There's Something About Gödel
The Complete Guide to the Incompleteness Theorem
1. Edition November 2009
256 Pages, Hardcover
Wiley & Sons Ltd
Short Description
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 Incompleteness Theorem, while the second half, The World After Gödel, considers some of the most famous claims arising from Gödel's theorem in the areas of the philosophy of mathematics, metaphysics, and the philosophy of mind.
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
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
"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)