Set Theory and its Philosophy: A Critical Introduction

Paperback | May 12, 2004

byMichael Potter

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Michael Potter presents a comprehensive new 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 thatbedevil 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.Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

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From the Publisher

Michael Potter presents a comprehensive new 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 pro...

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).

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Format:PaperbackDimensions:360 pages, 9.21 × 6.14 × 0.71 inPublished:May 12, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199270414

ISBN - 13:9780199270415

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Table of Contents

I. Sets1. Logic2. Collections3. The hierarchy4. The theory of sets5. ClassesII. Numbers6. Arithmetic7. Counting8. Lines9. Real numbersIII. Cardinals and Ordinals10. Cardinals11. Basic cardinal arithmetic12. Ordinals13. Ordinal aritmeticIV. Further axioms14. Orders of infinity15. The axiom of choice16. Further cardinal arithmetic

Editorial Reviews

"Michael Potter has given us a wonderful new book. The mathematics are extremely clearly presented, it's an easy book to learn from. Potter is very good at explaining the motivations-both philosophical and technical-for various bits of mathematics, so one never has the feeling of wading through long pages of pointless technical minutiae. It is a rewarding read even for those who don't intend to follow all the technical details. Potter's book provides a great introduction to set theory and its philosophy, he has written the best philosophical introduction on the market." --Notre Dame Philosophical Reviews