Book contents
- Frontmatter
- Contents
- Preface
- Note to the Reader
- CHAPTER ONE Confidence
- CHAPTER TWO Evidence
- CHAPTER THREE The Bayesian Challenge
- CHAPTER FOUR Rational Belief
- CHAPTER FIVE The Bayesian Canon
- CHAPTER SIX Decision Theory as Epistemology
- APPENDIX 1 Principles and Definitions
- APPENDIX 2 Proofs
- APPENDIX 3 Probabilism – Some Elementary Theorems
- Bibliography
- Index
APPENDIX 1 - Principles and Definitions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Note to the Reader
- CHAPTER ONE Confidence
- CHAPTER TWO Evidence
- CHAPTER THREE The Bayesian Challenge
- CHAPTER FOUR Rational Belief
- CHAPTER FIVE The Bayesian Canon
- CHAPTER SIX Decision Theory as Epistemology
- APPENDIX 1 Principles and Definitions
- APPENDIX 2 Proofs
- APPENDIX 3 Probabilism – Some Elementary Theorems
- Bibliography
- Index
Summary
Principles that are rejected in the pages above are marked with an asterix.
Chapter 1
Definition. A is a well-mannered state of affairs just in case, for some set of mutually exclusive and jointly exhaustive hypotheses, {P1, …, Pn} and some set of real numbers, {a1, …, an}, A is identical to ($a1 if P1, …, Pn).
1.1 Ordering. Where A, B and C are any well-mannered states of affairs between no pair of which you are undecided,
(i) you do not prefer A to A; and
(ii) if you do not prefer A to B and you do not prefer B to C, then you do not prefer A to C.
1.2 Dominance. Where A is the well-mannered state of affairs ($a1 if P1, …, $an if Pn) and B is the well-mannered state of affairs ($b1 if P1, …, $Pn),
(i) if ai > bi for every i, then you prefer A to B; and
(ii) if ai = bi for every i, then you are indifferent between A and B.
1.3 Confidence. For any hypotheses P and Q, you are more confident that P than you are that Q if and only if you prefer ($1 if P, $0 if ~P) to ($1 if Q, $0 if ~Q).
- Type
- Chapter
- Information
- Decision Theory as Philosophy , pp. 191 - 198Publisher: Cambridge University PressPrint publication year: 1996