Set Theory and Its Philosophy A Critical Introduction [Paperback]

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. 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 Philosophyis a key text for philosophy, mathematical logic, and computer science.

I. Sets
1. Logic
2. Collections
3. The hierarchy
4. The theory of sets
5. Classes
II. Numbers
6. Arithmetic
7. Counting
8. Lines
9. Real numbers
III. Cardinals and Ordinals
10. Cardinals
11. Basic cardinal arithmetic
12. Ordinals
13. Ordinal aritmetic
IV. Further axioms
14. Orders of infinity
15. The axiom of choice
16. Further cardinal arithmetic

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 DamePhilosophical Reviews

Michael Potter is University Lecturer in Philosophy, and Fellow of Fitzwilliam College, at Cambridge. He is the author ofSets(1990), on which the present work draws but which was written for a more specialist readership, andReason's Nearest ls