Journal Article

De Finetti, Countable Additivity, Consistency and Coherence

Colin Howson

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 59, issue 1, pages 1-23
Published in print March 2008 | ISSN: 0007-0882
Published online March 2008 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axm042
De Finetti, Countable Additivity, Consistency and Coherence

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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. 1

Introduction

2

Coherence and Consistency

3

The Infinite Fair Lottery

4

The Puzzle Resolved—But Replaced by Another

5

Countable Additivity, Conglomerability and Dutch Books

6

The Probability Axioms and Cox's Theorem

7

Truth and Probability

8

Conclusion: ‘Logical Omniscience’

Journal Article.  10477 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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