Overview

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 technically 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 Gödel'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 connections and illuminating comparisons, and offers a wealth of ideas for future work in the subject.

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9780198250418

Table of Contents

Reviews

... illuminating. Zentralblatt Math Reading this book is an informative and challenging experience. It not only elucidates various attempts which have been made to come to terms with a satisfactory foundation for arithmetic, but does so in a way that proves rewarding, at least for the philosphically minded. Mathematical Reviews An instructive and absorbing history of a critical fifty-year period in the philosophy of mathematics ... There is much of value in the book, not just for those interested in the philosophy of mathematics. Michael Potter, Times Literary Supplement Refreshingly different from much of the recent work in the field ... both stimulating and insightful. Mind

... illuminating. Zentralblatt Math Reading this book is an informative and challenging experience. It not only elucidates various attempts which have been made to come to terms with a satisfactory foundation for arithmetic, but does so in a way that proves rewarding, at least for the philosphically minded. Mathematical Reviews An instructive and absorbing history of a critical fifty-year period in the philosophy of mathematics ... There is much of value in the book, not just for those interested in the philosophy of mathematics. Michael Potter, Times Literary Supplement Refreshingly different from much of the recent work in the field ... both stimulating and insightful. Mind

`both stimulating and insightful' MIND, Vol.110, No.439 `Another virtue of the book is its careful attention to the interaction of technical and philosophical issues. Adept in mathematics, Potter nicely brings out the mathematical content of various philosophical positions. His chapter on the Tractatus is particularly admirable in this respect; it must be one of the best discussions available of the philosophy of mathematics developed in that work' MIND, Vol.110, No.439 `refreshingly different from much of the recent work in the field' MIND, Vol.110, No.439 `There is much of value in the book, not just for those interested in the philosophy of mathematics.' Michael Potter, TLS `an instructive and absorbing history of a critical fifty-year period in the philosophy of mathematics' Michael Potter, TLS

Author Information

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

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