Let ZF denote Zermelo-Fraenkel set theory (without the axiom of choice), and let $M$ be a countable transitive model of ZF. The method of forcing extends $M$ to another model $M\lbrack G\rbrack$ of ZF (a "generic extension"). If the axiom of choice holds in $M$ it also holds in $M\lbrack G\rbrack$, that is, the axiom of choice is preserved by generic extensions. We show that this is not true for many weak forms of the axiom of choice, and we derive (...) an application to Boolean toposes. (shrink)

Human values, by their very nature, are situational and culture specific. It would, therefore, be unrealistic to think that we can 'transplant' or 'transport' values from one country or culture to another with ease. This text identifies suitable human values which cut across national boundaries and cultures to facilitate organisations wishing to advance their businesses and strategic management capabilities towards a functionally humane organisation (FHO).

This is a collection of the key articles written by renowned Wittgenstein scholar, G.P. Baker, on Wittgenstein’s later philosophy, published posthumously. Following Baker’s death in 2002, the volume has been edited by collaborator and partner, Katherine Morris. Contains articles previously only available in other languages, and one previously unpublished paper. Completely distinct from the widely-known work Baker did with P.M.S. Hacker in the Analytical Commentary on the Philosophical Investigations.

Plotinus (204/5–270 CE) was the first and greatest of Neoplatonic philosophers. His writings were edited by his disciple Porphyry, who published them sometime between 301 and 305 CE in six sets of nine treatises each (Enneads), with a biography of his master in which he also explains his editorial principles.

Among the most outstanding discoveries of the last century is one that is not quite as momentous as the theory of relativity or cybernetics. It may even still be enigmatic. It has no one single author, it is not expressed in a single formula, conception, or invention. Nonetheless it is worth all the others combined.

The development of a content-full Christian bioethics requires an analysis of the particular contents and traditions which different Christians bring to morality. For Hauerwas, the content of Christian ethics is the speech and practices of the community. For Engelhardt, only a content-full tradition, such as the Orthodox tradition, will be able to arrive at closure on the moral issues presented by the contemporary practice of medicine. Capaldi calls, in contrast, for a Kantian society of autonomous self-legislators whose responsible freedom is (...) grounded in a cosmic order that must be explicated and retrieved in particular practices. The manner in which we view our own traditions and the shortcomings of modernity determine the content that Christianity brings to bioethics. (shrink)

In ‘Wittgenstein on Language and Rules’, Professor N. Malcolm took us to task for misinterpreting Wittgenstein's arguments on the relationship between the concept of following a rule and the concept of community agreement on what counts as following a given rule. Not that we denied that there are any grammatical connections between these concepts. On the contrary, we emphasized that a rule and an act in accord with it make contact in language. Moreover we argued that agreement in judgments and (...) in definitions is indeed necessary for a shared language. But we denied that the concept of a language is so tightly interwoven with the concept of a community of speakers as to preclude its applicabilty to someone whose use of signs is not shared by others. Malcolm holds that ‘This is an unwitting reduction of Wittgenstein's originality. That human agreement is necessary for “shared” language is not so striking a thought as that it is essential for language simpliciter.’ Though less striking, we believe that it has the merit of being a true thought. We shall once more try to show both that it is correct, and that it is a correct account of Wittgenstein's arguments. (shrink)

This chapter contains sections titled: The Tractatus and rules of logical syntax From logical syntax to philosophical grammar Rules and rule‐formulations Philosophy and grammar The scope of grammar Some morals.

The title of this article will perhaps seem excessively contentious to the reader. What solitude of Vladimir Ivanovich Vernadskii, he might ask, if he has even the slightest familiarity with the scientist's biography?

Vague language refers to expressions with unspecified meaning (for instance, 'I kind of want that job'), and is an important but often overlooked part of linguistic communication. This book is a comparative study of vague language based on naturally occurring data of a rare combination: L1 (American) and L2 (Chinese and Persian) speakers in academic settings. The findings indicate that L2 learners have diverse and culturally specific needs for vague language, and generally use vague words in a more concentrated fashion (...) compared with L1s. The book explores the interconnection and continuum between the linguistic realizations of a vague term and the functions it serves, and how 'elasticity' underpins the frequency and functions of vague language. The implication is that vague language may be integrated into the curriculum of English language teaching as part of L2 speakers' communicative competence. This book will be of great interest to researchers in the fields of intercultural education and applied linguistics. (shrink)

This chapter offers an essay on the evolution of evolvability. It investigates the most frequently cited arguments against the possibility that the evolution of evolvability might be the result of selection favoring more evolvable genotypes. The chapter argues that all these arguments have not been rigorously analyzed by their proponents, and are thus a self-inflicted blind spot in evolutionary biology, and indicates that there are no deep conceptual obstacles for population genetic theory to explain the evolution of evolvability. The very (...) focus on this subject will help shift the perspective of evolutionary biology toward a more holistic, systemic view of evolution. (shrink)

The dictum ‘“ought” implies “can”’ has a status in moral philosophy in some respects like that of ‘a good player needs good co-ordination’ in talk about ball-games. Clearly, you say something important but not conclusive about proficiency in playing a ball-game when you say that it requires good co-ordination: similarly, you say something important but not conclusive about obligation when you say that it implies a certain possibility or power or ability. Each dictum is a reminder: the one about such (...) courses of physical instruction, the other about such exhortations to duty, as are worth persevering with. It would be hopeless to keep on teaching a boy the moves and tricks of rugby football if he could never co-ordinate well enough to get his eye in, so to speak. Correspondingly, it would be meaningless to recommend that someone ought to do something the specification of which involved a contradiction, and pointless to suggest that he ought to do something which, for quite general reasons, was not, and was certain to remain not, within his power. So each dictum expresses a bluff, no-nonsense wisdom which we should count on before involving ourselves in certain more detailed commitments. But probably this is as far as the comparison between the two sayings can well be taken. (shrink)

Despite traditionally being characterised as a melancholy thinker with a propensity to dwell on existential anxiety, sin and despair, scholarly interest in the place of love in Søren Kierkegaard’s ethical thought is currently gaining significant traction. In particular, Kierkegaard’s Works of Love has increasingly come under the academic spotlight as a text with potentially rich and previously underappreciated insights for Christian ethics. This article aims to contribute to this ongoing illumination, by highlighting the moral psychology and theological anthropology of Kierkegaard’s (...) Christian lover in discourses II–V of Works of Love’s second series. In doing this, I aim to put forward an overarching ethical framework which can be seen to structure these moral deliberations. (shrink)

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate and pulse vaccination strategy. We have defined two positive numbers $$R_{0}$$ R 0 and $$R_{1}$$ R 1. It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{0} 1.$$ R 1 > 1. The important mathematical findings for the dynamical behaviour of the Chlamydia disease model are also numerically verified using MATLAB. Finally epidemiological implications of (...) our analytical findings are addressed critically. (shrink)