Oxford University Press, March 2000
Hardback £74 ISBN 0-19-825041-X
Paperback £25 ISBN 0-19-925261-0
How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmetic that were brilliantly original both techically and philosophically. Michael Potter's innovative study presents them all as finding that content in various aspects of the complex linkage between experience, language, thought, and the world. Potter's reading places them all in Kant's shadow, since it was his attempt to ground arithmetic in the spatio-temporal structure of reality that they were reacting against; but it places us in Godel's shadow too, since his incompleteness theorems supply us with a measure of the richness of the content they were trying to explain. This stimulating reassessment of some of the classic texts in the philosophy of mathematics reveals many unexpected connections and illuminating comparisons, and offers a wealth of ideas for future work in the subject.
Contents
- Kant
- Grundlagen
- Dedekind
- Grundgesetze
- Russell's account of classes
- The Tractatus
- The second edition of Principia
- Ramsey
- Hilbert's programme
- Gödel
- Carnap
- Conclusion
Reviews
- Teun Koetsier, Zentralblatt 1016.03003
- Gregory Landini, History and Philosophy of Logic 21 (2000) 231-4
- Adrian Moore, TLS no. 5108 (2001) 31
- J. MacFarlane, Journal of the History of Philosophy 39 (2001) 454-6
- Mary Tiles, Isis 92 (2001) 439
- William Demopoulos, British J. Phil. Sci. 52 (2001) 599-612
- Øystein Linnebo, Mind 110 (2001) 810-13
- Marco Ruffino, Erkenntnis, 56 (2002) 264-8
- Sanford Shieh, Philosophical Review 111 (2002) 442-6
- Joseph W. Dauben, MR 2003b:03005
- Susan Sterrett, Philosophical Books 44 (2003) 294-6
- Richard Zach, Notre Dame Journal of Formal Logic 46 (2005) 503-13
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