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
Prologue.
Acknowledgments.
Part I: The Gödelian Symphony.
1 Foundations and Paradoxes.
1 This sentence is false .
2 The Liar and Gödel.
3 Language and metalanguage.
4 The axiomatic method, or how to get the non-obvious out of the obvious.
5 Peano's axioms … .
6 … and the unsatisfied logicists, Frege and Russell.
7 Bits of set theory.
8 The Abstraction Principle.
9 Bytes of set theory.
10 Properties, relations, functions, that is, sets again.
11 Calculating, computing, enumerating, that is, the notion of algorithm.
12 Taking numbers as sets of sets.
13 It's raining paradoxes.
14 Cantor's diagonal argument.
15 Self-reference and paradoxes.
2 Hilbert.
1 Strings of symbols.
2 … in mathematló‡
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