Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement (...) calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. (shrink)

This paper argues for a non-moral interpretation of the libertarian conception of interpersonal liberty as ‘the absence of imposed cost.’ In the event of a clash of imposed costs, observing such liberty entails ‘minimising imposed costs’. Three fundamental criticisms are examined: strictly interpreted, this would logically imply genocide in practice; it is impractically unclear and moralised; it could entail mob rule of some kind. Self-ownership and private property are then non-morally derived merely from applying this formula in a state of (...) nature. Various subsidiary issues arise throughout. (shrink)

A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view.

Categories may be viewed as deductive systems or as algebraic theories. We are primarily interested in the interplay between these two views and trace it through a number of structured categories and their internal languages, bearing in mind their relevance to the foundations of mathematics. We see this as a common thread running through the six contributions to this issue of Studia Logica.

This study explores the reactions of 412 business students to a range of ethical marketing dilemmas. Reviewing some of the comparable Australian and U.S. research in the field, the study examines the ethical judgements for potential demographic differences. The findings suggest that a majority of students are prepared to act unethically in order to gain some competitive or personal advantage. Yielding the highest ethical response are situations of potential and significant social impact. The results support some previous research that shows (...) the existence of gender and age differences in ethical response and likely behaviour. This (gender) difference was most divergent on the issue of portrayal of women in advertising. In particular, females and older students respond more ethically in a majority of situations. The research concludes a number of opportunities for new directions in education, public policy making and further research. (shrink)

Robert Boyle's corpuscular philosophy was an important instance in the history of thought of a use of metaphysical principles in formulating new methods for physical science. Since Boyle nowhere completely and explicitly discussed his metaphysic, I shall undertake to reconstruct it and trace its influence on his scientific work.

The paper presents a new paradox in the sphere of the classical mechanics of infinite systems. The paradox, which implies the existence of an interaction at a distance as well as gravitation, would seem to require an extension of the concept of mechanical explanation. However, it is not clear how such an extension might be carried out.

It is generally accepted that prion infection is due solely to a protein i.e. the protein-only hypothesis. The essential constituent of infectious prions is the scrapie prion protein (PrPSc) which is chemically indistinguishable from the normal, cellular protein (PrPC) but exhibits distinct secondary and tertiary structure. This very unusual feature seems to be in contradiction with a major paradigm of present structural biology stated by Anfinsen: a protein folds to the most stable conformation, this means only one structure.In order to (...) reconcile the results obtained on prions with the biophysics of protein folding, a model is proposed. It is based on the hypothesis that a thermodynamically irreversible step is involved in protein folding. The model is then extended to chaperone-assisted protein folding. It is shown that, under certain conditions, the transitory secondary structure formed during the earlier step of folding could interact with chaperone. Analysis shows that chaperone may help the protein to find correct conformation. On the other hand, analysis reveals the possibility that more than one structure may form from a single polypeptide chain. Under these conditions, the behaviour of chaperones resembles the characteristics of prion diseases. (shrink)

Lemmon argues that dilemmas occur between classes of 'oughts;' duties, obligations, and moral principles. He claims that there are not conflicts within each class, presumably because he is a utilitarian, and thinks that moral principles will always be univocal.

In quantum mechanics it is usually assumed that mutually exclusives states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmatic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum mechanics.

Most agents can acquire information about their environments as they operate. A good plan for such an agent is one that not only achieves the goal, but is also executable, i.e., ensures that the agent has enough information at every step to know what to do next. In this paper, we present a formal account of what it means for an agent to know how to execute a plan and to be able to achieve a goal. Such a theory is (...) a prerequisite for producing specifications of planners for agents that can acquire information at run time. It is also essential to account for cooperation among agents. Our account is more general than previous proposals, correctly handles programs containing loops, and incorporates a solution to the frame problem. It can also be used to prove programs containing sensing actions correct. (shrink)

In an individualistic society and in the increasingly competitive business environment people do not seem inclined to forgive others their trespasses. One is more likely to choose to ignore the virtue of forgiveness as a way of handling personnel situations involving intense conflict or mild disagreements, favoring instead the negative feelings of resentment, anger, revenge or retaliation. Business people seem less concerned with growth in virtue and character; interestingly they allow their character and ultimately their work relationships to deteriorate because (...) they hold onto feelings of anger and resentment. Is there a place for forgiveness in our interpersonal relationships in general and in corporate life in particular? I believe there is. A study of the virtue of forgiveness shows that it is a misunderstood virtue, but one that deserves attention. In this article I will examine the virtue of forgiveness, defining what forgiveness is and is not, and will illustrate how it might be situated as an essential human resource management strategy. (shrink)

Two essays on utilitarianism, written from opposite points of view, by J. J. C. Smart and Bernard Williams. In the first part of the book Professor Smart advocates a modern and sophisticated version of classical utilitarianism; he tries to formulate a consistent and persuasive elaboration of the doctrine that the rightness and wrongness of actions is determined solely by their consequences, and in particular their consequences for the sum total of human happiness. In Part II Bernard Williams offers a sustained (...) and vigorous critique of utilitarian assumptions, arguments and ideals. He finds inadequate the theory of action implied by utilitarianism, and he argues that utilitarianism fails to engage at a serious level with the real problems of moral and political philosophy, and fails to make sense of notions such as integrity, or even human happiness itself. This book should be of interest to welfare economists, political scientists and decision-theorists. (shrink)

In the Quebec city area, 400 women owner-managers of business in the three industrial sectors answered a detailed questionnaire, and 75 of these subsequently underwent in-depth interviews. The main dimensions explored were the characteristics of the entrepreneurs and their firms, the experience of starting a business, the success criteria used, and their vision for the future of their firms. The results suggest the importance, to these women, of a model of small and stable business. This is not a transitory phase (...) for their firm: most choose and value such a scale of business, and they seek recognition for what they do. This model seems to represent an innovative adaptation to their professional, social, family and personal demands and challenges our definitions of entrepreneurship and of serious business. (shrink)

We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).

Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of (...) Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)

Conduct that satisfies certain bioethical doctrines may come into conflict with the needs and ethics of public health. The growth of antibiotic resistance in bacteria and the spread of HIV both contribute to the difficulty of controlling infectious disease. These two sets of priorities need to be reconciled and this is likely to require a reassessment of prevailing ethical doctrines in the face of the needs of public health.

Controversy over the adequacy of the regularity or covering law theory of explanation when applied to historical actions continues to rage. A detailed analysis is here made of Professor A. Donagan's recent attack on this theory, as representative of many others. His alternative model of deductive non-law explanation, based on Popper's notion of the "logic of the situation," is then shown to be invalid and generally defective. Finally, four sources of the difficulty are elicited which, when resolved, provide support for (...) the regularity theory in its probabilistic version. We suggest that this theory, despite recent criticism, can be fruitfully extended to historical explanation by uncovering and codifying a major difference between history and science, the rational actions of historical agents, without distorting it. (shrink)

Michael J. Zimmerman explores whether and how our ignorance about ourselves and our circumstances affects what our moral obligations and moral rights are. He rejects objective and subjective views of the nature of moral obligation, and presents a new case for a 'prospective' view.

J.N. Findlay was a South African philosopher who published from the late 1940s into the 1980s. He had a prestigious international academic career, holding many academic posts around the world. This article uses a textual comparative approach and focuses on Findlay’s Gifford Lecture at St Andrews University between 1965 and 1970. The objective of the article is to highlight the extent to which Findlay’s philosophical writings were influenced by Mahāyāna Buddhism. Although predominantly a Platonist, Findlay drew influence from Asian philosophy (...) and religion, particularly Mahāyāna Buddhism. In these lectures, he applies the metaphor of the Platonic Cave to investigate Hegelian and Husserlian approaches to knowledge. Though he was a leading Hegel and Husserl scholar, his reading of these two philosophers is strongly influenced by Mahāyāna Buddhism, resulting in a unique mystical interpretation of these two philosophers. Revisiting Findlay’s writings is significant for two reasons; firstly, he investigated Buddhism prior to the Asian religions being included in Religious Studies departments’ purview in South African universities, and secondly, his interpretation of two prominent Western philosophers along Buddhist lines provides an early attempt at decolonising the predominance of Western philosophical views of knowledge.Contribution: This contribution forms part of a larger collection of essays investigating philosophical works that have had a significant impact on the study of religion. This contribution investigates the Buddhist influence on J.N. Findlay’s philosophical readings of Husserl and Hegel. (shrink)

This manuscript reports on a landmark symposium on the ethical, legal and technical challenges of xenotransplantation in the UK. King’s College London, with endorsement from the British Transplantation Society (BTS), and the European Society of Organ Transplantation (ESOT), brought together a group of experts in xenotransplantation science, ethics and law to discuss the ethical, regulatory and technical challenges surrounding translating xenotransplantation into the clinical setting. The symposium was the first of its kind in the UK for 20 years. This paper (...) summarises the content of the expert lectures showcasing the progress which has been made in xenotransplantation including—the history of xenotransplantation, advances in gene edited animals and progress towards clinical xenotransplantation. We then set out the ethical and legal issues still to be resolved. Finally, we report the themes of the roundtable discussion highlighting areas of consensus and controversy. While the detail of the legal discussion was directed towards the UK, the principles and summary reported here are intended to be applicable to any jurisdiction seeking to implement clinical xenotransplantation. (shrink)

It is a pleasure for me to give this opening address to the Royal Institute of Philosophy Conference on ‘Explanation’ for two reasons. The first is that it is succeeded by exciting symposia and other papers concerned with various special aspects of the topic of explanation. The second is that the conference is being held in my old alma mater, the University of Glasgow, where I did my first degree. Especially due to C. A. Campbell and George Brown there was (...) in the Logic Department a big emphasis on absolute idealism, especially F. H. Bradley. My inclinations were to oppose this line of thought and to espouse the empiricism and realism of Russell, Broad and the like. Empiricism was represented in the department by D. R. Cousin, a modest man who published relatively little, but who was of quite extraordinary philosophical acumen and lucidity, and by Miss M. J. Levett, whose translation of Plato's Theaetetus formed an important part of the philosophy syllabus. (shrink)

Despite its uniform appearance, the cerebellar cortex is highly heterogeneous in terms of structure, genetics and physiology. Purkinje cells (PCs), the principal and sole output neurons of the cerebellar cortex, can be categorized into multiple populations that differentially express molecular markers and display distinctive physiological features. Such features include action potential rate, but also their propensity for synaptic and intrinsic plasticity. However, the precise molecular and genetic factors that correlate with the differential physiological properties of PCs remain elusive. In this (...) article, we provide a detailed overview of the cellular mechanisms that regulate PC activity and plasticity. We further perform a pathway analysis to highlight how molecular characteristics of specific PC populations may influence their physiology and plasticity mechanisms. (shrink)