Superior Beings. If They Exist, How Would We Know? - Game-Theoretic Implications of Omnipotence, Omniscience, Immortality, and Incomprehensibility

Acknowledgments

Contents

Introduction

The Rationality of Belief in a Superior Being

2.1. Introduction

2.2. The Revelation Game

2.3. The Revelation Game Paradox

2.4. The Knowability Games

2.6. Conclusions

Omniscience and Partial Omniscience

3.1. Introduction

3.2. Some Effects of Omniscience

3.3. Newcomb's Problem

3.4. Which Principle, and Is There a Conflict?

3.5. Newcomb's Problem Symmetricized: Prisoners' Dilemma

3.6. A Solution to Prisoners' Dilemina

3.7. Cooperation or Noncooperation?

3.8. Implications of Mutual Predictability for SB and P

3.9. Conclusions

The Paradox of Omniscience and the Theory of Moves

4.1. Introduction

4.2. The Paradox of Omniscience

4.3. A Resolution of the Paradox of Omniscience

4.4. Theory of Moves

4.5. A Second Paradox: Moves May Provide No Resolution

4.6. Conclusions

Omnipotence: Moving and Staying Power

5.1. Introduction

5.2. Moving Power

5.3. Is There a Paradox of Moving Power?

5.4. Theological Interpretations of Moving Power

5.5. Staying Power

5.6. An Algorithm for Determining S- Power Outcomes

5.7. M-Power Versus S-Poiver in the Commitment Game and Other Situations

5.8. Conclusions

Immortality and Incomprehen-sibility

6.1. Introduction

6.2. Threats and Immortality

6.3. Repeated Plays

6.4. Threat Power in the Punishment Game: When Immortality Is Decisive in an Asymmetrical Game

6.5. Deception by the Superior Being

6.6. The Truth Game and the Problem of Evil

6.7. Conclusions

Superior Beings: They May Be Undecidable

7.1. Introduction

7.2. Undecidability

7.3. Arbitrariness and Undecidability

Appendix

Glossary

Bibliography

Index