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.
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.
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, Naming and Necessity, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. Kripke will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers.
When philosophers today debate the age-old problem of the relation of mind or soul to matter or body, they tend to get involved quickly in discussing not just what actually is but also what possibly may be or by contrast what necessarily must be. No thesis in this much-disputed area has been the topic of more extended discussion than that of the “supervenience”, as it is called, of the mental on the physical, according to which for any difference in the mental to have been possible, some difference in the physical would have been necessary. In this book a recognized authority on modal logic, the logic of the necessary and the possible, critically examines, from a logician’s distinctive point of view, the supervenience debate in philosophy of mind and philosophical psychology, and ends up questioning not so much the truth as the significance of the supervenience thesis.
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.
A fascinating, vivid, and on-the-ground account of Russian Orthodoxy's resurgence 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.
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
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.
A brief account of philosophical logic from one of the world's leading authorities 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.
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 such objects, 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.
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.
The synthesis of macrocycles is an art in itself. Template-controlled synthesis provides elegant access to fascinating macrocyclic structures. Polyazamacrocycles, crown ethers, cryptands, rotaxanes, knots -- the range of macrocyclic compounds is as broad as their potential application as molecular switches, in ion exchange, electron transfer or catalysis. This book provides authoritative information on all aspects of template-controlled macrocyclizations. It covers in depth the current state of research on template processes - novel synthetic techniques and mechanistic approaches. The critical discussion of the diverse synthetic routes includes the detailed characterization of the broad variety of macrocyclic products. References to applications of macrocyclic compounds and over 1,500 citations make this handbook an indispensable tool for chemists in academia and industry. Researchers in organic and supramolecular chemistry, biotechnology, and inorganic chemistry will find inspiration for the design, synthesis, and myriad uses of new synthetic macrocycles.
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.
When philosophers today debate the age-old problem of the relation of mind or soul to matter or body, they tend to get involved quickly in discussing not just what actually is but also what possibly may be or by contrast what necessarily must be. No thesis in this much-disputed area has been the topic of more extended discussion than that of the “supervenience”, as it is called, of the mental on the physical, according to which for any difference in the mental to have been possible, some difference in the physical would have been necessary. In this book a recognized authority on modal logic, the logic of the necessary and the possible, critically examines, from a logician’s distinctive point of view, the supervenience debate in philosophy of mind and philosophical psychology, and ends up questioning not so much the truth as the significance of the supervenience thesis.
Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, Naming and Necessity, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. Kripke will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers.
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.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.
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.
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 looks to Orthodoxy to help the North American Protestant churchwhich has seen membership decline to below 50% of the population for the first timefind new ways to worship, teach, and spread its message. He considers Orthodox rituals, icons, the attention to saints and miracles, monastic life, and Eucharistic theology and practice. He then explores whether and how Protestants can use these elements of Orthodoxy to help revitalize the mainline church. Burgess helpfully demonstrates the ways in which Orthodoxy calls us back to what is most important in Christian faith and life.
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.
This book addresses the role of religion in the massive political changes that took place in Eastern Europe in 1989. In particular, it examines the role played by the East German church in that country's bloodless revolution. Although some scholars and political commentators have noted that the East German church provided a free space in which dissident groups could meet, they have neither described nor assessed the theology that guided the church's political involvement. Drawing on his own research in East Germany and relying primarily on sources published in East Germany itself, John Burgess demonstrates the roots of the church's theology in Barth, Bonhoeffer, and in the Barmen declaration, which in 1934 pronounced Christianity and Nazi ideology to be incompatible. He explores how the dissident groups drew on church symbols and language to develop a popular alternative theology, and finally shows how the theological tension between the church and the dissidents provided impulses for political democratization.
The Colour of Metal Compounds is devoted to the qualitative and quantitative treatment of colour in inorganic and coordination compounds. In order to understand the use of colour as a source of structural and analytical information, the book explains in depth the interrelation between colour and structural properties of compounds. Trichromatic colorimetry is introduced as a method for the quantitative evaluation of colour. Further chapters cover chromaticity and spectroscopy, lanthanides, colour centres, colour in mineralogy, pigments, coloured glass, and the colour use in teaching. Fully revised from the original Polish edition, this book is recommended as a supplementary text for undergraduate and graduate level courses on transition metal chemistry, coordination chemistry, spectroscopy and colour chemistry. It will also be of interest to researchers in chemistry, physics, mineralogy and the pigment and glass industry.
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