Godel & Cognitive Science

Preface

Glossary of the Symbols

CHAPTER 1_ Cognitive Science
1.1 Cognition as Mapping
1.2 Cognitive Science
1.3 Theses for Cognitive Science

CHAPTER 2_ G?del's Incompleteness Theorems
2.1 Formal Mathematical Systems
2.2 G?del's First Incompleteness Theorem
2.2 G?del's Second Incompleteness Theorem

CHAPTER 3_ G?del and Symbolic Cognitive Science
3.1 Mapping from Mind to Machine
3.2 Turing Machines
3.3 The Computability of Turing Machine
3.4 G?del's Objection to Turing's Mechanism
3.5 Turing Machine Beyond G?DEL'S iNCOMPLETENESS

CHAPTER 4_ G?del and Connectionist Cognitive Science
4.1 Mapping from Mind to Brain
4.2 Neural Networks
4.3 The Computability of Neural Network
4.4 Consistency and Order of Neural Network
4.5 Neural Network Beyond G?del's Incompleteness

CHAPTER 5_ G?del's Cognitive Science
5.1 G?del's Incompleteness and Mathematical Thinking
5.2 G?del's Incompleteness and Human Mind
5.3 G?del's Speed-up Theorem
5.4 G?del's Doctrine
5.5 G?del's Disjunctive Conclusion

Bibliography