This chapter contains sections titled: The Cutting Edge Automated Reasoning, Principles and Elements Significant Successes Myths, Mechanization, and Mystique.

detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XC B = e(x e(e(e( ) e( )) z)) a single axiom for the classical equivalential calculus when the rules of inference consist..

This article features long-sought proofs with intriguing properties (such as the absence of double negation and the avoidance of lemmas that appeared to be indispensable), and it features the automated methods for finding them. The theorems of concern are taken from various areas of logic that include two-valued sentential (or propositional) calculus and infinite-valued sentential calculus. Many of the proofs (in effect) answer questions that had remained open for decades, questions focusing on axiomatic proofs. The approaches we take are of (...) added interest in that all rely heavily on the use of a single program that offers logical reasoning, William McCune's automated reasoning program OTTER. The nature of the successes and approaches suggests that this program offers researchers a valuable automated assistant. This article has three main components. First, in view of the interdisciplinary nature of the audience, we discuss the means for using the program in question (OTTER), which flags, parameters, and lists have which effects, and how the proofs it finds are easily read. Second, because of the variety of proofs that we have found and their significance, we discuss them in a manner that permits comparison with the literature. Among those proofs, we offer a proof shorter than that given by Meredith and Prior in their treatment of ukasiewicz's shortest single axiom for the implicational fragment of two-valued sentential calculus, and we offer a proof for the ukasiewicz 23-letter single axiom for the full calculus. Third, with the intent of producing a fruitful dialogue, we pose questions concerning the properties of proofs and, even more pressing, invite questions similar to those this article answers. (shrink)

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...) of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study. (shrink)

Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.

How should the well-off respond to the world's needy? Renowned ethicist Larry S. Temkin challenges common beliefs about philanthropy and Effective Altruism, exploring the complex ways that global aid may do more harm than good, and considers the alternatives available when neglecting the needy is morally impermissible.

Being a patient and living a life -- Clinical space and traits of healing -- False starts and frequent failures -- Three journeys : A.'Ibuprofen and love', B. 'Staying tuned up', C. 'We all want the same things' -- Being a patient : the moral field -- Rethinking healthcare ethics : the patient's moral authority.

In The Responsive Environment, Larry D. Busbea takes up this concept of environment as an object and method of design at the height of its aesthetic, technical, and discursive elaboration. Exploring novel models of environmental perception, patterning, and control as developed by Gregory Bateson, Edward T. Hall, Wolf Hilbertz, György Kepes, Marshall McLuhan, Nicholas Negroponte, Paolo Soleri, and others, he shows how living space was reimagined as a domain capable of modification through input from its newly sensitized inhabitants.

In this two-volume set, Larry D. Barnett delves into the macrosociological sources of law concerned with society-important social activities in a structurally complex, democratically governed nation. Barnett explores why, when, and where particular proscriptions and prescriptions of law on key social activities arise, persist, and change. The first volume, Societal Agents in Law: A Macrosociological Approach, puts relevant doctrines of law into a macrosociological framework, uses the findings of quantitative research to formulate theorems that identify the impact of several (...) society-level agents on doctrines of law, and takes the reader through a number of case analyses. The second volume, Societal Agents in Law: Quantitative Research, reports original multivariate statistical studies of sociological determinants of law on specific types of key social activities. Taken together, the two volumes offer an alternative to the almost-total monopoly of theory and descriptive scholarship in the macrosociology of law, comparative law, and history of law, and underscore the value of a mixed empirical/theoretical approach. (shrink)

In this two-volume set, Larry D. Barnett delves into the macrosociological sources of law concerned with society-important social activities in a structurally complex, democratically governed nation. Barnett explores why, when, and where particular proscriptions and prescriptions of law on key social activities arise, persist, and change. The first volume, Societal Agents in Law: A Macrosociological Approach, puts relevant doctrines of law into a macrosociological framework, uses the findings of quantitative research to formulate theorems that identify the impact of several (...) society-level agents on doctrines of law, and takes the reader through a number of case analyses. The second volume, Societal Agents in Law: Quantitative Research, reports original multivariate statistical studies of sociological determinants of law on specific types of key social activities. Taken together, the two volumes offer an alternative to the almost-total monopoly of theory and descriptive scholarship in the macrosociology of law, comparative law, and history of law, and underscore the value of a mixed empirical/theoretical approach. (shrink)

There is extensive discussion in current Just War literature about the normative principles which should govern the initiation of war (jus ad bellum) and also the conduct of war (jus in bello), but this is the first book to treat the important and difficult issue of justice after the end of war. Larry May examines the normative principles which should govern post-war practices such as reparations, restitution, reconciliation, retribution, rebuilding, proportionality and the Responsibility to Protect. He discusses the emerging (...) international law literature on transitional justice and the problem of moving from a position of war and possible mass atrocity to a position of peace and reconciliation. He questions the Just War tradition, arguing that contingent pacifism is most in keeping with normative principles after war ends. His discussion is richly illustrated with contemporary examples and will be of interest to students of political and legal philosophy, law and military studies. (shrink)

This book interrogates the meaning and consequences of the unsettling parallel relationship between today’s critical theory and Right-wing political philosophy.

