 of the Critique of the Power of Judgment (1790). It is a critique inasmuch as Kant unravels previous assumptions regarding aesthetic perception. For Kant, the comparative edge of a “judgment” implicates communicability, which in turn gives it a public face; yet “reflection” points to autonomy, and the “aesthetic” shifts the emphasis away from objective properties to the subjective response evoked by the (...) object. Contrary to the view he had inherited, Kant did not treat aesthetic judgments as confused perceptions or inferior cognitions, but rather put them in a category of their own. For Kant, aesthetic reflective judgments implicated not only the processes involved in understanding the empirical world but also the processes involved in ascribing ideas or meaning to experience (which go beyond what is given in perception/cognition). This “going beyond cognition” may have been referred to by Kant as non-cognitive, but it is conditioned on a way of cognizing the object. Kant describes the features of such judgments in the Analytic of the Beautiful before addressing their possibility in subtle ways throughout the Deduction of Pure Aesthetic Judgments. Kant’s critique gives rise to three apparent dichotomies: immediate intuition and prior learning; autonomy and communicability; and non-cognitive response and aesthetic ideas. An interpretation of Kant’s theory can be deemed correct to the degree that it succeeds in showing that the contradictions are only apparent. I will argue that the resulting positive account of Kant’s aesthetic theory offers an understanding of aesthetic reflective judgment that is quite different from the standard formalism that the critics of formalism usually target and by which they misrepresent Kant’s aesthetic theory. When I refer to Kant’s formalism, then, I mean something quite different by this than what is meant by “standard formalism.” The latter is the representation given Kant’s formalism by its contemporary critics and is the typical account of formalism found in the art theory and philosophy of art literature, as will be demonstrated. (shrink)

What is the appropriate degree of abstraction from existing social facts when engaging in normative political theory? Through a focus on American Indian and other indigenous claims over historically expropriated lands, this essay argues that highly abstracted forms of normative analysis can often misunderstand the core moral problems at stake in real cases, and that they can pose moral dangers when they do so. As argued, the hard moral issues involved in indigenous land claims within countries such as Canada and (...) the United States often have far more to do with questions about competing uses for public lands than with abstract property theory as such. The essay argues that normative theorists will often do more social good, and pose fewer dangers, when they pay close attention to the real moral challenges that social actors face on the ground than when they become captured by abstract questions with ambiguous practical importance. (shrink)

This chapter suggests that the state of nature is a continuum notion that lies in a segment along a larger continuum of the scope of private judgment, as does the continuum notion of civil authority. Jean Hampton saw Thomas Hobbes's state of nature as a “presocietal” condition of “isolated asocial individuals,” “stripped of their social connections.” There is plentiful evidence against Hampton's interpretation of the state of nature as an “asocial” condition in Hobbes's insistence across all his political writings that (...) men care deeply about their relative social standing and reputations, and that this is a major source of conflict in a state of nature. A potentially more promising way of understanding the state of nature is as a lawless condition. Societies exhibiting a high degree of consensus among private judgments may be able to tolerate incomplete removal from the mere state of nature, without threat to their stability. (shrink)

It has become commonplace to ask, whenever anything has gone wrong, what lessons can be learned from the experience. But the appearance of open‐endedness in that question is misleading: not every answer that we could give to it is acceptable. There are, in the context of such a question, tacit constraints in what counts as a valid lesson to be learned. The article considers what these constraints might be and the different kinds of lessons one might learn from experience, which (...) the common way of taking the question ignores. Initially I attempt to distinguish between lessons that have to do with action and those that have to do with understanding, between lessons that are about the results of our actions and those that are about the meaning of actions and events. On closer examination, however, these distinctions are seen to break down, to represent a difference of degree rather than of kind. In the latter part of the article, therefore, I find the crucial distinction to be between lessons that we can apply, while being ourselves unchanged, and lessons which, by changing the way in which we see and respond to people and events, re‐constitute ourselves and thus express themselves through us willy‐nilly in our subsequent thoughts, words and actions. (shrink)

