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On the Brink of Paradox By Agustin Rayo (Professor, Massachusetts Institute of Technology)

On the Brink of Paradox by Agustin Rayo (Professor, Massachusetts Institute of Technology)

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Summary

An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory.

On the Brink of Paradox Summary

On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo (Professor, Massachusetts Institute of Technology)

An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory.

This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof.

The book covers Cantor's revolutionary thinking about infinity,
which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Goedel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

On the Brink of Paradox Reviews

On the Brink of Paradox is a surprisingly delightful read. The book contains an amazing amount of accesible material even to college mathematics majors, while offering value or review for mathematicians, but never in a stale way.

-Mathematical Association of America

About Agustin Rayo (Professor, Massachusetts Institute of Technology)

Agustin Rayo is Professor of Philosophy at MIT and the author of The Construction of Logical Space.

Additional information

GOR011056817
9780262039413
0262039419
On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo (Professor, Massachusetts Institute of Technology)
Used - Like New
Hardback
MIT Press Ltd
2019-04-02
320
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
The book has been read, but looks new. The book cover has no visible wear, and the dust jacket is included if applicable. No missing or damaged pages, no tears, possible very minimal creasing, no underlining or highlighting of text, and no writing in the margins

Customer Reviews - On the Brink of Paradox