The general framework of this paper is a reformulation of Hilbert’s program using the theory of locales, also known as formal or point-free topology [P.T. Johnstone, Stone Spaces, in: Cambridge Studies in Advanced Mathematics, vol. 3, 1982; Th. Coquand, G. Sambin, J. Smith, S. Valentini, Inductively generated formal topologies, Ann. Pure Appl. Logic 124 71–106; G. Sambin, Intuitionistic formal spaces–a first communication, in: D. Skordev , Mathematical Logic and its Applications, Plenum, New York, 1987, pp. 187–204]. Formal topology presents (...) a topological space, not as a set of points, but as a logical theory which describes the lattice of open sets. The application to Hilbert’s program is then the following. Hilbert’s ideal objects are represented by points of such a formal space. There are general methods to “eliminate” the use of points, close to the notion of forcing and to the “elimination of choice sequences” in intuitionist mathematics, which correspond to Hilbert’s required elimination of ideal objects. This paper illustrates further this general program on the notion of valuations. They were introduced by Dedekind and Weber [R. Dedekind, H. Weber, Theorie des algebraischen Funktionen einer Veränderlichen, J. de Crelle t. XCII 181–290] to give a rigorous presentation of Riemann surfaces. It can be argued that it is one of the first example in mathematics of point-free representation of spaces [N. Bourbaki, Eléments de Mathématique. Algèbre commutative, Hermann, Paris, 1965, Chapitre 7]. It is thus of historical and conceptual interest to be able to represent this notion in formal topology. (shrink)

We associate with any game G another game, which is a variant of it, and which we call . Winning strategies for have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over , and vice versa. Through we can express in algorithmic form, as a recursive winning strategy, many common proofs of non-constructive Mathematics, namely exactly the theorems of the (...) sub-classical logic Limit Computable Mathematics [6], Hayashi and Nakata [7]). (shrink)

This work concerns constructive aspects of measure theory. By considering metric completions of Boolean algebras – an approach first suggested by Kolmogorov – one can give a very simple construction of e.g. the Lebesgue measure on the unit interval. The integration spaces of Bishop and Cheng turn out to give examples of such Boolean algebras. We analyse next the notion of Borel subsets. We show that the algebra of such subsets can be characterised in a pointfree and constructive way by (...) an initiality condition. We then use our work to define in a purely inductive way the measure of Borel subsets. (shrink)

Our ultimate purpose is to give an axiomatic treatment of recursion theory sufficient to develop the priority method. The direct or abstract approach is to keep in mind as clearly as possible the methods actually used in recursion theory, and then to formulate them explicitly. The indirect or experimental approach is to look first for other mathematical theories which seem similar to recursion theory, to formulate the analogies precisely, and then to search for an axiomatic treatment which covers not only (...) recursion theory but also the analogous theories as particular cases.The first approach is more general because it does not depend on the existence of analogues. A concrete mathematical theory, it seems, need have no such analogues and still be important, as e.g. classical number theory. In such a case, an axiomatic treatment may still be useful for exhibiting the mathematical structure of the theory considered and the assumptions on which it rests. However, it will lack one of the most heavily advertised advantages of the axiomatic method, namely, the “economy of thought” which results from an uniform theory for several different and interesting cases: we cannot hope for this if, by hypothesis, we know of only one particular case. In contrast, the second approach, if successful at all, is bound to achieve such “economy” because we start out with several interesting particular cases. Another possible virtue of the second approach is that of field work over insight: the abstract pattern that we are looking for and hoping to formalize in axioms, may not be evident in any one mathematical theory, but may spring to the eye if one happens to look simultaneously at several theories which happen to realize the pattern. (shrink)

This full-length study of Plato's dialogue Phaedrus, now in paperback, is written in the belief that such concerted scrutiny of a single dialogue is an important part of the project of understanding Plato so far as possible 'from the inside' - of gaining a feel for the man's philosophy. The focus of this account is on how the resources both of persuasive myth and of formal argument, for all that Plato sets them in strong contrast, nevertheless complement and reinforce each (...) other in his philosophy. Not only is the dialogue in its formal structure a dovetail of myth and argument, but the philosophic life that it praises is also shaped by an acknowledgement of the limitations of argument and the importance of mythical understanding. By means of this correlation of form and content Plato invites his readers, through the very act of reading, to take a first step along the path of the philosophical life. (shrink)

Much light can be shed on events which characterize or underlie scandals at firms such as Enron, Arthur Andersen, Worldcom, ImClone, and Tyco by appealing to the notion of ethical distance. Various inquiries have highlighted the difficulties in finding or identifying particular individuals to blame for particular events, and in the context of situations as complex as these it can sometimes be helpful to investigate the comparative ethical distance of various participants in these events. In this essay I offer a (...) characterization of ethical distance in terms of moral responsibility, and in doing so I describe and illustrate the rough inverse correlation between moral distance and degrees of moral responsibility. I urge that the concept of ethical distance is capable of shedding light upon situations in which several people are involved in bringing about a state of affairs. I then argue that moral responsibility cannot do justice to all situations involving ethical distance. When the distance between a person and a state of affairs grows sufficiently large, a different type of treatment is called for, and I introduce the notion of moral taint to describe the moral status of agents in these situations. (shrink)

