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Set Theory and its Philosopy : A Critical Introduction - Michael Potter

Set Theory and its Philosopy

A Critical Introduction


Published: 1st March 2004
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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 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. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

"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

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

ISBN: 9780199270415
ISBN-10: 0199270414
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 360
Published: 1st March 2004
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.17 x 15.6  x 1.88
Weight (kg): 0.52