Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It provides beginning undergraduates with a rigourous grounding in the basic tools and techniques of the discipline and prepares them for further more advanced studies in analysis, differential equations, and algebra. This edition contains additional material on secret codes, permutations, and prime numbers. It features more than 200 exercises, with many completely new. The text is organized into (...) relatively independent chapters, allowing instructors to tailor the book to meet their individual course needs. · Contains extra material concerning prime numbers, forming the basis for data encryption · Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics Discusses Permutations and their importance in many topics in discrete mathematics. (shrink)

Precision Medicine has become a common label for data-intensive and patient-driven biomedical research. Its intended future is reflected in endeavours such as the Precision Medicine Initiative in the USA. This article addresses the question whether it is possible to discern a new ‘medical cosmology’ in Precision Medicine, a concept that was developed by Nicholas Jewson to describe comprehensive transformations involving various dimensions of biomedical knowledge and practice, such as vocabularies, the roles of patients and physicians and the conceptualisation of disease. (...) Subsequently, I will elaborate my assessment of the features of Precision Medicine with the help of Michel Foucault, by exploring how precision medicine involves a transformation along three axes: the axis of biomedical knowledge, of biomedical power and of the patient as a self. Patients are encouraged to become the managers of their own health status, while the medical domain is reframed as a data-sharing community, characterised by changing power relationships between providers and patients, producers and consumers. While the emerging Precision Medicine cosmology may surpass existing knowledge frameworks; it obscures previous traditions and reduces research-subjects to mere data. This in turn, means that the individual is both subjected to the neoliberal demand to share personal information, and at the same time has acquired the positive ‘right’ to become a member of the data-sharing community. The subject has to constantly negotiate the meaning of his or her data, which can either enable self-expression, or function as a commanding Superego. (shrink)

After presenting a variety of arguments in support of the idea that ordinary names are indexical, I respond to John Perry's recent arguments against the indexicality of names. I conclude by indicating some connections between the theory of names defended here and Wittgenstein's observations on naming, and suggest that the latter may have been misconstrued in the literature.

After presenting a variety of arguments in support of the idea that ordinary names are indexical, I respond to John Perry's recent arguments against the indexicality of names. I conclude by indicating some connections between the theory of names defended here and Wittgenstein's observations on naming, and suggest that the latter may have been misconstrued in the literature.

In Fiction, Truth and Literature, Lamarque and Olsen argue that if a critic claims or attempts to prove that the outlook of a work of literature is true or false, he is not engaging in literary or aesthetic appreciation. This paper argues against this position by adducing cases where literary critics discuss the truth or falsity of a work’s view, when their opinions are obviously relevant to the work’s aesthetic assessment. The paper considers in detail the way factual errors damage (...) a work’s aesthetic standing, and shows that Lamarque and Olsen’s alternative account of the role of propositional truths in literature only looks plausible because it considers a restricted range of examples. Finally, it considers the role intention, date and genre play in discussions of the aesthetic damage done by literal falsehood. (shrink)

An attitude which hopes to derive aesthetic pleasure from an object is often thought to be in tension with an attitude which hopes to derive knowledge from it. The current article argues that this alleged conflict only makes sense when the aesthetic attitude and knowledge are construed unnaturally narrowly, and that when both are correctly understood there is no tension between them. To do this, the article first proposes a broad and satisfying account of the aesthetic attitude, and then considers (...) and rejects twelve reasons for thinking that deriving knowledge from something is incompatible with maintaining an aesthetic attitude towards it. Two main conclusions are drawn. 1) That the representational arts are often in a good position to communicate non-propositional knowledge about human beings. 2) That while our desire to obtain pleasure from a work's manifest properties, and our desire to obtain knowledge from it, are not the same motive, the formal similarities between them are sufficiently impressive to warrant both being seen as elements of the aesthetic attitude. (shrink)

The influence of Goethe on Wittgenstein is just beginning to be appreciated. Hacker and Baker, Westphal, Monk, and Haller have all drawn attention to significant affinities between the two men's work, and the number of explicit citations of Goethe in Wittgenstein's texts supports the idea that we are not dealing simply with a matter of deeplying similarities of aim and method, but of direct and major influence. These scholarly developments are encouraging because they help to place Wittgenstein's work within an (...) important tradition of German letters which goes far beyond his contemporaries and immediate forebears in Vienna; and they show that Wittgenstein's profound interest in literature and music is ceasing to be merely a matter of biographical anecdote, and is being used to illuminate some of the most central areas of his work. (shrink)

Among bioethicists and members of the public, genetics is often regarded as unique in its ethical challenges. As medical researchers and clinicians increasingly combine genetic information with a range of non-genetic information in the study and clinical management of patients with common diseases, the unique ethical challenges attributed to genetics must be re-examined. A process of genetic routinisation that will have implications for research and clinical ethics, as well as for public conceptions of genetic information, is constituted by the emergence (...) of new forms of genetic medicine, in which genetic information is interpreted in a multifactorial frame of reference. Although the integration of genetics in medical research and treatment may be a helpful corrective to the mistaken assumptions of genetic essentialism or determinism, the routinisation of genetics may have unintended consequences for the protection of genetic information, perceptions of non-genetic information and the loss of genetic research as a laboratory for exploring issues in research and clinical ethics. Consequently, new ethical challenges are presented by the increasing routinisation of genetic information in both biomedical and public spheres. (shrink)

