Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and (...) solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size. (shrink)

Rigorous formal proof is one of the key techniques in the natural sciences, engineering, and of course also in the formal sciences. Progress in automated reasoning increasingly enables computer systems to support, and even teach, users to conduct formal a.

Ethical self-management; an introduction to systematic personality psychology, by M. C. Katz.--Four axiological proofs of the infinite value of man, by R. S. Hartman.--Some thoughts regarding the current philosophy of the behavioral sciences, by C. R. Rogers.--Autonomy and community, by D. Lee.--Synergy in the society and in the individual, by A. H. Maslow.--Human nature: its cause and effect; a theoretical framework for understanding human motivation, by M. C. Katz.--Mental health; a generic attitude, by G. W. Allport.--Love feelings in courtship couples; (...) an analysis, by R. P. Hattis.--Economic policies and human well-being, by W. A. Weisskopf.--The great transformation, by H. F. W. Perk.--Contingencies of reinforcement in the design of a culture, by B. F. Skinner.--For further reading. (shrink)

The application of ontology has thus far [in 1998] been confined almost exclusively to the field of knowledge representation. Ontology has been applied, for example, in the design of medical databases and in the construction of geographical information systems. One area which is naturally suited to ontological analysis is that of the law and of social institutions in general. -/- Legal systems are composed of legal entities, such as laws, contracts, obligations, and rights. Their application yields new categories of entities (...) such as: corporations, trademarks, marriages, and parcels of real estate. The categorization of these entities by different legal systems has not, by-and-large, been conducted in ways which exploit the tools of modern ontology. Consequently, contradictions and inconsistencies often arise in the law when, for instance, one type of entity is forced into two mutually exclusive categories (e.g., when software is considered both patentable and copyrightable). Papers are invited which consider these and related issues from a philosophical point of view. (shrink)

This Companion provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general. The sixteen essays, by authors who represent various academic disciplines, bring a spectrum of interpretive approaches to bear in order to aid the understanding of a wide-ranging audience, from first-time readers of the Republic who require guidance, to more experienced readers who wish to explore contemporary currents in the work’s interpretation. The (...) three initial chapters address aspects of the work as a whole. They are followed by essays that match closely the sequence in which topics are presented in the ten books of the Republic. Since the Republic returns frequently to the same topics by different routes, so do the authors of this volume, who provide the readers with divergent yet complementary perspectives by which to appreciate the Republic’s principal concerns. (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)

Tracing a central theme of Plato's Republic , G. R. F. Ferrari reconsiders in this study the nature and purpose of the comparison between the structure of society and that of the individual soul. In four chapters, Ferrari examines the personalities and social status of the brothers Glaucon and Adeimantus, Plato's notion of justice, coherence in Plato's description of the decline of states, and the tyrant and the philosopher king—a pair who, in their different ways, break with the terms of (...) the city-soul analogy. In addition to acknowledging familiar themes in the interpretation of the Republic —the sincerity of its utopianism, the justice of the philosopher's return to the Cave—Ferrari provocatively engages secondary literature by Leo Strauss, Bernard Williams, and Jonathan Lear. With admirable clarity and insight, Ferrari conveys the relation between the city and the soul and the choice between tyranny and philosophy. City and Soul in Plato's Republic will be of value to students of classics, philosophy, and political theory alike. (shrink)

The ability to feel pain is a property of human beings that seems to be based entirely in our biological natures and to place us squarely within the animal kingdom. Yet the experience of pain is often used as an example of a mental attribute with qualitative properties that defeat attempts to identify mental events with physiological mechanisms. I will argue that neurophysiology and psychology help to explain the interwoven biological and subjective features of pain and recommend a view of (...) pain which differs in important respects from the one most commonly accepted. (shrink)

First published in 2000, this translation of one of the great works of Western political thought is based on the assumption that when Plato chose the dialogue form for his writing, he intended these dialogues to sound like conversations - although conversations of a philosophical sort. In addition to a vivid, dignified and accurate rendition of Plato's text, the student and general reader will find many aids to comprehension in this volume: an introduction that assesses the cultural background to the (...) Republic, its place within political philosophy, and its general argument; succinct notes in the body of the text; an analytical summary of the work's content; a full glossary of proper names; a chronology of important events; and a guide to further reading. The result is an accomplished and accessible edition of this seminal work, suitable for philosophers and classicists as well as historians of political thought at all levels. (shrink)

This paper presents a theoretical elaboration of the ethical framework of classical capitalism as formulated by Adam Smith in reaction to the dominant mercantilism of his day. It is seen that Smith's project was profoundly ethical and designed to emancipate the consumer from a producer and state dominated economy. Over time, however, the various dysfunctions of a capitalist economy — e.g., concentration of wealth, market power — became manifest and the utilitarian ethical basis of the system eroded. Contemporary capitalism, dominated (...) as it is by large corporations, entrenched political interests and persistent social pathologies, bears little resemblance to the system which Smith envisioned would serve the common man. Most critiques of capitalism are launched from a Marxian-based perspective. We find, however, that by illustrating the wide gap between the reality of contemporary capitalism and the model of amoral political economy developed by Smith, the father of capitalism proves to be the most trenchant critic of the current order. (shrink)

Informed consent is required for any medical procedure although the situations in which it is given are beset by uncertainties and indeterminacies. These make medicolegal scrutiny of such situations very difficult. Although some people find the decision in the Sidaway case incomprehensible because of its continuing regard for a 'professional practice standard' in informed consent, I will argue that an important fact in many cases is the moral integrity of the doctor concerned and the pattern of his practice. This may (...) provide the only morally principled and legally accessible evidence enabling a correct decision to be made in a difficult case. Although the epistemological significance of a professional practice standard is thereby defended the 'prudent patient standard' for what counts as consent is left intact. (shrink)

The purpose of this study is to determine the relative frequency of course offerings on social issues and business ethics in American business schools. Specifically, a random sample of the curricula of 119 American business schools were analyzed in order to gauge the importance given to coursework on ethics and social issues. The findings indicated that the incidence of such courses was generally low in American business curricula, particularly at the graduate level. These findings are discussed in light of the (...) current concern for more responsible corporate behavior. (shrink)

Decompressive craniectomy is a technically straightforward procedure whereby a large section of the cranium is temporarily removed in cases where the intracranial pressure is dangerously high. While its use has been described for a number of conditions, it is increasingly used in the context of severe head injury. As the use of the procedure increases, a significant number of patients may survive a severe head injury who otherwise would have died. Unfortunately some of these patients will be left severely disabled; (...) a condition likened to the RUB, an acronym for the Risk of Unacceptable Badness. Until recently it has been difficult to predict this outcome, however an accurate prediction model has been developed and this has been applied to a large cohort of patients in Western Australia. It is possible to compare the predicted outcome with the observed outcome at 18 months within this cohort. By using predicted and observed outcome data this paper considers the ethical implications in three cases of differing severity of head injury in view of the fact that it is possible to calculate the RUB for each case. (shrink)