This article is an attempt to clarify a confusion in the brain death literature between logical sufficiency/necessity and natural sufficiency/necessity. We focus on arguments that draw conclusions regarding empirical matters of fact from conceptual or ontological definitions. Specifically, we critically analyze arguments by Tom Tomlinson and Michael B. Green and Daniel Wikler. which, respectively, confuse logical and natural sufficiency and logical and natural necessity. Our own conclusion is that it is especially important in discussing the brain death issue to observe (...) the distinction between logical and natural sufficiency/necessity in a strict fashion. (shrink)

Quasi-probability distribution functions fj WW, fj MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fj sph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.

This Companion provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general. The sixteen essays, by authors who represent various academic disciplines, bring a spectrum of interpretive approaches to bear in order to aid the understanding of a wide-ranging audience, from first-time readers of the Republic who require guidance, to more experienced readers who wish to explore contemporary currents in the work’s interpretation. The (...) three initial chapters address aspects of the work as a whole. They are followed by essays that match closely the sequence in which topics are presented in the ten books of the Republic. Since the Republic returns frequently to the same topics by different routes, so do the authors of this volume, who provide the readers with divergent yet complementary perspectives by which to appreciate the Republic’s principal concerns. (shrink)

A simple model for the description of atomic and ionic species with spectra exhibiting a quantum defect is solved using the Lie algebra su(1, 1). The quantum defect of bound states is related to the phase shift of scattering states. The resonances are discussed in terms of the nonunitary representations of this algebra.