The many-worlds interpretation has usually been regarded as immune to nonlocality, and similar claims have been made for the consistent-histories interpretation (1-3). However, for a thought experiment of the Hardy type, the argument for nonlocality in the usual interpretation can be extended to both these other interpretations.

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.

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.

The proposition that a decreasing sequence of ordinals necessarily terminates has been given a new, and perhaps unexpected, importance by the rôle which it plays in Gentzen's proof of the freedom from contradiction of the “reine Zahlentheorie.” Gödel's construction of non-demonstrable propositions and the establishment of the impossibility of a proof of freedom from contradiction, within the framework of a certain type of formal system, showed that a proof of freedom from contradiction could be found only by transcending the axioms (...) and proof processes of that formal system. Gentzen's proof succeeds by utilisingtransfinite inductionto prove that certain sequences of reduction processes, enumerated by ordinals less than ε (the first ordinal to satisfy ε = ὡ) are finite. Were it possible to provethe restricted ordinal theorem, that a descending sequence of ordinals, less thanε, is finite, in Gentzen's “reine Zahlentheorie,” then it would be possible to determine a contradiction in that number system. In his paper, Gentzen proves the theorem of transfinite induction, which he requires, by an intuitive argument. There is also a method of reducing transfinite induction, for ordinals less than ε, to a number-theoretic principle given by Hilbert and Bernays, and a similar method by Ackermann. None of these proofs of transfinite induction isfinitist. (shrink)

This paper attempts to explore a number of conceptual issues surrounding genetic testing. It looks at the meaning of the terms, genetic information and genetic testing in relation to the definition set out by the Advisory Committee on Genetic Testing in the UK, and by the Task Force on Genetic Testing in the USA. It argues that the special arrangements that may be required for the regulation of genetic tests should not be determined by reference to the nature or technology (...) of the test, but by considering those morally relevant features that justify regulation. Failure to do so will lead to the regulation of genetic tests that need not be regulated, and would fail to cover other tests which should be regulated. The paper also argues that there is little in the nature of the properties of gene tests, using DNA or chromosomes, that in itself justifies a special approach. (shrink)

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)

World Mental Health Day serves as a timely reminder of the need to recognize and prioritize mental well-being amidst the growing complexities of modern life. Despite advancements in technology that have created comfort and convenience, these external developments often overshadow our inner well-being, leading to a neglect of mental health. This letter underscores the importance of nurturing our mental and emotional states, which serve as the foundation for overall health and a harmonious existence. Acknowledging the interplay between technology, distraction, and (...) mental stability is crucial in redefining what it means to lead a balanced life today. -/- . (shrink)

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)

This graduate-level_text by a master in the field builds a function theory of the rational field that combines aspects of classical and intuitionist analysis. Topics include recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.

The intersection of biology and religion has spawned exciting new areas of academic research that raise issues central to understanding our own humanity and the living world. In this comprehensive and accessible survey, Michael L. Peterson and Dennis R. Venema explain the engagement between biology and religion on issues related to origins, evolution, design, suffering and evil, progress and purpose, love, humanity, morality, ecology, and the nature of religion itself. Does life have a chemical origin - or must there be (...) a divine spark? How can religious claims about divine goodness be reconciled with widespread predation, suffering, and death in the animal kingdom? Peterson and Venema develop a philosophical discussion around such controversial questions. The book situates each topic in its historical, scientific, and theological context, making it the perfect introduction for upper-level undergraduates, graduate students, scholars, and the interested general reader. (shrink)

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: In the light of the almost brilliant equilibrium of the author, who manages to compose a resourceful explanation, switching between the notional conditionality and the expected contextual understanding, I intend to focus on the interdisciplinary potential of some suggestions that offer new perspectives on conceiving society, which are driven by a non-analytical and holistic vision.