I propose to begin with some fairly unexciting and uncontroversial remarks about possibility-statements, and then in their light to examine two problems philosophers have raised about certain statements of this kind which might be made in Christian theology where it touches on the doctrine of the Incarnation.

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the (...) class='Hi'>Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

Mr D. H. Mellor, in his article of this title in Religious Studies , Vol. 5 , distinguishes three senses of words such as ‘probable’ which might be used in a religious context, especially in that of attempted theistic proofs: statistical, subjective, and inductive probability. In each case he concludes that it is misleading to use these words in such contexts at all. With his discussion of the second I do not wish to quarrel; but there seem to me to (...) be serious defects in his discussions of the first and third. (shrink)

Addressing both collegiate and professional sports, the updated edition of Fair Play: The Ethics of Sport explores the ethical presuppositions of competitive athletics and their connection both to ethical theory and to concrete moral dilemmas that arise in actual athletic competition. This fourth edition has been updated with new examples, including a discussion of Spygate by the New England Patriots and recent discoveries on the use of performance enhancing drugs by top athletes. Two additional authors, Cesar R. Torres and Peter (...) F. Hager, bring to this edition a discussion of the moral issues involved in youth sports and the ethics of being a fan, as well as a fresh perspective on the theories of broad internalism and the quest for excellence. Furthermore, major criticisms of broad internalism by philosophers William J. Morgan and Scott Kretchmar add a new dimension to the discussion on the moral foundations of winning. (shrink)

When philosophers approach philosophy of religion, they typically ask two questions: are there any sound arguments to prove the existence of God; and is talk about God even rationally intelligible? Theologians, for their part, primarily expound the meaning and relevance of Christianity. I am by profession a philosopher, but apart from Secs. VI and VII I am here writing as a puzzled twentieth-century man. My prime worry is whether we philosophers and theologians are beginning with the right questions.

After discussing the interests that ground the right to democratic political participation, arguments for the disenfranchisement of those who commit serious criminal offenses are examined. The arguments are divided into two groups. The first group consists of arguments that are relatively independent of the justifying aims of punishment. It is conceded that two of these arguments establish that some, though by no means all, serious offenders should lose the vote for a period of time that does not necessarily overlap with (...) the duration of the other sanctions visited upon them. These arguments also imply that the state is justified in attempting to exclude the offenders in question from all forms of political participation, a position that arguably runs afoul of moral limits on punishment. The second group of arguments makes explicit reference to the justifying aims of punishment. None supports the blanket disenfranchisement of felons, though some may justify it in relation to some serious offenders for certain periods of time. All of the arguments supporting the disenfranchisement of serious offenders are most persuasive on the assumption that they live in reasonably just societies that are genuinely democratic. If that assumption is false or questionable, then it is argued that the force of such arguments may be weakened considerably. (shrink)

The ‘traditional’ view among philosophical theologians, that God is eternal not merely in the sense of being everlasting but in the sense of being outside time altogether, has come under sharp criticism in recent years, both from biblical theologians and from philosophers. It is against the latter form of attack, particularly as represented by the detailed criticisms of Professor Nelson Pike, that I wish to try and defend the notion of a divine timelessness.

I have come to believe that the whole framework of our current thought is about to begin a long and radical transformation, based on what I shall call a new science of pure consciousness. The content of most of the matters to be considered by this science have hitherto been the concern of some areas of religion, particularly what in our culture we call ‘mysticism’; but the treatment of it would legitimately be called scientific. Thus one aspect of the transformation (...) would be to overcome that apparent conflict between ‘science’ and ‘religion’, which has been so characteristic of our culture over the last few centuries. (shrink)

Mole's (2008 [this issue]) argument that consciousness is a necessary concomitant of attention rests on the question of what is being attended in spatial attention. His answer is space. Some authors, including ourselves, claim that the fact that the processing of unseen objects can be modulated by spatial attention (e.g. Kentridge et al., 1999; 2004; 2008; Marzouki et al., 2007; Sumner et al., 2006) demonstrates that visual attention is not a sufficient precondition for visual awareness. Mole, however, contends that as (...) space, rather than any object that might occupy that space, is what is being attended, these experiments do not constitute evidence for a dissociation between attention and consciousness. We disagree. To understand the source of this disagreement we need to understand the various processes encompassed by the term 'attention' and to consider experimental evidence illustrating how these processes operate. We review evidence that spatial attention can be deployed with the specific goal of determining the properties of objects occupying the attended region of space. One might, for example, attend to a location with the goal of determining the colour of objects occupying that space as efficiently as possible. Mole's assumption that all that is attended in spatial attention is space is not consistent with this evidence. We conclude that attention can be directed at objects by mechanisms of so- called 'spatial attention' without those objects necessarily eliciting conscious visual experience and hence that attention is not a sufficient precondition for visual awareness. (shrink)

Thomas Hill Green was one of the most influential English thinkers of his time, and he made significant contributions to the development of political liberalism. Much of his career was spent at Balliol College, Oxford: having begun as a student of Jowett, he later acted effectively as his second-in-command at the college. Interested for his whole career in social questions, Green supported the temperance movement, the extension of the franchise, and the admission of women to university education. He became Whyte's (...) professor of moral philosophy at Oxford in 1878, and his lectures had a lasting influence on a generation of students. Much of Volume 1, edited by Green's pupil R. L. Nettleship and published in 1885, consists of Green's work on David Hume. In his essay, 'Introductions to Hume's Treatise of Human Nature', Green gives a detailed critique of Hume's metaphysical thought. (shrink)

Each stage has its difficulties and its points of interest, and I will examine each in turn.

In computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, (...) eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology. (shrink)