This paper describes and defends the view that minimal chemical life essentially involves the chemical integration of three chemical functionalities: containment, metabolism, and program (Rasmussen et al. in Protocells: bridging nonliving and living matter, 2009a ). This view is illustrated and explained with the help of CMP and Rasmussen diagrams (Rasmussen et al. In: Rasmussen et al. (eds.) in Protocells: bridging nonliving and living matter, 71–100, 2009b ), both of which represent the key chemical functional dependencies among containment, metabolism, and (...) program. The CMP model of minimal chemical life gains some support from the broad view of life as open-ended evolution, which I have defended elsewhere (Bedau in The philosophy of artificial life, 1996 ; Bedau in Artificial Life, 4:125–140, 1998 ). Further support comes from the natural way the CMP model resolves the puzzle about whether life is a matter of degree. (shrink)

The world of the Na'vi is much more feminine. Na'vi women are equal partners with their men and are just as capable as their male counterparts. And as the tsahìk (spiritual leader) of the Omaticaya clan, Neytiri's mother Mo'at exercises an unrivalled degree of power and influence due to her ability to interpret the will of Eywa, the Na'vi's female deity. Historically, women are the ones who have had the most intimate experience of care, since they have traditionally been the (...) ones tasked with providing it for children, the sick, the disabled, and the elderly. The philosopher Sara Ruddick (1935–2011), one of the pioneers of care ethics, identified three activities at the core of what she calls “maternal work”: preserving the life of the child, fostering the growth of the child, and training the child for social acceptability. (shrink)

We construct a nonlow2 r.e. degree d such that every positive extension of embeddings property that holds below every low2 degree holds below d. Indeed, we can also guarantee the converse so that there is a low r.e. degree c such that that the extension of embeddings properties true below c are exactly the ones true belowd.Moreover, we can also guarantee that no b ≤ d is the base of a nonsplitting pair.

With the recent Clinical Trials Directive, a degree of harmonisation into research ethics committees across Europe, including the time taken to assess a trial proposal and the kinds of issues a committee should take into account, has been introduced by the European Union . How four different member states—Hungary, Portugal, Sweden and the UK—have chosen to implement the directive is shown. Although this has resulted in four very different ways of structuring RECs, similar themes are present in all four cases, (...) such as centralisation of control over RECs within member states, harmonisation of REC procedures across the EU and increased role of political decision making with regard to such committees. (shrink)

Background: The magnitude of bullying and harassment among psychiatrists is reportedly high, yet no peer-review published studies addressing this issue could be found. Therefore, it was decided to conduct a pilot study to assess the degree of the problem, the types of bullying/harassment and to provide some insights into the situation.Methods and Principal Findings: Following multiple focus group meetings, a yes/no response type questionnaire was developed to assess the degree and type of bullying and harassment experienced by psychiatrists. Over a (...) 3-month period the questionnaire was administered to a random sample of 60 psychiatrists. 57 out of the 60 psychiatrists reported harassment and bullying. Frequencies of the following response variables are presented in descending order: rumours 40% ; defamation 20% ; passing remarks 20% ; false accusations 15% ; threats 13.3% ; verbal abuse 13.3% ; unjustified complaints 13.3% ; promotion blocked 13.3% ; humiliation 13% ; bad reference given 10% ; credentials questioned 8.3% ; physical attacks 5% ; termination 5% ; derogatory remarks 1.7% and 1.7% were subjected to personal work. As a result of being subjected to harassment, 66.7% of the psychiatrists did not take any action, whereas 33.3% confronted the person they believed responsible. Asked whether the bullying and harassment caused distress, 18.3% of the psychiatrists did not report any effect, 30% reported mild distress, 40% moderate distress and severe distress was reported by 11.7%.Conclusions: It was concluded that the magnitude of bullying and harassment among psychiatrists may be quite high, as evidenced by this pilot study. There is a need for extensive systematic studies on this subject and to establish strategies to prevent and address this issue at a national and regulatory level. (shrink)

We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half of a nontrivial relativized $\mathcal {K}$ -pair. This leads to a structural dichotomy in the enumeration degrees.

