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If natural law arguments struggle to gain traction in contemporary moral and political discourse, could it be because we moderns do not share the understanding of nature on which that language was developed? Building on the work of important thinkers of the last half-century, including Leo Strauss, Eric Voegelin, John Finnis, and Bernard Lonergan, the essays in Concepts of Nature compare and contrast classical, medieval, and modern conceptions of nature in order to better understand how and why the concept of nature no longer seems to provide a limit or standard for human action. These essays also evaluate whether a rearticulation of pre-modern ideas (or perhaps a reconciliation or reconstitution on modern terms) is desirable and/or possible. Edited by R. J. Snell and Steven F. McGuire, this book will be of interest to intellectual historians, political theorists, theologians, and philosophers.

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Manchester Beethoven studies presents ten original chapters by scholars with close ties to the University of Manchester. It throws new light on many aspects of Beethoven’s life and works, with a special emphasis on early or little-known compositions such as his concert aria Erste Liebe, his String Quintet Op. 104 and his folksong settings. Biographical elements are prominent in a wide-ranging reassessment of his religious attitudes and beliefs, while Charles Hallé, founder of the Manchester-based Hallé Orchestra, is revealed to have been a tireless and energetic promoter of Beethoven’s music in the later nineteenth century. -- .

Beethoven's piano sonatas are a cornerstone of the piano repertoire and favourites of both the concert hall and recording studio. The sonatas have been the subject of much scholarship, but no single study gives an adequate account of the processes by which these sonatas were composed and published. With source materials such as sketches and correspondence increasingly available, the time is ripe for a close study of the history of these works. Barry Cooper, who in 2007 produced a new edition of all 35 sonatas, including three that are often overlooked, examines each sonata in turn, addressing questions such as: Why were they written? Why did they turn out as they did? How did they come into being and how did they reach their final form? Drawing on the composer's sketches, autograph scores and early printed editions, as well as contextual material such as correspondence, Cooper explores the links between the notes and symbols found in the musical texts of the sonatas, and the environment that brought them about. The result is a biography not of the composer, but of the works themselves.

This title offers an exploration of case-focused methods as a means of bridging the quantitative-qualitative divide and the key methodological issues. This book challenges the divide between qualitative and quantitative approaches that is now institutionalized within social science. Rather than suggesting the 'mixing' of methods, "Challenging the Qualitative-Quantitative Divide" provides a thorough interrogation of the arguments and practices characteristic of both sides of the divide, focusing on how well they address the common problems that all social research faces, particularly as regards causal analysis. The authors identify some fundamental weaknesses in both quantitative and qualitative approaches, and explore whether case-focused analysis - for instance, in the form of Qualitative Comparative Analysis, Analytic Induction, Grounded Theorising, or Cluster Analysis - can bridge the gap between the two sides.

Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.

This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues.

The list of contributors includes: S Abramsky, P Adriaans, M Agrawal, M Arslanov, G Ausiello, J Diaz, Y Ershov, G Longo, W Maass, I Nemeti, A Nerode, D Normann, G Odifreddi, M Rathjen, G Rozenberg, M Vardi, and P Welch.

Beethoven's piano sonatas are a cornerstone of the piano repertoire and favourites of both the concert hall and recording studio. The sonatas have been the subject of much scholarship, but no single study gives an adequate account of the processes by which these sonatas were composed and published. With source materials such as sketches and correspondence increasingly available, the time is ripe for a close study of the history of these works. Barry Cooper, who in 2007 produced a new edition of all 35 sonatas, including three that are often overlooked, examines each sonata in turn, addressing questions such as: Why were they written? Why did they turn out as they did? How did they come into being and how did they reach their final form? Drawing on the composer's sketches, autograph scores and early printed editions, as well as contextual material such as correspondence, Cooper explores the links between the notes and symbols found in the musical texts of the sonatas, and the environment that brought them about. The result is a biography not of the composer, but of the works themselves.

In Child Composers and Their Works: A Historical Survey, Barry Cooper examines over 100 composers born before 1900 who wrote substantial musical works before age 16. The book provides a general overview of the subject, examining the ways and identifying possible reasons these works have been marginalized in the general literature. The book also contains an annotated checklist of over 100 notable child composers, presenting a valuable and handy reference of these creators and their early works. The annotated checklist presents a chronological listing of child composers born before 1900 and features a descriptive list of what they wrote, often including analytical commentary and offering occasional music examples for illustration. The list also includes a select catalog of works, suggestions for further reading, and recordings when available. Complete with a bibliography and an index of composers, this resource is invaluable to scholars and historians.

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences.

Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level.

The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science.

Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

In The West at War, Bradley C. S. Watson brings together renowned scholars and public policy experts to reflect on perhaps the most pressing problem of our time-the West's increasingly bloody conflict with forces that seek nothing less than its destruction. In eleven provocative chapters, contributors deal with the internal challenges and external conflicts facing Western civilization in the context of the "war on terror." Ranging from the nature of Islam and the West, to ethics and terror, to the western way of warfare, the volume deals thematically with major issues raised by this conflict in a way that no other single-volume does. Contributors bring to bear arguments on the philosophic, political, religious, ethical, and policy dimensions of the war. As the title of the book suggests, this conflict implicates all of Western civilization, demonstrating that this not merely an "American" concern.

