Book contents
- Frontmatter
- Contents
- Preface
- 1 The logic of preference
- 2 Transitivity and normality
- 3 Independence
- 4 Subjective probability in science
- 5 Diachronic rationality
- 6 The concept of acceptance
- 7 The significance of acceptance
- 8 Representation theorem
- 9 Scientific values
- Appendixes
- A Proof for Section 5.1.6
- B Proof of Theorem 8.1
- C Sufficient conditions for Axiom 10
- D Proof of Theorem 8.2
- Bibliography
- Index
C - Sufficient conditions for Axiom 10
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- Preface
- 1 The logic of preference
- 2 Transitivity and normality
- 3 Independence
- 4 Subjective probability in science
- 5 Diachronic rationality
- 6 The concept of acceptance
- 7 The significance of acceptance
- 8 Representation theorem
- 9 Scientific values
- Appendixes
- A Proof for Section 5.1.6
- B Proof of Theorem 8.1
- C Sufficient conditions for Axiom 10
- D Proof of Theorem 8.2
- Bibliography
- Index
Summary
This appendix proves that when Axioms 1–8 are satisfied, then the following conditions are jointly sufficient (but not necessary) for Axiom 10:
(i) There are “best” and “worst” acts; that is, there exist k, l ∈ D such that, for all f ∈ D, k ≲ f ≲ l.
(ii) For all f ∈ D, if k ≲ f or f ≲ l, then there exists h ∈ ∪L such that h ≲ f or f ≲ h (respectively).
As in Appendix B, we here use the fact that the set of simple acts in D is ∪L.
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- Betting on Theories , pp. 265 - 266Publisher: Cambridge University PressPrint publication year: 1993