Fixing Frege by John P. Burgess
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Fixing Frege
By John P. Burgess

Fixing Frege

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Format: Hardback

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Fixing Frege by John P. Burgess

Book Awards

  • Joint winner for Association for Symbolic Logic: Shoenfield Prize 2007.

Book 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 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.

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Book Details

ISBN: 9780691122311
ISBN-10: 0691122318
Format: Hardback
(216mm x 140mm x 19mm)
Pages: 272
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 5-Jul-2005
Country of Publication: United States

Books By Author John P. Burgess

Holy Rus' by John P. Burgess Holy Rus', Hardback (April 2017)

A fascinating, vivid, and on-the-ground account of Russian Orthodoxy's resurgence

Rigor and Structure by John P. Burgess Rigor and Structure, Hardback (February 2015)

John P. Burgess presents an illuminating study of the nature of mathematical rigor and of mathematical structure, and above all of the relation between them. He considers recent developments in the field including experimental mathematics and computerized formal proofs, and surveys many historical developments in mathematics, philosophy, and logic.

» View all books by John P. Burgess

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Author Biography - John P. Burgess

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".

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