Fixing Frege by John P. Burgess (English) Hardcover Book

Description: Fixing Frege by John P. Burgess Surveys the assortment of methods put forth for fixing Freges system, in an attempt to determine just how much of mathematics can be reconstructed in each. This work considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 Freges 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 Freges 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. Notes This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come. -- Kit Fine, New York University I suspect that this will become a must-read among those working in the philosophy of mathematics and the foundations of mathematics. It will most certainly be a significant contribution to the field. -- Stewart Shapiro, Ohio State University Back Cover "This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come." --Kit Fine, New York University "I suspect that this will become a must-read among those working in the philosophy of mathematics and the foundations of mathematics. It will most certainly be a significant contribution to the field." --Stewart Shapiro, Ohio State University Flap "This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come." --Kit Fine, New York University "I suspect that this will become a must-read among those working in the philosophy of mathematics and the foundations of mathematics. It will most certainly be a significant contribution to the field." --Stewart Shapiro, Ohio State University Author Biography John P. Burgess is Professor of Philosophy at Princeton University. He is the author of numerous articles on mathematical and philosophical logic and philosophy of mathematics and coauthor of A Subject with No Object. Table of Contents Acknowledgments ix CHAPTER 1: Frege, Russell, and After 1 CHAPTER 2: Predicative Theories 86 CHAPTER 3: Impredicative Theories 146 Tables 215 Notes 227 References 241 Index 249 Review Co-Winner of the 2007 Shoenfield Prize, Association for Symbolic Logic "Fixing Frege fills a serious gap in the Freges literature (always increasing but perhaps with an excessive attention paid to semantics and the philosophy of language) and should remain for a long time a necessary reference for scholars in the field."--Ignacio Angelelli, Review of Modern Logic Promotional This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come. -- Kit Fine, New York University I suspect that this will become a must-read among those working in the philosophy of mathematics and the foundations of mathematics. It will most certainly be a significant contribution to the field. -- Stewart Shapiro, Ohio State University Prizes Joint winner of Association for Symbolic Logic: Shoenfield Prize 2007 Long Description 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 Freges 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 Freges 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. Review Quote This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come. Details ISBN0691122318 Author John P. Burgess Short Title FIXING FREGE Publisher Princeton University Press Series Princeton Monographs in Philosophy Language English ISBN-10 0691122318 ISBN-13 9780691122311 Media Book Format Hardcover Year 2005 Imprint Princeton University Press Place of Publication New Jersey Country of Publication United States Pages 272 Birth 1954 Illustrations 12 tables. Translated from English DOI 10.1604/9780691122311 UK Release Date 2005-07-25 NZ Release Date 2005-07-25 US Release Date 2005-07-25 Publication Date 2005-07-25 DEWEY 510.1 Audience Professional & Vocational AU Release Date 2005-10-03 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:8377595;

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