The Philosophy of Set Theory
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The Philosophy of Set Theory
Book Details
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Author: Mary Tiles
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Publisher: Dover
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Edition: Later Printing
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Binding: Paperback
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ISBN: 9780486435206
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Pages: 256
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Release Date: 18-06-2004
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Dimensions: 8.3 x 5.5 x 0.7 inches
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Languages: English
About the Book
"The Philosophy of Set Theory" by Mary Tiles offers an engaging and accessible exploration into the foundational aspects of modern mathematics. The book provides a guided tour through the key concepts of set theory, including its philosophical underpinnings and mathematical implications. Starting with fundamental discussions on finite universes, Aristotelian logic, and permutations, it builds towards more advanced topics like Cantor’s transfinite sets, axiomatic set theory, and the continuum hypothesis.
Key Topics Covered:
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Finite Universe & Finitism: An exploration of the early notions of finite sets and logic.
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Zeno's Paradoxes & Infinity: Discussions on the philosophical paradoxes related to infinity.
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Cantor’s Transfinite Paradise: Introducing Cantor’s groundbreaking work on transfinite numbers and set theory.
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Axiomatic Set Theory: A look into Zermelo-Fraenkel set theory (ZF) and its axioms.
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Transfinite Numbers & Ordinals: Detailed analysis of Cantor’s continuum hypothesis and ordinal numbers.
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Russell's Logicist Reduction: Investigating Bertrand Russell’s contributions to logic and set theory.
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Godel’s Constructible Universe: Exploring Kurt Godel’s work on the constructible universe and its implications.
The book also delves into mathematical intuition and logical paradoxes, guiding readers through the philosophical and practical dimensions of set theory. Written for a broad audience, it provides valuable insights for those interested in the intersection of philosophy and mathematics, particularly in the foundations of set theory.
With over 32 figures and an extensive bibliography, "The Philosophy of Set Theory" is an essential read for anyone delving into the philosophy of mathematics or the logical structure of modern mathematical theory.
