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Beschreibung
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
* 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
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
* 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
Inhaltsverzeichnis
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
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
Inhaltsverzeichnis
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
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
Warnhinweis