The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of "and", "or", (...) "not" and "conditioning" are then defined on these conditional events with variable conditions. The probabilities of the disjunction and of the conjunction of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed. (shrink)

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events is due (...) to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be "inapplicable" (or "undefined") in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b = d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the 'influence-at-a-distance', quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that "hidden variables" are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. (shrink)

Reflecting on some distinctive contributions of the tradition of Reformed theology to our understanding of the nature and prospects of humans qua creatures within the economy of salvation, this article looks to draw out key themes which may serve to orient contemporary Christian engagements with the discourse of transhumanism.

Modern International Relations theory has consistently underestimated the depth of the problem of anarchy in world politics. Contemporary theories of globalisation bring this into bold relief. From this perspective, the complexity of transboundary networks and hierarchies, economic sectors, ethnic and religious ties, civil and cross-border wars, and internally disaggregated and transnationally connected state actors, leads to a complex and multidimensional restructuring of the global, the local and the uneven connections in between. We ought to abandon the idea of ‘high’ and (...) ‘low’ politics, ‘inside’ and ‘outside’ once and for all. This does not remove the problem of anarchy but rather deepens it, involving multidimensional tensions and contradictions variously described as ‘functional differentiation’, ‘multiscalarity’, ‘fragmegration’, disparate ‘landscapes’, the ‘new security dilemma’ and ‘neomedievalism’. Approaching anarchy from the perspective of plural competing claims to authority and power forces... (shrink)

Paul L. Lehmann was one of the leading Protestant theologians and ethicists of his generation. Working directly from archival sources and early writings, this article offers an account of the formation of key features of his distinctive theological perspective up to and including the first decades of his professional career. It argues that Lehmann prosecutes a distinctive and markedly Protestant form of public theology, centred on an understanding of the Word of God as a present, dynamic and humanising power, to (...) which Christian faith, life and thought give witness and serve catalytically. In this, Lehmann shows himself to be a premier advocate for lines of thinking he first encountered in the work of Karl Barth and of his friend, Dietrich Bonhoeffer. (shrink)

The claims of Mt. 5:17—20 are often taken to provide the interpretive key to the ethical claims of the Sermon on the Mount as a whole. The theological issue at stake here is the determinative relation between Christ's person and work and his teaching. This article explores the vital role played by the identity of Christ as the `fulfiller of the law' and `bringer of the Kingdom' in the exegesis of the Sermon offered by Eduard Thurneysen and Dietrich Bonhoeffer in (...) their respective works Die Bergpredigt (1936) and Nachfolge (1937). Both readings assert that the force and nature of the claims of the Sermon cannot be understood aright apart from constant attention to the difference made by the fact that Christ is the preacher. Out of this shared conviction, both theologians advance a reading of the Sermon as `the gospel itself' in the light of the eschatological identity of Jesus. Such readings of the Sermon, arising amidst the German Kirchenkampf of the 1930s, represent substantial contributions to the `responsible interpretation' of the Barmen Declaration (1934) whose second article states that, `As Jesus Christ is God's assurance of the forgiveness of all our sins, so in the same way and with the same seriousness is he also God's mighty claim upon our whole life.'. (shrink)

The claims of Mt. 5:17—20 are often taken to provide the interpretive key to the ethical claims of the Sermon on the Mount as a whole. The theological issue at stake here is the determinative relation between Christ's person and work and his teaching. This article explores the vital role played by the identity of Christ as the `fulfiller of the law' and `bringer of the Kingdom' in the exegesis of the Sermon offered by Eduard Thurneysen and Dietrich Bonhoeffer in (...) their respective works Die Bergpredigt (1936) and Nachfolge (1937). Both readings assert that the force and nature of the claims of the Sermon cannot be understood aright apart from constant attention to the difference made by the fact that Christ is the preacher. Out of this shared conviction, both theologians advance a reading of the Sermon as `the gospel itself' in the light of the eschatological identity of Jesus. Such readings of the Sermon, arising amidst the German Kirchenkampf of the 1930s, represent substantial contributions to the `responsible interpretation' of the Barmen Declaration (1934) whose second article states that, `As Jesus Christ is God's assurance of the forgiveness of all our sins, so in the same way and with the same seriousness is he also God's mighty claim upon our whole life.'. (shrink)

Christian ethicist Nancy Duff has suggested that an apocalyptic hearing of the gospel elicits a parabolic understanding of the Christian moral life. How might the theological basis and rationale of this claim be elaborated? What is it about human life funded by the gospel of God’s apocalypse in Jesus Christ that makes ‘parable’ an apt description of the quality of its action? And how might these notions be elaborated to enrich our understanding of responsible moral action more generally? This article (...) explores these questions by way of a running conversation with the work of J. Louis Martyn, Christopher Morse and Paul Ricoeur. It concludes by showing the salience of these themes in relation to Bonhoeffer’s later reflections upon the distinctive quality of Christian life in the wreckage of Christendom. Overall, the solid currency of a parabolic construal of the character of Christian moral action for the present pursuit of theological ethics is recommended. (shrink)

