Reasons Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Paperback | June 15, 2002

byMichael Potter

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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 latenineteenth 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 technically and philosophically. Michael Potter's innovative studypresents 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 werereacting against; but it places us in Godel's shadow 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 connectionsand illuminating comparisons, and offers a wealth of ideas for future work in the subject.

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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 latenineteenth to the mid-twentieth century. In th...

Michael Potter is Fellow of Fitzwilliam College, Cambridge, and University Lecturer in Philosophy, having previously been Director of Studies in Mathematics.

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Format:PaperbackDimensions:315 pages, 9.21 × 6.14 × 0.69 inPublished:June 15, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199252610

ISBN - 13:9780199252619

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Table of Contents

Introduction1. Kant2. Grundlagen3. Dedekind4. Frege's account of classes5. Russell's account of classes6. The Tractatus7. The second edition of Principia8. Ramsey9. Hilbert's programme10. Godel11. CarnapConclusionBibliography, index

Editorial Reviews

`Review from previous edition This is an excellent book: informative, suggestive, and a genuine pleasure to read. Potter offers analyses of Kant, Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, Godel, and Carnap that are always elegantly presented, and often brilliantly clear. Thediscussion of Hilbert and Godel is particularly elegant; that of Ramsey breaks new ground; the account of the Tractatus, with its illuminating comparison of the work to Hilbert's program, is one of the most accessible I have read.'William Demopoulos, British Journal for the Philosophy of Science