The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

This paper will discuss the behaviour of and in the Homeric poems. These words are allotted a variety of different ‘meanings’ by the lexicographers. For example, LSJ s.v. I. pray, II. vow, III. profess loudly, boast, vaunt; s.v. I. prayer, II. boast, vaunt, or object of boasting, glory; s.v. I. thing prayed for, object of prayer, II. boast, vaunt. I shall, of course, discuss the whole range of these words; but I begin with some observations on ‘prayer’. It may appear (...) at first sight that ‘prayer’ is a simple word, with only one conceivable ‘meaning’, which must have that ‘meaning’ in any language. We might suggest that ‘request addressed to a god’ is an adequate representation of that ‘meaning’, and that when we have rendered by ‘pray’ in what appear to us to be appropriate contexts we have conveyed the full sense of the original. (shrink)

In this article, an ethical analysis of an educational programme on renal replacement therapy options for patients and their social network is presented. The two main spearheads of this approach are: (1) offering an educational programme on all renal replacement therapy options ahead of treatment requirement and (2) a home-based approach involving the family and friends of the patient. Arguments are offered for the ethical justification of this approach by considering the viewpoint of the various stakeholders involved. Finally, reflecting on (...) these ethical considerations, essential conditions for carrying out such a programme are outlined. The goal is to develop an ethically justified and responsible educational programme. (shrink)

It is always possible to construct a real function φ, given random quantities X and Y with continuous distribution functions F and G, respectively, in such a way that φ(X) and φ(Y), also random quantities, have both the same distribution function, say H. This result of De Finetti introduces an alternative way to somehow describe the `opinion' of a group of experts about a continuous random quantity by the construction of Fields of coincidence of opinions (FCO). A Field of coincidence (...) of opinions is a finite union of intervals where the opinions of the experts coincide with respect to that quantity of interest. We speculate on (dis)advantages of Fields of Opinion compared to usual `probability' measures of a group and on their relation with a continuous version of the well-known Allais' paradox. (shrink)

© 2016 Regents of the University of California.The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous (...) tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group. The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. (shrink)

This volume presents a selection of the most important writings in the debate on the nature of meaning and reference which started one hundred years ago with Frege's classic essay "On Sense and Reference." Contributors include Bertrand Russell, P.F. Strawson, W.V. Quine, Donald Davidson, John McDowell, Michael Dummett, Hilary Putnam, Saul Kripke, David Wiggins, and Gareth Evans. The aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a wide variety of (...) sources, mostly periodicals, which may not be conveniently available to the university student or the general reader. (shrink)

In the philosophy of mathematical practice, the aim is to understand the various aspects of this practice. Even though definitions are a central element of mathematical practice, the study of this aspect of mathematical practice is still in its infancy. In particular, there is little empirical evidence to substantiate claims about definitions in practice. In this article, we address this gap by reporting on an empirical investigation on how mathematicians create definitions and which roles and properties they attribute to them. (...) On the basis of interviews with thirteen research mathematicians, we provide a broad range of relevant aspects of definitions. In particular, we address various roles of definitions and show that definitions are not just a product of mathematical factors, but also of social and contingent factors. Furthermore, we provide concrete examples of how mathematicians interact and think about definition. This broad empirical basis with a variety of examples provides an optimal starting point for future investigations into definitions in mathematical practice. (shrink)

DR. G. Zuntz's excellent paper on these verses in Proc. Brit. Acad. xlii , 209–46, deserves all our thanks for the clarity and good sense of its exposition, and for clearing away much unnecessary comment that has been encumbering the fragment, especially Bignone's theory that it derives its philosophy directly from Aristotle's Protreptikos, with Körte's supplement that it is indivisible—that there is no break at v. 7; see Körte's Menandri quae supersunt , ii. 147–8. There is, however, I think, room (...) for further comment on Zuntz's interpretation of the lines, and on his view that die fragment known as Papyrus Didotiana b may belong to the same play, Hypobolimaios. (shrink)

