There's Something about Gödel - by Francesco Berto (Paperback)

Book Synopsis

Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments.

• Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters
• Discusses interpretations of the Theorem made by celebrated contemporary thinkers
• Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories
• Written in an accessible, non-technical style

From the Back Cover

There's Something About Gödel is a lucid and accessible guide to Gödel's revolutionary Incompleteness Theorem, considered one of the most astounding argumentative sequences in the history of human thought. It is also an exploration of the most controversial alleged philosophical outcomes of the Theorem.

Divided into two parts, the first section introduces the reader to the Incompleteness Theorem - the argument that all mathematical systems contain statements which are true, yet which cannot be proved within the system. Berto describes the historical context surrounding Gödel's accomplishment, explains step-by-step the key aspects of the Theorem, and explores the technical issues of incompleteness in formal logical systems. The second half, The World After Gödel, considers some of the most famous - and infamous - claims arising from Gödel's theorem in the areas of the philosophy of mathematics, metaphysics, the philosophy of mind, Artificial Intelligence, and even sociology and politics.

This book requires only minimal knowledge of aspects of elementary logic, and is written in a user-friendly style that enables it to be read by those outside the academic field, as well as students of philosophy, logic, and computing.

Review Quotes

"This is a beautifully clear and accurate presentation of the material, with no technical demands beyond what is required for accuracy, and filled with interesting philosophical suggestions." (John Woods, University of British Columbia)

"There's Something about G]odel is a bargain: two books in one. The first half is a gentle but rigorous introduction to the incompleteness theorems for the mathematically uninitiated. The second is a survey of the philosophical, psychological, and sociological consequences people have attempted to derive from the theorems, some of them quite fantastical." (Philosophia Mathematica, 2011)

"There is a story that in 1930 the great mathematician John von Neumann emerged from a seminar delivered by Kurt Gödel saying: 'It's all over.' Gödel had just proved the two theorems about the logical foundations of mathematics that are the subject of this valuable new book by Francesco Berto. Berto's clear exposition and his strategy of dividing the proof into short, easily digestible chunks make it pleasant reading ... .Berto is lucid and witty in exposing mistaken applications of Gödel's results ... [and] has provided a thoroughly recommendable guide to Gödel's theorems and their current status within, and outside, mathematical logic." (Times Higher Education Supplement, February 2010)

About the Author

Francesco Berto teaches logic, ontology, and philosophy of mathematics at the universities of Aberdeen in Scotland, and Venice and Milan-San Raffaele in Italy. He holds a Chaire d'Excellence fellowship at CNRS in Paris, where he has taught ontology at the École Normale Supérieure, and he is a visiting professor at the Institut Wiener Kreis of the University of Vienna. He has written papers for American Philosophical Quarterly, Dialectica, The Philosophical Quarterly, the Australasian Journal of Philosophy, the European Journal of Philosophy, Philosophia Mathematica, Logique et Analyse, and Metaphysica, and runs the entries "Dialetheism" and "Impossible Worlds" in the Stanford Encyclopedia of Philosophy. His book How to Sell a Contradiction has won the 2007 Castiglioncello prize for the best philosophical book by a young philosopher.