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
claimedwere 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.