What is the relation between ‘full’ or ‘outright’ belief and the various levels of confidence that agents can have in the propositions that concern them? This paper argues for a new answer to this question. Decision theory implies that in making decisions, rational agents must treat certain propositions as though they were completely certain; but on most forms of decision theory, these propositions are not ones for which any finite agent could have maximal justification – the agent will clearly have (...) less justification for these propositions than for elementary logical truths. Thus, every adequate model of a finite rational agent's belief‐system must involve two set of credences – theoretical credences and practical credences . A full or outright belief in p can be defined as the state of being stably disposed to assign a practical credence of 1 to p, for all normal practical purposes. This definition allows for a kind of reconciliation between the pragmatist and intellectualist approaches in epistemology. (shrink)

This article falls into two parts: the first is an analysis, in the light of my earlier discussions of and of the Homeric usage of and the second, an attempt to show that, as in the case of the effects of Homeric usage persist to a considerable degree in the moral philosophy of Aristotle. In the earlier discussions I have argued that the higher value placed upon the competitive in Greek entails that co-operative relationships, even when valued and necessary, take (...) the form dictated by the more valued qualities, the The most general words to denote co-operative relationships in Greek are and its derivatives: my purpose here is to show how the Homeric usage of these words is related to the Homeric standard and to Homeric society, and to sketch in the outline of a wider discussion, which I hope to be able to fill in later. (shrink)

The study aimed to identify the role of administrative procedures and systems in enhancing the performance of the educational institutions in the Islamic University in Gaza. To achieve the research objectives, the researchers used the analytical descriptive approach to collect information. The researchers used the questionnaire distributed to three categories of employees at the Islamic University (senior management, faculty members, their assistants and members of the administrative board). A random sample of 314 employees was selected and 276 questionnaires were retrieved (...) with a recovery rate of 88.1%. The Statistical Analysis Program (SPSS) was used to enter process and analyze data. The results of the research showed a positive role for the administrative procedures and systems in enhancing the performance of the Islamic University from the point of view of the members (senior management, teaching staff and their assistants and the administrative body), where the relative weight of all the paragraphs (73.728%). The analysis of the results revealed that the administrative procedures at the Islamic University in Gaza are used to an acceptable degree. The relative weight of all the paragraphs is 70%. This indicates a relationship between administrative procedures and regulations and the performance of the Islamic University in the Gaza Strip. The study found that there was a good degree of approval from the sample regarding the administrative procedures and their relationship to the job performance. There exist a sufficient degree of powers to the deans and department managers to carry out their tasks, with the use of plans as control tools. And that there are rules and procedures provided for decision-making in the University Council. It also has full powers to manage the university to improve the teaching and learning environment. The researchers also recommended a number of recommendations, including the need to follow up on the procedures and systems of management and update them continuously in the light of changes that may occur and to ensure the existence of a strong system of electronic information systems within the university. There is a need to provide mechanisms for obtaining information about the surrounding external environment, and effective mechanisms to provide managers with the necessary information in a timely manner. The importance of providing channels of communication that enables staff to communicate information about any violations and breaches. The study also recommended the follow-up, review, procedures and administrative systems, and work to modify them in line with the mission of the university and the objectives that the university seeks to reach. (shrink)

This article falls into two parts: the first is an analysis, in the light of my earlier discussions of and of the Homeric usage of and the second, an attempt to show that, as in the case of the effects of Homeric usage persist to a considerable degree in the moral philosophy of Aristotle. In the earlier discussions I have argued that the higher value placed upon the competitive in Greek entails that co-operative relationships, even when valued and necessary, take (...) the form dictated by the more valued qualities, the The most general words to denote co-operative relationships in Greek are and its derivatives: my purpose here is to show how the Homeric usage of these words is related to the Homeric standard and to Homeric society, and to sketch in the outline of a wider discussion, which I hope to be able to fill in later. (shrink)

