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.

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)

It is an unresolved question in quantum mechanics whether quantum states apply to individual quantum systems, or to ensembles of quantum systems. We show by way of a thought experiment that quantum states apply only to ensembles of quantum systems. A further unresolved question is whether quantum systems possess ontic states. If a quantum state is the state of an ensemble, as we claim, the answer to this question is that quantum states are not ontic. However, a notable recent result (...) in quantum foundations shows that if there are any ontic states at all, then the quantum state must be ontic. Collectively, these two results imply that there are no ontic states. We examine the assumptions required for these results, and suggest that the retrospective effect on state preparations by entangling measurements provides good reason for relaxing the assumption of preparation independence at the ontic level. (shrink)

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)

D J O’Connor; The Nature of Educational Theory, Journal of Philosophy of Education, Volume 6, Issue 1, 30 May 2006, Pages 97–109, https://doi.org/10.1111/j.1467.

The importance of this book, which appeared in the original German in 1969 under the title Zur Sache des Denkens, 743), is attested to by the rapidity with which it has been translated into English. The title of the English translation is that of the lead essay, the highly celebrated lecture which Heidegger gave in 1962 and which bears the same title as the never published "third division" of the "first half" of Being and Time. This lecture is perhaps the (...) most significant document to be added to the Heideggerian corpus since the Letter on Humanism. It is of course dramatically different from Being and Time and so cannot be regarded as a "continuation of the text of Being and Time." "Time and Being" thematizes the central notion of Heidegger’s later work, "Das Eregignis," [[sic]] translated happily by Miss Stambaugh as "Event of Appropriation". The "Event of Appropriation" is the "It" which "gives" Being and time in the sequence of epochs which constitute the history of Western metaphysics. The lecture is followed by an instructive "seminar" conducted by Heidegger on the text of "Time and Being." There is found here also a penetrating essay entitled "The End of Philosophy and the Task of Thinking," as well as a fascinating piece of autobiography entitled "My Way in Phenomenology." Miss Stambaugh’s translation is superb, something readers of the "Heidegger, Works" series which she edits with J. Glenn Garay have become accustomed to.—J. D. C. (shrink)

We briefly review the history of de Broglie's notion of the “double solution” and of the ideas which developed from this. We then go on to an extension of these ideas to the many-body system, and bring out the nonlocality implied in such an extension. Finally, we summarize further developments that have stemmed from de Broglie's suggestions.

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French philosopher’s (...) fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory. (shrink)

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be (...) more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments. (shrink)

That both parts of the sentence refer to the same person is now generally agreed; it is not so much that a change of subject would be, as the commentators are wont to say, ‘un-Sophoclean’, but simply that it would be awkward and clumsy. But to whom do the lines refer?D. B. Gregor argues for Clytaemnestra, but despite the apparent force of some of his arguments I cannot agree. He adds too that the reference to echoes the motif of Electra's (...) speech, but it is just as much the motif of Clytaemnestra's speech, in fact more so. Finally, the first part of the sentence, it is true, could be asserted by the chorus on the strength of some such gesture as the heaving of the bosom, but I cannot see how they could then deduce that Clytaemnestra ‘no longer cares whether justice is on her side’. (shrink)