The concept of supererogation is an act that it is right to do but not wrong not to do. The moral trinity of the deontic logic excludes such acts from moral theory. A moral theory that is based on duty or obligation unqualified seems inevitably to make all good acts obligations, whether construed from a teleological or deontological point of view. If supererogation is a moral fact, no moral theory can survive without acknowledging it. One way to distinguish supererogation from (...) obligation that is not arbitrary is to draw the line of obligation at death and dismemberment. Such a limit to obligation is often implicit in moral theory. Inclusive obligation requires us all to be heroes all of the time. The moral limit to obligation is one of Hobbes's teachings. Though it is seldom noted in contemporary political and moral theory, it is, for example, implied in Rawls's definition of ‘supererogation.’ In this definition it is said that heroic supererogation would be a duty but for the high cost associated with it. This cost is the risk of life and limb;.it distinguishes supererogation from both benevolence and obligation.A supererogation is a good act with a high cost. The goodness of the act, however determined, must be proportionate to the cost to the agent. If life is risked, life or something deemed no less valuable must be gained. The intention to effect such important goods for others is sufficient for an act to be supererogatory even if it fails.If moral reality is inevitably vague, complex, and incomplete, then it is no surprise that moral theory is that way, too. The challenge is that moral theory be no more vague, complex, and incomplete than necessary and in ways justified by the nature of moral reality. A science, Aristotle advised, can be no more precise than its subject matter permits. (shrink)

The idea underlying this article was that the humanities in general and business ethics in particular should be more firmly embedded in business management programs. A number of areas have been identified for students to use as topics for research projects in management ethics. These ranged from Biblical and classical times to the present day. Some were drawn from sources that were less well known e.g. the De consolatione philosphiae ‘The Consolation of Philosophy’ by Boethius 524 AD. This was chosen (...) partly for its ethical content, but also because Boethius was magister officiorum i.e. head of the civil service. Aelfred the Great (849–899) King of Wessex (he who burnt those cakes) was chosen because he promoted the intellectual, moral and spiritual qualities that were to serve as guidelines for his executives. Nineteenth century literature (Dickens, Thackeray, Trollope and Galsworthy) was also chosen as a source of topics for research projects in business ethics. The writer acknowledges the work of earlier writers in the fields of management, organisation theory, and business ethics. (shrink)

Besides its intrinsic interest, the definition of ‘game’ is important for three reasons. Firstly, in Wittgenstein's Philosophical Investigations ‘game’ is the paradigm family resemblance concept. If he is wrong in thinking that ‘game’ cannot be defined, then the persuasive force of his argument against definition generally will be considerably weakened. This, in its turn, will have important consequences for our understanding of concepts and philosophical method. Secondly, Wittgenstein's later writings are full of analogies drawn from games—chess alone is mentioned scores (...) of times—and a proper understanding of ‘game’ can lead us to exercise more caution when considering the parallels between games and non-games. Thirdly, games and play are intriguingly and closely related to art and ritual, and an analysis of games can throw considerable light on both of the latter. (shrink)

The theory of personal identity should illuminate and be illuminated by the theory of personality, of which it is a part. I believe that Locke's theory succeeds in this more than that of any other great philosopher, and the modifications which it may need are not fundamental ones. The problems raised by Butler and Flew can be made to disappear.

A bracket abstraction algorithm is a means of translating $\lambda$-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each $\lambda$-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schonfinkel [4] algorithm plus two mappings which convert the Schonfinkel abstract into the new abstract. This paper shows how the new (...) abstraction can be done more directly, in fact, using only 2n - 1 algorithm steps if there are n occurrences of the variable to be abstracted in the term. Some properties of the Broda-Damas combinators are also considered. (shrink)

The theory of personal identity should illuminate and be illuminated by the theory of personality, of which it is a part. I believe that Locke's theory succeeds in this more than that of any other great philosopher, and the modifications which it may need are not fundamental ones. The problems raised by Butler and Flew can be made to disappear.

Realities are structured categorially, and comprehension of our internal and external conditions do not appear to be global or unitary. Rather, both human and non human animals function within their worlds and understand these by categorizing their experiences. Drawing upon many areas of life, the authors consider the ontological, mereological and multi-faceted structure of experience to explore how an understanding of categories can further knowledge.

Work with plant cell cultures has developed rapidly in recent years, progress being manifested particularly by the development of commercial process technology for the synthesis of selected natural products. The economics of operating a plant‐cell culture process are, however, still questionable, and a great deal still needs to be done to strengthen the underlying science before the technology can be regarded as industrially commonplace. Nonetheless, the great versatility of plants as centres of chemical synthesis suggests that, with appropriate developments in (...) cell culture technology, this area may have a significant role to play in the fine chemicals industry of the future. (shrink)

Pure Type Systems, PTSs, were introduced as a generalization of the type systems of Barendregt's lambda cube and were designed to provide a foundation for actual proof assistants which will verify proofs. Systems of illative combinatory logic or lambda calculus, ICLs, were introduced by Curry and Church as a foundation for logic and mathematics. In an earlier paper we considered two changes to the rules of the PTSs which made these rules more like ICL rules. This led to four kinds (...) of PTSs. Most importantly PTSs are about statements of the form M:A, where M is a term and A a type. In ICLs there are no explicit types and the statements are terms. In this paper we show that for each of the four forms of PTS there is an equivalent form of ICL, sometimes if certain conditions hold. (shrink)

Goethe and Wittgenstein -- Criticism without theory -- Wittgenstein's romantic inheritance -- Arnold and the socratic personality -- The dissolution of goodness : measure for measure and classical ethics -- Lamarque and Olsen on literature and truth -- The definition of 'art' -- Poetry and abstraction -- Larkin's 'Aubade'.