Robert Veatch has proposed a model of the doctor-patient relationship that has as its foundation the sharing of values between the doctor and the patient. This paper uses qualitative research conducted with six doctors involved in the long term, specialised care of HIV positive patients in South Australia to explore the practical application of Veatch’s value sharing model in that setting. The research found that the doctors in this study linked “values” with sexual identity such that they defined value sharing, (...) in part, as a shared set of values and beliefs about sexual identity and practices. They voluntarily identified themselves as either homosexual or heterosexual and they regarded the relation between their own sexual identity and that of their patients as important for the provision of quality care. None of the doctors thought that value sharing, in the way they defined it, was essential to the clinical relationship, but the homosexual doctors attributed a greater degree of importance to it than their heterosexual colleagues. (shrink)

The paper examines a single, apparently simple argument for the existence of incompatibilities between the virtues as traits of character. This argument appeals not to empirical truths about human psychology or human nature but to the possibility of conflict between the exercise of different virtues in action. There are, for example, situations in which we can exercise the virtue of truthfulness only at the expense of not exercising the virtue of tact, as when we are asked a question to which (...) the straightforward answer will pain our questioner. The person who in these situations would give a straightforward answer possesses the virtue of truthfulness to a higher degree than the person who would respond more evasively, whereas the latter person possesses the virtue of tact to a higher degree than the former. But since the two responses are mutually exclusive, it follows that the degree to which we possess the virtue of truthfulness must, at least in some measure, correlate inversely with the degree to which we possess the virtue of tact. And similarly for many other pairs of virtues. My paper focusses on the two cardinal assumptions of this argument, viz., (i) that sometimes the exercise of one virtue can conflict with the exercise of another, and (ii) that the degree to which a person possesses a virtue correlates directly with the extent of its exercise, and defends both assumptions against a variety of objections which allege that, in different ways, they are insensitive to the complexity of the virtues. (shrink)

We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half a nontrivial relativized K-pair. This leads to a structural dichotomy in the enumeration degrees.

This article falls into two parts: the first is an analysis, in the light of my earlier discussions of and of the Homeric usage of and the second, an attempt to show that, as in the case of the effects of Homeric usage persist to a considerable degree in the moral philosophy of Aristotle. In the earlier discussions I have argued that the higher value placed upon the competitive in Greek entails that co-operative relationships, even when valued and necessary, take (...) the form dictated by the more valued qualities, the The most general words to denote co-operative relationships in Greek are and its derivatives: my purpose here is to show how the Homeric usage of these words is related to the Homeric standard and to Homeric society, and to sketch in the outline of a wider discussion, which I hope to be able to fill in later. (shrink)

For-profit degree granting institutions are a growing and under-researched market segment that represents an extreme level of business involvement in academe. Permitting such institutions to grant degrees is a concern because the profit motive gives an incentive to operators to misrepresent the quality and benefits of such degrees. This paper addresses the issue of how adequately government quality assurance processes are able to protect the public interest. The degree program approval processes in three countries are evaluated using the (...) UNESCO guidelines for cross-border quality provision in higher education as an internationally accepted standard of quality assurance. (shrink)

To approach the many challenges involved in the notion of engineering concepts, it is important to have a clear idea of the starting point – the concepts that people use in their everyday lives, in conversations and in expressing beliefs, desires, intentions and so forth. The first Section of this chapter introduces evidence that I have accumulated over the last many years concerning the flexibility, context-dependence, and vagueness of such common concepts. The concept engineer needs to understand the structure of (...) the “raw material” with which she is working. In Section 2, I summarise some results concerning the amount of individual variation that exists within a single relatively homogenous population of individuals, both in what examples are considered most typical of a category, and in what properties are considered most central to a category (Hampton & Passanisi, 2016). The demonstration of a significant degree of reliable variation in responses to these questions, that is stable over time, illustrates the potential for conceptual engineering interventions to affect individuals’ concepts. Concepts are rarely fixed or uniformly understood in the same way. I then discuss the different ways in which concepts track the world, and I speculate about how different conceptual domains are governed by different criteria of validity or acceptability. This reflection will lead to Section 3 in which I summarise some results from recent research (Thorne, Quilty-Dunn, Smortchova, Shea, & Hampton, 2021), investigating for the first time how people view the value of different familiar concepts. Knowing how people appraise concepts will be a key to developing ideas for improving the reliability and validity of the concepts that they commonly use. A final section contains some (largely speculative) discussion about the implications of work in psychology of concepts for the project of conceptual engineering. (shrink)

