Set Theory and its Philosophy
A Critical Introduction
Seiten
2004
Oxford University Press (Verlag)
978-0-19-926973-0 (ISBN)
Oxford University Press (Verlag)
978-0-19-926973-0 (ISBN)
Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. This is a comprehensive philosophical introduction to the field offering a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates.
A comprehensive philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true.
A comprehensive philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true.
Michael Potter is University Lecturer in Philosophy, and Fellow of Fitzwilliam College, at Cambridge. He is the author of Sets (1990), on which the present work draws but which was written for a more specialist readership, and Reason's Nearest Kin (2000).
I. SETS ; II. NUMBERS ; III. CARDINALS AND ORDINALS ; IV. FURTHER AXIOMS
| Erscheint lt. Verlag | 1.3.2004 |
|---|---|
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 163 x 241 mm |
| Gewicht | 653 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-19-926973-4 / 0199269734 |
| ISBN-13 | 978-0-19-926973-0 / 9780199269730 |
| Zustand | Neuware |
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