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)

Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.

Classical mechanics is presented so as to render the new formulation valid for an arbitrary temporal variable, as opposed to Newton’s Absolute Time only. Newton’s theory then becomes formally identical (in a precise sense) to relativity, albeit in a three-dimensional manifold. (The ultimate difference between the two dynamics is traced to the existence of the relativistic ‘mass-shell’ condition.) A classical Lagrangian is provided for our formulation of the equations of motion and it is related to one of the known forms (...) of the corresponding relativistic Lagrangian, which is the analogue of the Polyakov Lagrangian of string theory. (shrink)

We investigate a possible form of Schrödinger’s equation as it appears to moving observers. It is shown that, in this framework, accelerated motion requires fictitious potentials to be added to the original equation. The gauge invariance of the formulation is established. The example of accelerated Euclidean transformations is treated explicitly, which contain Galilean transformations as special cases. The relationship between an acceleration and a gravitational field is found to be compatible with the picture of the ‘Einstein elevator’. The physical effects (...) of an acceleration are illustrated by the problem of the uniformly-accelerated harmonic oscillator. (shrink)

Oxford Scholarly Classics brings together a number of great academic works from the archives of Oxford University Press. Reissued in a uniform series design, they will enable libraries, scholars, and students to gain fresh access to some of the finest scholarship of the last century.

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)

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.

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.

Pleidooi voor een metafysische visie op hedendaagse sociale en economische problemen.

Presumably it is common ground that this verb has in addition to the basic sense ‘recognize’ the derivative sense ‘oread’, and that one must judge from the context whether reading to one or more other people, or private reading, is meant. The reading of the text of a law to a jury at an orator's request is marked by the circumstances themselves as public reading; so is the reading of the Athenian decree to the Mitylenaeans in Thucydides. When Theaetetus answers (...) in the affirmative the question whether he has read the book of Protagoras which contains the statement that man is the measure of all things (); or when it is asked ‘Why is it that some people, if they begin to read, are overcome by sleep even against their will, whereas others wishing to be overcome by sleep are kept awake by taking up a book?’ Evidently what is intended is reading in the privacy of one's own room. When Socrates in the Phaedo says that he heard a person reading from Anaxagoras and eagerly took the book home to read , both senses are found within a few pages. (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)

Recent studies using functional magnetic resonance imaging of patients in a vegetative state have raised the possibility that such patients retain some degree of consciousness. In this paper, the ethical implications of such findings are outlined, in particular in relation to decisions about withdrawing life-sustaining treatment. It is sometimes assumed that if there is evidence of consciousness, treatment should not be withdrawn. But, paradoxically, the discovery of consciousness in very severely brain-damaged patients may provide more reason to let them die. (...) Although functional neuroimaging is likely to play an increasing role in the assessment of patients in a vegetative state, caution is needed in the interpretation of neuroimaging findings. (shrink)

Tens of thousands of students have learned to be more discerning at constructing and evaluating arguments with the help of Patrick J. Hurley. Hurley’s lucid, friendly, yet thorough presentation has made A CONCISE INTRODUCTION TO LOGIC the most widely used logic text in North America. In addition, the book’s accompanying technological resources, such as CengageNOW and Learning Logic, include interactive exercises as well as video and audio clips to reinforce what you read in the book and hear in (...) class. In short, you’ll have all the assistance you need to become a more logical thinker and communicator. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

Presumably it is common ground that this verb has in addition to the basic sense ‘recognize’ the derivative sense ‘oread’, and that one must judge from the context whether reading to one or more other people, or private reading, is meant. The reading of the text of a law to a jury at an orator's request is marked by the circumstances themselves as public reading; so is the reading of the Athenian decree to the Mitylenaeans in Thucydides. When Theaetetus answers (...) in the affirmative the question whether he has read the book of Protagoras which contains the statement that man is the measure of all things (); or when it is asked ‘Why is it that some people, if they begin to read, are overcome by sleep even against their will, whereas others wishing to be overcome by sleep are kept awake by taking up a book?’ Evidently what is intended is reading in the privacy of one's own room. When Socrates in the Phaedo says that he heard a person reading from Anaxagoras and eagerly took the book home to read, both senses are found within a few pages. (shrink)