In this thesis I argue for the following theory: constitutive Russellian phenomenal bonding panpsychism. To do so I do three main things: 1) I argue for Russellian panpsychism. 2) I argue for phenomenal bonding panpsychism. 3) I defend the resultant phenomenal bonding panpsychist model. The importance of arguing for such a theory is that if it can be made to be viable, then it is proposed to be the most promising theory of the place of consciousness within nature. This is (...) because constitutive Russellian panpsychism has all the theoretical virtues of physicalism and dualism but does not face the problems they do. The combination problem, however, is the most significant problem for the Russellian panpsychist, and, hence, in order to show the viability of the theory I address this problem. Moreover, I present a novel ”mereological argument’ for panpsychism which makes it necessary that the Russellian panpsychist addresses the combination problem. The focus of this thesis is therefore addressing this problem. I argue that the combination problem can indeed be solved. To do so I argue for the phenomenal bonding solution proposed by Goff. I argue that this solution works and that we can form a positive concept of the phenomenal bonding relation. This forces the panpsychist to make sense of how experiencing subjects can be proper parts of other experiencing subjects. I then argue that this can indeed be made sense of and show that we can indeed be composite subjects made of other subjects. To show that we can be subjects made up of other subjects I defend this proposal from various objections from throughout the literature. All these objections can be responded to by the constitutive Russellian phenomenal bonding panpsychist. Ultimately this leaves us with a novel and interesting account of what conscious subjects are, and what the material world is: they are both composite entities made wholly of conscious matter. (shrink)

This article discusses the concept of God with a focus on the translation of God in the Chinese and Yoruba religious contexts. Translating the word God is of the essence when comparing concepts of god. The translation of the Christian God as Olodumare misrepresents the latter. As suggested by Africanists, there should be appropriate translations for God, Olodumare, and other African gods. As a preliminary comparative attempt, this article presents a case on the introduction of God to the Chinese people. (...) The translation of God into Chinese reflects different views regarding the correlation between the Christian God and the Chinese gods. (shrink)

Like all research, embryo research can take a variety of forms, some posing substantially more risks to persons than others. Savulescu et al argue persuasively that regulatory regimes specially designed for sensitive embryo research should differentiate between person-affecting and non-person-affecting embryo research, with substantial scrutiny only warranted for the former.1 Yet if we find Savulescu et al ’s argument persuasive, what practical implications would it have? In this commentary, we focus in particular on how such an argument might apply in (...) Singapore, one of the jurisdictions with special regulations for embryo research. We will summarise the way in which approval for oocyte and embryonic research operates in Singapore, and suggest that Savulesc et al ’s distinction requires specification to be useful in such contexts. We propose adopting a risk-stratified framework similar to that employed with Institutional Review Boards. This requires a wider view of risks than the focus by Savulescu et al on future persons. We then illustrate how such a framework would apply in five scenarios discussed in Savulescu et al. Research with embryos and oocytes is regulated in Singapore under the Human Biomedical Research Act.2 Enacted in 2015, this law sets out requirements for consent, IRB review and research oversight. By definition, all research involving gametes and embryos fall within the remit of the Act. Moreover, such research is defined as ‘restricted’; besides the Act, research involving oocytes and embryos is also subject to control under the Human Biomedical Research …. (shrink)

Medical decisions regarding end-of-life care have undergone significant changes in recent decades, driven by changes in both medicine and society. Catholic tradition in medical ethics offers clear guidance in many issues, and a moral framework accessible to those who do not share the same faith as well as to members of its faith community. In some areas, a Catholic perspective can be seen clearly and confidently, such as in teachings on the permissibility of suicide and euthanasia. In others, such as (...) withdrawal of nutrition and hydration, the Church does not yet speak with one voice and has not closed out the discussion. Yet, it is not in the teaching on individual issues that a Catholic moral tradition offers the most help and comfort, but in its account of what it means to lead a life in Christ, and to prepare for a Christian death. As in the problem of pain and suffering, it is the spiritual support more than the ethical guidance that helps both patients and physicians bear the unbearable and fathom the unfathomable. (shrink)

This article presents evidence supporting the claim that ethical reasoning is a skill that can be taught and assessed. We propose a working definition of ethical reasoning as 1) the ability to identify, analyze, and weigh moral aspects of a particular situation, and 2) to make decisions that are informed and warranted by the moral investigation. The evidence consists of a description of an ethical reasoning education program—Ethical Reasoning in Action —designed to increase ethical reasoning skills in a variety of (...) situations and areas of life. ERiA is housed at a public, major comprehensive U.S. university—James Madison University—and assessment of the program focuses on interventions delivered prior to and during orientation for incoming first-year students. Findings indicate that the interventions measurably enhance the ability of undergraduate students to reason ethically. ERiA’s competency-targeted program and positive student learning outcomes offers a promising model for higher education ethics programs seeking to connect classroom learning in ethics to decision-making in everyday life. (shrink)

Underlying this paper is the conviction that it is of utmost importance that business ethics should indeed become an integral part of business culture in all, and therefore also in developing countries. It is not to be denied that business ethics has to a much larger extent become part of the business culture in developed countries than in developing countries. In this paper, I first of all wish to provide an explanation for the fact that business ethics is fighting an (...) uphill battle in becoming part of the business culture in developing countries. Secondly I want to give a thumbnail sketch of the preconditions that have to be fulfilled in order to stimulate the development of a moral business culture in developing countries. In order to achieve these goals I will focus mainly on Africa, and more specifically on South Africa. (shrink)

In this paper, the author attempts to explore some of the problems connected with the formulation and application of international biomedical ethical guidelines, with particular reference to Africa. Recent attempts at revising and updating some international medical ethical guidelines have been bedevilled by intractable controversies and wrangling regarding both the content and formulation. From the vantage position of relative familiarity with both African and Western contexts, and the privilege of having been involved in the revision and updating of one of (...) the international ethical guidelines, the author reflects broadly on these issues and attempts prescribing an approach from both the theoretical and practical angles liable to mitigate, if not completely eliminate, some of the problems and difficulties. (shrink)

The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. (...) The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays. (shrink)