This paper argues that Calvin provides an account of the radical unmaking of the human moral subject at the hands of sin and its even more radical remaking at the hands of divine grace. The moral significance of human continuity during this soteriological transit, including such things as reason and will as such, is shown to be overreached by that of what becomes of the human creature in its history at the hands of both sin and God’s grace. Calvin’s treatment (...) of the first and third uses of the law confirms and illumines this claim decisively. Insight into this matter is aided by consideration of J. Louis Martyn’s discussion of the status of the moral subject in Pauline paraenesis A Reformed theological ethic that takes its cues from Calvin’s teaching in this regard will thus regard the adventitious realities of sin and grace, and their serial consequences for the constitution of the human moral agent, to represent the most important meta-ethical realities to be considered. (shrink)

Volume 20, Issue 4, May 2020, Page 35-37.

A landmark study in the field of political science, The Changing Architecture of Politics charts the profound structural changes taking place in the late twentieth-century state. Looking at both theory and practice, Cerny argues that political structures--states in the broadest sense--are the key to understanding both the history and the future of modern politics. Included for discussion are such salient topics as the problem of locating institutional and structural theory within political and social science, how to describe and classify the (...) main elements of political structures, and a penetrating analysis of the structured action field that lies at the crossroads of political structuration. In addition, he explores several core areas in practice, including how states will operate in the next century and how states will interact with the manifold changes in social and economic processes--at both the domestic and international levels. Through his masterly portrayal of the architecture of contemporary politics, Cerny lays the foundations for an understanding of new political structures that are needed if the pursuit of human values is to continue into the next century. As such, this fascinating volume will appeal to all those interested in the paradigms of political and social science, whether from a purely theoretical or from a more empirical standpoint. "This is the best introduction available in English to contemporary academic discussions about the purpose and prospects of applying the comparative method to political science. Cerny's book is comprehensive in scope and accomplishes three, quite rare tasks: it brings together material on North America, Western Europe, and Japan; it combines theories of comparative politics and international relations; it pays equal attention to systems of party competition and of interest intermediation, although its primary focus is upon the state. Philip Cerny has produced a tour de force, an intelligent, erudite, and comprehensive text that cuts decisively through artificial barriers within the discipline." --Political Science Quarterly. (shrink)

Moral philosophy and education, by H. D. Aiken.--The moral sense and contributory values, by C. I. Lewis.--Realms of value, by P. W. Taylor.--The role of value theory in education, by J. D. Butler.--Does ethics make a difference? By K. Price.--Educational value statements, by C. Beck.--Educational values and goals, by W. K. Frankena.--Conflicts in values, by H. S. Broudy.--Levels of valuational discourse in education, by J. F. Perry and P. G. Smith.--Education and some moves toward a value methodology, by A. S. (...) Clayton.--You can't pray a lie, by M. Twain.--Men, machines, and morality, by J. F. Soltis.--Teaching and telling, by I. Scheffler.--Reason and habit, by R. S. Peters.--The two moralists of the child, by J. Piaget.--Causes and morality, by R. S. Peters.--On education and morals, by R. W. Sleeper.--Moral autonomy and reasonableness, by T. D. Perry. (shrink)

This book offers a roadmap for determining when and how to regulate risky reproductive technologies on behalf of future children. It starts by explaining our intuitive, but paradoxical, belief that reproductive choices can be both life-giving and harmful. Next, it recommends a case-by-case method for reconciling the interests of future children with the reproductive liberty of prospective parents. Finally, it applies this framework to four past and future medical interventions, including cloning and genetic engineering. Drawing lessons from these case studies, (...) it criticizes the current lack of regulatory oversight. (shrink)

These essays deal with the scholarly study of the genesis, transmission, and editorial reconstitution of texts by exploring the connections between textual instability and textual theory, interpretation, and pedagogy. What makes this collection unique is that each essay brings a different theoretical orientation-New Historicism, Poststructuralism, or Feminism-to bear upon a different text, such as Whitman's Leaves of Grass , Faulkner's The Sound and the Fury, or hypertext fiction, to explore the dialectical relationship between texts and textuality. The essays bring some (...) of the textual theories that compete with each other today into contact with a broad range of primarily literary textual histories. That texts are intrinsically unstable, frequently consisting of a series of determinate historical versions, has consequences for all students of literature, because different versions of a literary work frequently help shape different readings independently of the interpretations brought to bear upon them. Textual instability of the works is relevant to our understanding of how the meanings of texts are generated. The contributors build on the numerous challenges to the Anglo-American editorial tradition mounted during the past decade by scholars as diverse as Jerome McGann, D.F. McKenzie, Peter Shillingsburg, D.C. Greetham, Hershel Parker, and Hans Walter Gabler. The volume contributes to the paradigm shift in textual scholarship inaugurated by these scholars. Index. (shrink)

The writers respond to the commentary “Physician Burnout Calls for Legal Intervention,” by Sharona Hoffman, in the November‐December 2019 issue of the Hastings Center Report.