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Fixing Frege
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 meth...
Philosophical Logic
"Philosophical Logic is a clear and concise critical survey of nonclassical logic, 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. The book provides a 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 stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Requiring minimal background and arranged to make the more technical material optional, Philosophical Logic offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject."--Page 4 de la couverture.
Truth
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.
Rigor and Structure
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 gr...
Holy Rus'
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.
A Subject With No Object
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.
Computability and Logic
This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.
Kripke
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 acco...
Encounters with Orthodoxy
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.
Set Theory
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.