The Johns Hopkins-Fogarty African Bioethics Training Program (FABTP) has offered a fully-funded, one-year, non-degree training opportunity in research ethics to health professionals, ethics committee members, scholars, journalists and scientists from countries across sub-Saharan Africa. In the first 9 years of operation, 28 trainees from 13 African countries have trained with FABTP. Any capacity building investment requires periodic critical evaluation of the impact that training dollars produce. In this paper we describe and evaluate FABTP and the efforts of its trainees.Our data (...) show that since 2001, the 28 former FABTP trainees have authored or co-authored 105 new bioethics-related publications; were awarded 33 bioethics-related grants; played key roles on 78 bioethics-related research studies; and participated in 198 bioethics workshops or conferences. Over the past nine years, trainees have collectively taught 48 separate courses related to bioethics and have given 170 presentations on various topics in the field. Many former trainees have pursued and completed doctoral degrees in bioethics; some have become editorial board members for bioethics journals. Female trainees were, on average, less experienced at matriculation and produced fewer post-training outputs than their male counterparts. More comprehensive studies are needed to determine the relationships between age, sex, previous experience and training program outputs. (shrink)

We work with weakly precomplete equivalence relations introduced by Badaev. The weak precompleteness is a natural notion inspired by various fixed point theorems in computability theory. Let E be an equivalence relation on the set of natural numbers $$\omega $$, having at least two classes. A total function f is a diagonal function for E if for every x, the numbers x and f(x) are not E-equivalent. It is known that in the case of c.e. relations E, the weak precompleteness (...) of E is equivalent to the lack of computable diagonal functions for E. Here we prove that this result fails already for $$\Delta ^0_2$$ equivalence relations, starting with the $$\Pi ^{-1}_2$$ level. We focus on the Turing degrees of possible diagonal functions. We prove that for any noncomputable c.e. degree $${\textbf{d}}$$, there exists a weakly precomplete c.e. equivalence E admitting a $${\textbf{d}}$$ -computable diagonal function. We observe that a Turing degree $${\textbf{d}}$$ can compute a diagonal function for every $$\Delta ^0_2$$ equivalence relation E if and only if $${\textbf{d}}$$ computes $${\textbf{0}}'$$. On the other hand, every PA degree can compute a diagonal function for an arbitrary c.e. equivalence E. In addition, if $${\textbf{d}}$$ computes diagonal functions for all c.e. E, then $${\textbf{d}}$$ must be a DNC degree. (shrink)

Our research’s aim is to assess the effect of cultural factors on business ethical decision-making process in a Western cultural context and in a non-Western cultural context. Specifically, this study investigates ethical perceptions, religiosity, personal moral philosophies, corporate ethical values, gender, and ethical intentions of U.S. and Moroccan business managers. The findings demonstrate that significant differences do exist between the two countries in idealism and relativism. Moroccan managers tend to be more idealistic than the U.S. managers. There is a strong (...) positive relationship between religiosity and idealism. There were mixed findings in examining the correlates of religiosity and various components of ethical intentions. Moroccan managers were more homogenous in their corporate ethical values than were the U.S. managers. The results demonstrate that (in general) idealism is a good predictor of ethical intentions and behaviors. Additionally, managers from the two countries differed in the degree of relationship between perceptions and intentions in three of the four scenarios. This study’s results confirm other research findings that, in general, female business managers have higher ethical sensitivity in terms of their ethical judgment than their male counterparts. Managerial implications are also discussed. (shrink)

