De Finetti, Countable Additivity, Consistency and Coherence |
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| Authors: | Howson Colin |
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| Institution: | Department of Philosophy, London School of Economics and Political Science |
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| Abstract: | Many people believe that there is a Dutch Book argument establishingthat the principle of countable additivity is a condition ofcoherence. De Finetti himself did not, but for reasons thatare at first sight perplexing. I show that he rejected countableadditivity, and hence the Dutch Book argument for it, becausecountable additivity conflicted with intuitive principles aboutthe scope of authentic consistency constraints. These he oftenclaimed were logical in nature, but he never attempted to relatethis idea to deductive logic and its own concept of consistency.This I do, showing that at one level the definitions of deductiveand probabilistic consistency are identical, differing onlyin the nature of the constraints imposed. In the probabilisticcase I believe that R.T. Cox's ‘scale-free’ axiomsfor subjective probability are the most suitable candidates.- 1 Introduction
- 2 Coherence and Consistency
- 3 The InfiniteFair Lottery
- 4 The Puzzle Resolved—But Replaced by Another
- 5 Countable Additivity, Conglomerability and Dutch Books
- 6The Probability Axioms and Cox's Theorem
- 7 Truth and Probability
- 8 Conclusion: ‘Logical Omniscience’
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