Reason's Nearest Kin
Philosophies of Arithmetic from Kant to Carnap
Seiten
2002
Oxford University Press (Verlag)
978-0-19-925261-9 (ISBN)
Oxford University Press (Verlag)
978-0-19-925261-9 (ISBN)
Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.
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.
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.
Michael Potter is Fellow of Fitzwilliam College, Cambridge, and University Lecturer in Philosophy, having previously been Director of Studies in Mathematics.
Introduction ; 1. Kant ; 2. Grundlagen ; 3. Dedekind ; 4. Frege's account of classes ; 5. Russell's account of classes ; 6. The Tractatus ; 7. The second edition of Principia ; 8. Ramsey ; 9. Hilbert's programme ; 10. Godel ; 11. Carnap ; Conclusion ; Bibliography, index
| Erscheint lt. Verlag | 13.6.2002 |
|---|---|
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 157 x 234 mm |
| Gewicht | 483 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Geisteswissenschaften ► Philosophie ► Philosophie der Neuzeit | |
| Geisteswissenschaften ► Philosophie ► Sprachphilosophie | |
| Mathematik / Informatik ► Mathematik | |
| Naturwissenschaften | |
| ISBN-10 | 0-19-925261-0 / 0199252610 |
| ISBN-13 | 978-0-19-925261-9 / 9780199252619 |
| Zustand | Neuware |
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