Real-world information is imperfect and is usually described in natural language (NL). Moreover, this information is often partially reliable and a degree of reliability is also expressed in NL. In view of this, the concept of a Z-number is a more adequate concept for the description of real-world information. The main critical problem that naturally arises in processing Z-numbers-based information is the computation with Z-numbers. Nowadays, there is no arithmetic of Z-numbers suggested in existing literature. This book is the first (...) to present a comprehensive and self-contained theory of Z-arithmetic and its applications. Many of the concepts and techniques described in the book, with carefully worked-out examples, are original and appear in the literature for the first time. The book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics. (shrink)

I explore the view that the imago Dei is essential to us as humans but accidental to us as persons. To image God is to resemble God, and resemblance comes in degrees. This has the straightforward—and perhaps disturbing—implication that we can be more or less human, and possibly cease to be human entirely. Hence, I call it the spectrum view. I argue that the spectrum view is complementary to the Biblical data, helps explain the empirical reality of horrendous evil, (...) and offers an elegant rapprochement between the traditional view of hell and its rivals. (shrink)

In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute (...) the distances between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region. Keywords: Neutrosophic Crisp Points; Neutrosophic Crisp Relations; Neutrosophic Crisp Sets; Neutrosophic Crisp Continuous Function; Neutrosophic Crisp Compact Spaces; Neutrosophic Crisp Nearly Open Sets; Neutrosophic Crisp Ideals; Neutrosophic Crisp Filter; Neutrosophic Crisp Local Functions; Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals; Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity; Neutrosophic Topological Region; Neutrosophic Closed Set and Neutrosophic Continuous Function; Neutrosophic Hesitancy Degree; Neutrosophic Crisp Topological Space; Neutrosophic Database; Neutrosophic Logic Manipulation; Neutrosophic Spatial Region. (shrink)

In order that a degree-of-belief function be coherent it is necessary and sufficient that it satisfy the axioms of probability theory. This theorem relies heavily for its proof on the two-valued sentential calculus, which emerges as a limiting case of a continuous scale of truth-values. In this "continuum of certainty" a theorem analogous to that instanced above is proved.

Referring to the phenomenon of structural injustice resulting from unintended consequences of the combination of the actions of many people, Iris Marion Young claims for a new understanding of responsibility. She proposes what she calls a social connection model of responsibility which assigns responsibility to individuals also for participating in ongoing structural and social processes. To remedy structural injustice Young claims for collective action of various actors in society and assigns different degrees of responsibility depending on the agent’s position (...) within the structural process. However, although Young mentions power, privilege, interest, and collective ability as parameters influencing the degree of an actor’s responsibility to contribute to structural change she does not elaborate which responsibilities concern which groups in society. As we will outline in our contribution, we hold the tenet of subsidiarity to be a useful supplement to the conception of Iris Marion Young which would allow for assigning such responsibilities to different layers in society. However, since the tenet of subsidiarity is only a supple principle which does not distinguish between different kinds of duties, we propose to enrich the tenet of subsidiarity by the Kantian conception of perfect and imperfect duties. (shrink)

Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study (...) a second-order equation was introduced similar to the second-order Dirac equation, based on a quadratic function of two operators which are the self-adjoint parts, in this new scalar product, of γμpμ. It is shown in this paper that one of these operators, in fact the one from which the gyromagnetic moment is obtained, can be used to construct a first-order equation. The corresponding quantum theory is somewhat analogous to Dirac's spinor form; the Hamilton equations appear to describe dynamical degrees of freedom in a spacelike hyperplane orthogonal to nμ (in Dirac's theory the motion appears to be lightlike). It is shown that the integration over nμ required by unitarity results in timelike motion (as in the expectation value of Dirac's α). Explicit forms are obtained for the wave functions and currents for free motion. The general form of the theory is written for the (five-dimensional) pre-Maxwell fields required by gauge invariance. (shrink)

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)