Definitions are traditionally seen as abbreviations, as tools for notational convenience that do not increase inferential power. From a Philosophy of Mathematical Practice point of view, however, there is much more to definitions. For example, definitions can play a role in problem solving, definitions can contribute to understanding, sometimes equivalent definitions are appreciated differently, and so on. This chapter reviews the literature on definitions and (to a certain extent) concepts in mathematical practice. It is structured according to four themes through (...) which definitions (and concepts) in mathematical practice have been studied. These themes concern (1) the nature of definitions, (2) whether and how concepts evolve, (3) definitions and concepts from a communal perspective, and (4) different values relating to definitions and concepts. (shrink)

Hegel is an immensely important yet difficult philosopher. His Philosophy of Mind is one of the main pillars of his thought. Michael Inwood, highly respected for his previous work on Hegel, presents this central work to the modern reader in an accurate new translation supported by a philosophically sophisticated editorial introduction and elucidating scholarly commentary.

In 1924 W. W. Tarn published an article in which he attempted to prove that the mother of Philip V of Macedon was the Epirot princess Phthia. Previously all historians had accepted the statement of Eusebius that Philip was the son of Demetrius II and Chryseis, whom, after the death of her husband, the Macedonians gave in marriage to Antigonus Doson. Despite the cogency of Tarn's arguments, his theory has been rejected by both Beloch and Dinsmoor, who adhere to the (...) traditional view. This problem of the identity of Philip's mother is one of considerable importance, and consequently in this paper I intend to collect the evidence once again and subject it to a careful analysis. The results will be found strongly to corroborate Tarn's contention. (shrink)

Introduction: The decision of “do not attempt resuscitation” in the event of cardiopulmonary arrest is usually made when the patients are critically ill and cannot make an informed choice. Although, various professional bodies have published guidelines, little is know about the patients’ own views regarding DNAR discussion.Aim: The aim of this study was to determine patients’ attitudes regarding discussing DNAR before they are critically ill.Methods: A prospective study was performed in a general out patients department. A questionnaire was distributed to (...) consecutive outpatients along with an explanatory leaflet in the adult outpatient clinic.Results: 364 patients completed the questionnaire . 90% of respondents wanted all patients to be asked regarding DNAR decision at some point during a hospital admission. The majority would not find a DNAR discussion distressing. Only 10% would find it upsetting, however, 48% of these still wanted a discussion. 37% of respondents wanted to discuss DNAR decisions on admission; 32% in outpatients; 17% at consent for surgery, 14% when they are critically ill. 87% of respondents would not object to their relatives being involved in making decisions about their resuscitation status. However, only 12% of the subjects in the study had been involved in discussing the resuscitation status of a relative and 21% would not be comfortable to discuss a relative’s resuscitation status. Although 33% of patients preferred their resuscitation status to simply be documented within their clinical notes, 77% wanted it to be more easily accessible.Conclusions: This study suggests that contrary to current practice most patients want to discuss their DNAR status prior to becoming critically ill. This includes half of the small number that find it distressing to discuss. Although most patients are comfortable with relatives being involved in discussing DNAR, a significant proportion do not want their relatives to be asked. Furthermore, once a decision has been made, the majority of patients want it to be more accessible than current practice allows. (shrink)

Abstract‘Yellow Rain’, an alleged biological warfare agent thought to be utilized in parts of both South East Asia and Afghanistan, may be composed in part of the mycotoxins, trichothecenes. However, more recent analyses suggest that the ‘Rain’ was mainly honey bee excreta. The history of the controversy together with the biological effects, chemistry as well as the fungi producing these mycotoxins and agricultural commodities affected by trichothecenes are reviewed.

This is volume XVIII in the Library of Living Philosophers. It contains Quine’s intellectual autobiography, “approximately one fifth [of which] recurs sporadically” in the much more inclusive The Time of My Life ; there follow twenty-four critical essays covering all aspects of his work by some of the most eminent living philosophers, with a reply by Quine to each; and finally there is a bibliography of his publications, running, remarkably, to eighteen pages and including seventeen books. The volume is required (...) reading for any serious student of Quine’s philosophy; that much is obvious. It is also necessary for any serious student of analytic philosophy; the fact that this is hardly less obvious is a measure of the importance and greatness of Quine’s contribution to the field. (shrink)

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.