"John Burgess has written a book of immense help to the church in this time of great conflict and division. It is wise, probing, and highly readable. . . . A combination of authentic piety and remarkable scholarship characterize this book, which is full of concrete suggestions for persons and and congregations. --Douglas W. Oldenburg, Moderator, 210th General Assembly, Presbyterian Church (USA) and President of Columbia Theological Seminary

John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics.

This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.

The pastoral office has always been a difficult calling. Today, the pastor is often asked to fulfill multiple roles: preacher, teacher, therapist, administrator, CEO. How can pastors thrive amid such demands? What is needed is a contemporary pastoral rule: a pattern for ministry that both encourages pastors and enables them to focus on what is most important in their pastoral task. This book, coauthored by three experts with decades of practical experience, explains how relying on a pastoral rule has benefited communities throughout the church's history and how such rules have functioned in the lives and work of figures such as Augustine, Calvin, Wesley, and Bonhoeffer. It also provides concrete advice on how pastors can develop and keep a rule that will help both them and their congregations to flourish.

"Philosophical Logic" is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject.

The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. "Philosophical Logic" provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading.

"Philosophical Logic" addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.

This is a concise introduction to current philosophical debates about truth. Combining philosophical and technical material, the book is organized around, but not limited to, the view known as deflationism. In clear language, Burgess and Burgess cover a wide range of issues, including the nature of truth, the status of truth-value gaps, the relationship between truth and meaning, relativism and pluralism about truth, and semantic paradoxes from Alfred Tarski to Saul Kripke and beyond. The book provides a rich picture of contemporary philosophical theorizing about truth, one that will be essential reading for philosophy students as well as philosophers specializing in other areas.

Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic's coming of age in the 20th century: Godel's completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification-once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs.

A fascinating, vivid, and on-the-ground account of Russian Orthodoxy's resurgence "A compelling picture."-Irina Papkova, Russian Review "Powerful."-Philip Jenkins, Christian Century A bold experiment is taking place in Russia. After a century of being scarred by militant, atheistic communism, the Orthodox Church has become Russia's largest and most significant nongovernmental organization. As it has returned to life, it has pursued a vision of reclaiming Holy Rus': that historical yet mythical homeland of the eastern Slavic peoples; a foretaste of the perfect justice, peace, harmony, and beauty for which religious believers long; and the glimpse of heaven on earth that persuaded Prince Vladimir to accept Orthodox baptism in Crimea in A.D. 988. Through groundbreaking initiatives in religious education, social ministry, historical commemoration, and parish life, the Orthodox Church is seeking to shape a new, post-communist national identity for Russia. In this eye-opening and evocative book, John Burgess examines Russian Orthodoxy's resurgence from a grassroots level, providing Western readers with an enlightening, inside look at the new Russia.

When author and theologian John P. Burgess first travelled to Russia, he was hoping to expand his theological horizons and explore the rebirth of the Orthodox Church since the fall of Communism. But what he found changed some fundamental assumptions about his own tradition of North American Protestantism. In this book, Burgess asks how an encounter with Orthodoxy can help Protestants better see both strengths and weaknesses of their own tradition. In a time in which North American Protestantism is in decline--membership has now fallen to below 50% of the population--Russian Orthodoxy can help Protestants rethink the ways in which they worship, teach, and spread the gospel. Burgess considers Orthodox rituals, icons, saints and miracles, monastic life, and Eucharistic theology and practice. He then explores whether and how Protestants can use elements of Orthodoxy to reform church life.

This book offers a Reformed perspective on contemporary ecumenical discussion by carefully exploring the biblical message of justification and then demonstrating how justification as a doctrine functions as an integrative theological principle. Written by an international group of distinguished Reformed scholars, with the support of the World Alliance of Reformed Churches, What Is Justification About? also considers the relevance of justification for social ethics and contemporary cultural issues. / Contributors: Martien Brinkman, John P. Burgess, George Hunsinger, Chris Mostert, Fazakas Sndor, Dirkie Smit, Laura Smit, Katherine Sonderegger, Henk M. Vroom, John Webster, Michael Weinrich.

John Burgess explores the distinctive qualities of Christian identity by demonstrating how baptism, the Eucharist, and the Commandments are basic points of orientation for Christians. He challenges the church and its members to identify and claim key practices and disciplines of faith to deepen baptismal identity and give the Christian life solid form today. His work ultimately seeks to stimulate pastors, educators, and church leaders to encourage the church to practice ways of life together that will lead to a more faithful living of the Christian faith.

Recent developments in the biological sciences pose challenging questions to its theology and to the church's understanding of what it means to be human--that is, made in the image of God. These essays by pastors, scientists, and theologians establish a dialogue between science and faith. Study guides accompany each chapter, making this book a uniquely helpful resource for individuals and church groups.

John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.

In the world's most developed democracies, anxiety about the future of democracy itself is palpable. The tension between moral aspiration and moral despair in modern political life has reached a point of crisis. Christian Realism arose during a similar time of crisis, when Reinhold Niebuhr used the insights of the Christian tradition to interpret the clash between democracy and totalitarianism in the first half of the 20th century. Beginning with Robin Lovin's account of Niebuhr's Christian realism as a nuanced blend of theological, moral, and political realisms, The Future of Christian Realism directly addresses fundamental topics in theology, ethics and politics. The contributors of this volume come from different traditions, span five continents, and together present a case for the continuing relevance of Christian realism. By paying close attention to many of the most pressing moral challenges facing societies today, the authors illustrate and evaluate the relevance of Christian realism in the contemporary world.

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entities, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed.

George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Godel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Burgess addresses the role of religion in the massive political changes that took place in Eastern Europe in 1989, focusing particularly on the role played by the East German Church in that country's bloodless revolution.

Numbers and other mathematical objects are exceptional in having no locations in space or time and no causes or effects in the physical world. This makes it difficult to account for the possibility of mathematical knowledge, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entitles, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed.