On the Brink of Paradox : Highlights from the Intersection of Philosophy and ...

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Características del artículo

Estado
Nuevo: Libro nuevo, sin usar y sin leer, que está en perfecto estado; incluye todas las páginas sin ...
Book Title
On the Brink of Paradox : Highlights from the Intersection of Phi
ISBN
9780262039413
Categoría

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Product Identifiers

Publisher
MIT Press
ISBN-10
0262039419
ISBN-13
9780262039413
eBay Product ID (ePID)
22038746073

Product Key Features

Number of Pages
320 Pages
Publication Name
On the Brink of Paradox : Highlights from the Intersection of Philosophy and Mathematics
Language
English
Subject
General, Study & Teaching, Logic
Publication Year
2019
Type
Textbook
Subject Area
Mathematics, Philosophy
Author
Agustin Rayo
Format
Hardcover

Dimensions

Item Height
0.9 in
Item Weight
23.6 Oz
Item Length
9.2 in
Item Width
7.3 in

Additional Product Features

Intended Audience
Trade
LCCN
2018-023088
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 --
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
510
Synopsis
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 G del'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., 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 G del'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.
LC Classification Number
QA11.2.R39 2019

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