This chapter provides comments on some current longevity research. The ultimate aim of longevity research is to stop the aging process, so that none of us need die of old age. The chapter indicates the attitudes towards death and science. It discusses some worries about immortality raised by Leon Kass and Bernard Williams. In “Mortality and Morality: The Virtues of Finitude,” Leon Kass, raised many deep worries about immortality. One was that many of our greatest creations resulted from the recognition (...) of our own mortality. Bernard Williams notes that if our lives persisted unendingly through time, then there would either be significant alterations in a person's deepest projects, commitments, and character, or there would not. The author suggests that we should favor living well over living longer, and ongoing reproduction over immortality, and we should think long and hard before proceeding with certain lines of longevity research. (shrink)

This book, the result of cooperation between the Center for Dewey Studies at Southern Illinois University Carbondale, and the Dewey Center at the University of ...

What would happen if you made your business decisions by the book? By the Bible that is. This updated version of the best-selling Business by the Book offers radical principles of business management that go beyond the Ten Commandments and other biblical maxims. Business by the Book is a step-by-step presentation of how businesses should be run according to the Creator of all management rules: God. Larry Burkett, founder and president of Christian Financial Concepts, provides business principles from his (...) own experience as well as what God’s Word says on topics such as: Hiring and Firing Decisions Pay Increases and Promotions Management Selection Employee Pay Decisions Borrowing and/or Lending Decisions Forming Corporations and Partnerships Business Tithing Retirement Whether you are the owner of a business, a corporate executive, or a manager, this best-selling classic is for you. (shrink)

This book from award winning author Dr. Larry Crabb seeks to think through a model of counseling which can be integrated into the functioning of the local church. It contains a chart appendix.

This chapter wades into the growing discussion surrounding embodied cognition and predictive processing. After surveying a recent debate between Jakob Hohwy and Andy Clark, it articulates two outstanding issues facing discussions of compatibility. It argues that headway on these issues can be made by drawing on the resources of philosophy of science.

Temkin's book is a very original and deeply unsettling work of skeptical philosophy that mounts an important new challenge to contemporary ethics.

This Major Reference series brings together a wide range of key international articles in law and legal theory. Many of these essays are not readily accessible, and their presentation in these volumes will provide a vital new resource for both research and teaching. Each volume is edited by leading international authorities who explain the significance and context of articles in an informative and complete introduction.

Diplomatic theory and practice -- International funding for animal protection -- International conferences and delegation management -- The media as a tool for diplomacy -- Important associations and international organizations -- Epilogue.

INTRODUCTION The appeal to teleological principles of explanation within the body of natural science has had an unfortunate history. ...

Charles Mills adhered to the highest standards of philosophical scholarship, while seeing his work firmly as a contribution to the cause of social justice. He had a deep appreciation for historical context and a history of ideas approach to racial/philosophical questions. He was one of the foremost Rawls interpreters or our time, though only a few years before his passing was he so recognized. He channeled his analytic training in his habit of demonstrating how a view is strengthened when an (...) author shows how objections can be systematically replied to. I wish he had tried to integrate class and race into a larger theoretical system, of both an explanatory and normative character. Class is sometimes an unnoted presence in his explanation of white supremacy. Charles saw himself contributing to a collective scholarly social justice project and was happy to acknowledge the greater expertise of others in allied areas to his. (shrink)

The problem of the relation between mind and brain has been among the most persistent in modern Western thought, one that even recent advances in neuroscience haven't been able to put to rest. Historian Larry McGrath's Making Spirit Matter is about how a particularly productive and influential generation of late nineteenth- and early twentieth-century French thinkers attempted to answer this puzzle by showing the mutual dependence of spirit and matter. The veritable revolution taking place across disciplines, from philosophy to (...) psychology, located our spiritual powers in the brain and offered a radical reformulation of the meaning of science, spirit, and the self. Pulling out connections between thinkers such as Bergson, Blondel, and Fouille̹e, among others, McGrath plots the intellectual movements that brought back to life themes of agency, time, and experience by putting into action the very sciences that seemed to undermine metaphysics and theology. In so doing, Making Spirit Matter lays bare the long legacy of this moment in the history of ideas and how it might renew our understanding of the relationship between mind and brain. (shrink)