Mending the Master
| Abstract | 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 the 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. (The work of George Boolos, Kit Fine, Bob Hale, Richard Heck, Stewart Shapiro, and Crispin Wright is singled out for particular attention in the present monograph.) 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.. | |||||||||
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Similar books and articlesØystein Linnebo (2006). Mending the Master (Critical Notice of John Burgess's Fixing Frege). Philosophia Mathematica 14 (3):338-351.
Kevin C. Klement (2001). Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's Response Adequate? History and Philosophy of Logic 22 (1):13-28.
Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
Michael A. E. Dummett (1991). Frege: Philosophy of Mathematics. Harvard University Press.
John P. Burgess (2005). Fixing Frege. Princeton University Press.
Øystein Linnebo (2006). Mending the Master: John P. Burgess, Fixing Frege. Princeton, N. J.: Princeton University Press, 2005. ISBN 0-691-12231-8. Pp. XII + 257. [REVIEW] Philosophia Mathematica 14 (3):338-400.
Sanford Shieh (2008). Frege on Definitions. Philosophy Compass 3 (5):992-1012.
Stewart Shapiro (2005). Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-Mathematics. Philosophia Mathematica 13 (1):61-77.
Michael Nelson (2008). Frege and the Paradox of Analysis. Philosophical Studies 137 (2):159 - 181.
Richard Heck (1995). Frege's Principle. In J. Hintikka (ed.), From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics. Kluwer.
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