Read more
Informationen zum Autor 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. Klappentext 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. Zusammenfassung There's Something About Godel is a lucid and accessible guide to Godel'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. Inhaltsverzeichnis PrologueAcknowledgmentsPart I: The Gödelian Symphony:1. Foundations and Paradoxes2. Hilbert3. Gödelization, or Say It with Numbers!4. Bits of Recursive Arithmetic ...5. ... And How It Is Represented in Typographical Number Theory6. "I Am Not Provable"7. The Unprovability of Consistency and the "Immediate Consequences" of G1 and G2Part II: The World after Gödel:8. Bourgeois Mathematicians! The Postmodern Interpretations9. A Footnote to Plato10. Mathematical Faith11. Mind versus Computer: Gödel and Artificial Intelligence12. Gödel versus Wittgenstein and the Paraconsistent InterpretationEpilogueReferencesIndex...
List of contents
Prologue
Acknowledgments
Part I: The Gödelian Symphony:
1. Foundations and Paradoxes
2. Hilbert
3. Gödelization, or Say It with Numbers!
4. Bits of Recursive Arithmetic ...
5. ... And How It Is Represented in Typographical Number Theory
6. "I Am Not Provable"
7. The Unprovability of Consistency and the "Immediate Consequences" of G1 and G2
Part II: The World after Gödel:
8. Bourgeois Mathematicians! The Postmodern Interpretations
9. A Footnote to Plato
10. Mathematical Faith
11. Mind versus Computer: Gödel and Artificial Intelligence
12. Gödel versus Wittgenstein and the Paraconsistent Interpretation
Epilogue
References
Index
Report
"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)
