Mending the master: John P. Burgess, fixing Frege. Princeton, N. J.: Princeton university press, 2005. ISBN 0-691-12231-8. Pp. XII + 257 [Book Review]

Philosophia Mathematica 14 (3):338-400 (2006)
Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege's writings have given rise, the book makes a large number of improvements and clarifications. Anyone with an interest in the philosophy of mathematics will enjoy and benefit from the careful and well-informed overview provided by the first of its three chapters. Specialists will find the book an indispensable reference and an invaluable source of insights and new results.Although Frege is widely regarded as the father of analytic philosophy, his work on the foundations of mathematics was for a long time rather peripheral to ongoing research. The main reason for this is no doubt Russell's discovery in 1901 that the paradox now bearing his name can be derived in Frege's logical system. But recent decades have seen a huge surge of interest in Fregean approaches to the foundations of mathematics. A variety of consistent theories have been discovered that can be salvaged from Frege's inconsistent system, and foundational and philosophical claims have been made on behalf of many of these theories.Burgess claims quite plausibly that the significance of any such modified Fregean theory will in large part depend on how much of ordinary mathematics it enables us to develop.1 His book is accordingly ‘a survey of various modified Fregean systems, attempting to determine the scope and limits of each’ .2 The book's agenda is thus predominantly technical, and its spirit open-minded and experimental. The author has no strong commitments of either a technical or a philosophical nature …
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DOI 10.1093/philmat/nkl012
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