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De finetti, countable additivity, consistency and coherence

Howson, Colin (2008) De finetti, countable additivity, consistency and coherence. The British Journal for the Philosophy of Science, 59 (1). pp. 1-23. ISSN 1464-3537

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Abstract

Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's ‘scale-free’ axioms for subjective probability are the most suitable candidates.

Item Type: Article
Official URL: http://www.oxfordjournals.org/our_journals/phisci/...
Additional Information: © 2008 The Author © 2008 Oxford University Press
Library of Congress subject classification: Q Science > Q Science (General)
Q Science > QA Mathematics
Sets: Departments > Philosophy, Logic and Scientific Method
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 23 May 2013 15:43
URL: http://eprints.lse.ac.uk/50298/

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