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On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics - Couverture rigide

Rayo, Agustin

 
9780262039413: On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics
Couverture rigide
ISBN 10 : 0262039419 ISBN 13 : 9780262039413
Editeur : The MIT Press, 2019

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 Gödel'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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
The MIT Press
Date d'édition
2019
Langue
anglais
ISBN 10 
0262039419
ISBN 13 
9780262039413
Reliure
Relié
Numéro d'édition
1
Nombre de pages
320
Coordonnées du fabricant
non disponible
Personne responsable
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