It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure $\langle \omega; +, P\rangle$ , where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of $\langle\omega; S, P\rangle$ is decidable, where S is the successor function. The latter result is proved using a general (...) result of A. L. Semenov on decidability of monadic theories, and a proof of Semenov's result is presented. (shrink)
The text is taken from the edition of D. E. Hill, Mnemosyne Supplement 79 . The following works are referred to by author's surname only: H. W. Garrod, P. Papini Stati Thebais et Achilleis ; L. Håkanson, Statins Thebaid ; A. Klotz, P. Papini Stati Thebais ; R. Kühner, C. Stegmann, and A. Thierfelder, Ausführliche Grammatik der lateinischen Sprache ; R. Lesueur, Stace Thébaïde ; J. H. Mozley, Statius ; E. C. Woodcock, A New Latin Syntax.
Plato's Euthyrphro, Apology, andCrito portray Socrates' words and deeds during his trial for disbelieving in the Gods of Athens and corrupting the Athenian youth, and constitute a defense of the man Socrates and of his way of life, the philosophic life. The twelve essays in the volume, written by leading classical philosophers, investigate various aspects of these works of Plato, including the significance of Plato's characters, Socrates's revolutionary religious ideas, and the relationship between historical events and Plato's texts.
In an article published in the C.Q. of October 1937 I collected instances of the use of colloquial words and expressions in the dialogue passages of Euripides. It was there noted that a few of these expressions also appear in Aeschylus and Sophocles, and the purpose of the present study is to collect these, together with other instances of colloquialism which are found in the two earlier tragedians and not in Euripides. The colloquial element in the language of Aeschylus and (...) Sophocles is, of course, much smaller than in Euripides, but is perhaps greater than is sometimes supposed, and the topic has apparently not been treated elsewhere. (shrink)
Can the Âtman in its infinity and transcendence be made the basis for civil rights? Can we deduce the idea of civil rights and their number from the conception of the Âtman? Can historicity be preserved in the bosom of the Âtman? It has been said that only ideas like that of the dictatorship are possible on the basis of the Âtman as conceived by Indian thinkers. Individual freedom and initiative necessary for new scientific discoveries and inventions are taught by (...) Christ and other Israel-born religions, and the discovery of the atom bomb is due to such ideas. Long ago the late Prof. C.A. Moore of Hawaii urged me several times to handle such criticisms of Indian philosophy and religion. I tried to answer them in some early papers. The most important considerations are: As Kant said, from the highest metaphysical reality it is not logically possible to deduce anything particular or even lower; for instance, we cannot even deduce from “All men are mortal” whether Socrates is or is not mortal, unless we add “Socrates is a man,” which is an empirical statement. And If the Âtman is one and all-comprehensive, no democracy is said to be possible because individual men cannot be real then; but it is overlooked that then nothing is possible, not even trees and stones. Again, if there is only one personal God and if his will is supreme, will he not be a tyrant or a Louis XIV of the heavens, thundering his unquestionable commands? Where do democracy and freedom of the individual go then? On the other hand, if every one is the Supreme Âtman in essence, then everyone is free with all the initiative one can have by birth. Civil rights will then have a metaphysical foundation because every finite individual is inherently one with the Supreme Person and has the same rights and freedom as any king or emperor. But these arguments and counter-arguments cannot impress every one because to deduce anything from the highest Being leads only to antinomies and will be counter-productive in our search for truth. In metaphysics or ontology we can go only from the lower to the higher in logic or discursive thinking, but not vice versa. (shrink)
Objectives: To quantify the use of do-not-resuscitate orders in a tertiary-care children’s hospital and to characterise the circumstances in which such orders are written.Design: Retrospective study conducted in a 500-bed children’s hospital in Taiwan.Patients: The course of 101 patients who died between January 2002 and December 2005 was reviewed. The following data were collected: age at death, gender, disease and its status, place of death and survival. There were 59 males and 42 females with a median age of 103 months (...) . 50 children had leukaemias, and 51 had malignancies other than leukaemia. The t test and the χ2 test were applied as appropriate.Results: The study found that 44% of patient deaths occurred in the paediatric oncology ward; 29% of patient deaths occurred in the intensive care unit; and 28% of patients died in their home or at another hospital. Other findings included the following: 46 of 101 patients died after attempted cardiopulmonary resuscitation and 55 died with a DNR order in effect. The mean age at death was 9.8 years in both groups with or without DNR orders.Conclusions: From the study of patient deaths in this tertiary-care children’s hospital, it was concluded that an explicit DNR order is now the rule rather than the exception, with more DNR orders being written for patients who have been ill longer, who have solid tumours, who are not in remission and who are in the ward. (shrink)
Students of the Orestes are fortunate to have two excellent commentaries at their disposal, by C. W. Willink and M. L. West . Neither will help them to understand this line, which is ‘the only allusion to Ganymede's horsemanship’ , because ‘no story of riding by Ganymede is known’ . But we are repeatedly reminded that the scene with the Phrygian has far fewer affinities with tragedy than with comedy, and εριπιδαριστοφαíζεται Comedy provides the clue, specifically at Ar. Vesp. 50If. (...) and Lys. 676ff. The reference is to the variety of equestrianism for which Ganymede is far from unknown . For Innoavvr) here describes a σχμα ρωτικóν and the line means Ganymedes concubinus, Iovis supini inguini insidens et equitans, sc. inter causas fuit malorum propter Iunonis invidiam Troianis immissorum. (shrink)