Preface

1. Deliberation: A Bayesian Framework

1.1. Acts, Conditions, Consequences

1.2. Desirabilities and Probabilities

1.3. Summary and Rationale

1.4. Incompletely Specified Desirabilities

1.5. Dominance, and a Fallacy

1.6. Problems

1.7. Ratifiability

1.8. Notes and References

2. Equivalent Scales

2.1. Equivalent Desirability Matrices

2.2. Conventions about Probabilities

2.3. A General Desirability Transformation

2.4. A Special Desirability Transformation

2.5. Problems

3. Ramsey's Theory

3.1. From Desirabilities to Probabilities

3.2. From Probabilities to Desirabilities

3.3. The von Neumann-Morgenstern Method

3.4. Ethical Neutrality; Probability 1/2

3.5. Calibrating the Desirability Scale

3.6. Measuring Probabilities

3.7. Conclusion

3.8. Problems

3.9. Notes and References

4. Propositional Attitudes

4.1. Belief and Desire

4.2. Justifying the Special Addition Law

4.3. Remarks on Fairness

4.4. Desirability

4.5. Sentences and Propositions

4.6. Notation

4.7. Belief versus Assent

4.8. Problems

4.9. References and Solutions

5. Preference

5.1. Computing Probabilities

5.2. The Propositions *T* and *F*

5.3. A Remark on Computing Probabilities

5.4. Computing Desirabilities

5.5. The Probability and Desirability Axioms

5.6. "Good," "Bad," "Indifferent"

5.7. Preference between News Items

5.8. Acts as Propositions

5.9. Desirabilities Determine Probabilities

5.10. Problems

5.11. Notes and References

6. Equivalence, Perspectives, Quantization

6.1. Bolker's Equivalence Theorem

6.2. Zero and Unit

6.3. Bounds on Desirabilities

6.4. Bounds on *c*

6.5. Perspective Transformations of Desirability

6.6. Probability Quantization

6.7. Problems

6.8. Acknowledgment

7. From Preference to Probability

7.1. The Existence, Closure, G, and Splitting Conditions

7.2. Determining Ratios of Probabilities

7.3. A Probability Scale for Indifferent Propositions

7.4. Nullity

7.5. A General Technique

7.6. Measuring Probabilities of Indifferent Propositions

7.7. Problems

8. Uniqueness

8.1. Uniqueness of Probabilities

8.2. A Scale of Desirabilities between 0 and 1

8.3. Uniqueness of the Scale

8.4. Uniqueness of Desirabilities in the Unit Interval

8.5. Uniqueness of Negative Desirabilities

8.6. Completing the Uniqueness Proof

8.7. Problems

8.8. Notes and References

9. Existence: Bolker's Axioms

9.1. Preference-or-Indifference as a Primitive

9.2. Prospects as Propositions

9.3. Averaging, Nullity, and Impartiality

9.4. Completeness, Atomlessness, Continuity

9.5. Notes and References

10. Boundedness; Causality

10.1. The St. Petersburg Paradox

10.2. Resolving the Paradox

10.3. Gambles as Causal Relationships

10.4. Our Theory Is Noncausal

10.5. Further Comparison with Ramsey's Theory

10.6. Justifying Quantization

10.7. Notes and References

11. Probability Kinematics

11.1. Conditionalization and Its Limits

11.2. The Problem

11.3. Solution for *n = 2*

11.4. Relevance

11.5. Comparison with Conditionalization

11.6. Solution for Finite n

11.7. Origination, Closure

11.8. The Continuous Case

11.9. Probabilistic Acts; Trying

11.10. Observation; Meaning

11.11. Notes and References

12. Induction and Objectification

12.1. Belief: Reasons versus Causes

12.2. Bayes's Theorem

12.3. Simple Induction

12.4. Confirming Generalizations

12.5. Objectivity and Learning

12.6. De Finetti's Representation Theorem

12.7. Objectification

12.8. Conclusion

12.9. Notes and References

Appendix: Preference among Preferences

Notes and References

Index