In The West at War, Bradley C. S. Watson brings together renowned scholars and public policy experts to reflect on perhaps the most pressing problem of our time-the West's increasingly bloody conflict with forces that seek nothing less than its destruction. In eleven provocative chapters, contributors deal with the internal challenges and external conflicts facing Western civilization in the context of the 'war on terror.' Ranging from the nature of Islam and the West, to ethics and terror, to the western way of warfare, the volume deals thematically with major issues raised by this conflict in a way that no other single-volume does. Contributors bring to bear arguments on the philosophic, political, religious, ethical, and policy dimensions of the war. As the title of the book suggests, this conflict implicates all of Western civilization, demonstrating that this not merely an 'American' concern.

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

This Lexington Books edition of Comparative Political Philosophy brings back into print a volume that was one of the first to move beyond a Eurocentric bias in the study of political philosophy and provide a well-balanced critique of the perilous transition from tradition to modernity. The book is evidence of the benefits to be reaped from comparison, from a reading of Aristotle together with the Arthashastra, of Mahatma Gandhi with Eric Voegelin, of Voltaire with Confucius. Focusing on key texts from Chinese, Indian, Western and Islamic political philosophy, chapter authors both describe the very different contexts from which philosophic traditions arose and discover basic tenets they have in common. In a new introduction, editors Anthony J. Parel and Ronald C. Keith discuss the changes in political contexts since the book's first publication, and they underscore the increasing importance of the comparative approach.

Beethoven composed far more folksong settings than any other type of composition. Most are British songs, including Auld Lang Syne and the The Miller of Dee , with text by such authors as Burns, Byron and Scott. Yet Beethoven's settings, commissioned by George Thomson of Edinburgh, have been neglected by performers and scholars alike, and nearly all accounts of them are both superficial and startlingly inaccurate. This book is based on a very elablorate study of a wide range of sources, and dispels the many myths that have been circulating about this music. Every one of the 179 settings is dated to within a few weeks and an account is given of the souces of the melodies and texts, the difficulties of sending the music across Europe during the Napoleonic Wars (smugglers were even called upon to assist!), the fees Beethoven received, and when and how the texts were added. By comparing Beethoven's settings with those of his predecessors Pleyel, Haydhn and Kozeluch, the author demonstrates that Beethoven comprehensively transcended the bounds of convention, producing settings of extra-ordinary quality and originality. This book is intended for scholars, students, and those interested i

Marking the 250th anniversary of the composer's birth, this volume presents twenty-one completely new essays on aspects of Beethoven's personal life, his composing process, his manuscripts, and his greatest works. Beethoven's music stands as a universal symbol of personal and artistic achievement. As we reach and then surpass the 250th anniversary of the composer's birth, Jeremy Yudkin has commissioned a collection of new essays from some of the most insightful writers on Beethoven's accomplishments and brought them together in this remarkable volume. Filled with careful explanations, this book gives us completely new insights into music known and loved by people around the world. Ordinary music lovers as well as scholars will find countless new discoveries about Beethoven and his music. Listeners will hear his compositions afresh, and scholars will find new results of research and analysis and new avenues for discovery. Topics include Beethoven's cultural milieu, his personal life, his friends, his publishers, his instruments, his working methods, his own handwritten scores, and, of course, his music. Many works are carefully discussed and explained in ways that reveal fascinating and previously unknown aspects of compositions that we thought we knew well. A landmark publication for all who admire some of the greatest music of our civilization.

The Bible makes big claims for itself. But do those claims stand up?

Aren't the stories just legends? Hasn't the information been corrupted over time? Isn't the Bible full of mistakes? And isn't it culturally outdated?

In this absorbing little book, Barry Cooper explores these questions - and many others - with warmth, wit and integrity.

Alan Turing (1912-1954) made seminal contributions to mathematical logic, computation, computer science, artificial intelligence, cryptography and theoretical biology. In this volume, outstanding scientific thinkers take a fresh look at the great range of Turing's contributions, on how the subjects have developed since his time, and how they might develop still further. The contributors include Martin Davis, J. M. E. Hyland, Andrew R. Booker, Ueli Maurer, Kanti V. Mardia, S. Barry Cooper, Stephen Wolfram, Christof Teuscher, Douglas Richard Hofstadter, Philip K. Maini, Thomas E. Woolley, Eamonn A. Gaffney, Ruth E. Baker, Richard Gordon, Stuart Kauffman, Scott Aaronson, Solomon Feferman, P. D. Welch and Roger Penrose. These specially commissioned essays will provoke and engross the reader who wishes to understand better the lasting significance of one of the twentieth century's deepest thinkers.

A critical edition of the 35 Piano Sonatas by Professor Barry Cooper, renowned Beethoven specialist. Includes a general Introduction covering performance practice, including tempo, articulation, pedalling and dynamics and commentary to each sonata, including history, full assessment of the sources and detailed notes on interpretation. Introductory CD included.

This book constitutes the refereed proceedings of the 11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014, held in Chennai, India, in April 2014. The 27 revised full papers presented were carefully reviewed and selected from 112 submissions. The papers explore the algorithmic foundations, computational methods and computing devices to meet today's and tomorrow's challenges of complexity, scalability and sustainability, with wide-ranging impacts on everything from the design of biological systems to the understanding of economic markets and social networks.

Together, Models and Computability and its sister volume Sets and Proofs will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, post-graduate researchers, and the informed and interested nonspecialist.

This stimulating guide will help students and their teachers to achieve stylish performances of music of the Classical period. Individual chapters from leading experts focus on historical background, notation and interpretation, and sources and editions, presenting the latest thinking on performance in a clear, helpful and practical way. There are also dedicated chapters of specialist advice for keyboard, string and wind players, and singers, plus a recommended playlist of illustrative, authoritative recordings. Fully illustrated throughout with many music examples, facsimiles and pictures, this is a valuable resource for students of the Classical period which will also add to the knowledge and understanding of amateur and professional musicians.