The evolution of the equation of mass conservation in fluid mechanics is studied. Following early hydraulic approximations, and progress by Daniel and Johann Bernoulli, its first expression as a partial differential equation was achieved by d’Alembert, and soon given definitive form by Euler. Later reworkings by Lagrange, Laplace, Poisson and others advanced the subject, but all based their derivations on the conserved mass of a moving fluid particle. Later, Duhamel and Thomson gave a simpler derivation, by considering mass flow into (...) and out of a fixed portion of space. The later propagation of these derivations in nineteenth-century British textbooks and treatises is also examined, including Maxwell’s on the kinetic theory of gases. (shrink)

I present an annotated development of the basic ideas of the Geneva School approach to the foundations of physics and the structures which emerge as mathematical representations of the physically dual notions of state and property.

An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of $\mathcal{C}$ - and $\mathfrak{D}$ -differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as a special case, quantisation in arbitrary curvilinear coordinates when space is (...) flat.) The influence of curvature is emphasised throughout, with an illustration provided by the Aharonov-Bohm effect. (shrink)

Background: The traditional approach to resolving ethics concerns may not address underlying organisational issues involved in the evolution of these concerns. This represents a missed opportunity to improve quality of care “upstream”. The purpose of this study was to understand better which organisational issues may contribute to ethics concerns. Methods: Directed content analysis was used to review ethics consultation notes from an academic children’s hospital from 1996 to 2006 (N = 71). The analysis utilised 18 categories of organisational issues derived (...) and modified from published quality improvement protocols. Results: Organisational issues were identified in 68 of the 71 (96%) ethics consult notes across a range of patient settings and reasons for consultation. Thirteen of the 18 categories of organisational issues were identified and there was a median of two organisational issues per consult note. The most frequently identified organisational issues were informal organisational culture (eg, collective practices and approaches to situations with ethical dimensions that are not guided by policy), policies and procedures (eg, staff knows policy and/or procedural guidelines for an ethical concern but do not follow it) and communication (eg, communication about critical information, orders, or hand-offs repeatedly does not occur among services). Conclusions: Organisational issues contribute to ethical concerns that result in clinical ethics consults. Identifying and addressing organisational issues such as informal culture and communication may help decrease the recurrence of future similar ethics concerns. (shrink)

Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...) the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions. (shrink)

D. J. Allan; XV—Aristotle's Criticism of Platonic Doctrine Concerning Goodness and The Good, Proceedings of the Aristotelian Society, Volume 64, Issue 1, 1 June.

The ordinary concept of death is analysed and compared with revisionary medical definitions, especially those based on irreversible loss of brain function. Prior critics of revisionary definitions have focused on the locus, the brain; I am concerned with the irreversibility condition. I argue that 1) the irreversibility condition is ambiguous, 2) it has unacceptable epistemic and other consequences on any plausible construal, and 3) irreversibility is not part of the ordinary concept of death. I conclude that recent medical definitions seek (...) illegitimately to obtain the certainty of a weak construal of 'irreversible' along with the freedom from moral obligation of the strong construal. (shrink)

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.

This article aims at linking empirical research to legal theories, in a way that could enhance the benefits of this synergy. Jurisprudence, until recently the usual term for theoretical approaches to law, is now often replaced by the term legal theory. Difference between legal theory and empirical research is reflected in their consideration of subject matters, aims, and methods of research. However, there also exist commonalities between the two, i.e. both aim at comprehending law and legal systems. While legal theory (...) uses philosophical tools, its subject matter still remains a social phenomenon, for social ends. And since empirical research is a means to gather information about law, it could act as a prime source of information for legal theory. While empirical research has its own end to follow, what is missing is, attention to some legal theory, not just general legal theory, but which can also critique philosophical discourses to legality. (shrink)