Authors
Colin Howson
Last affiliation: London School of Economics
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. 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’ CiteULike    Connotea    Del.icio.us    What's this?
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DOI 10.1093/bjps/axm042
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References found in this work BETA

Truth and Probability.Frank Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.
A Nonpragmatic Vindication of Probabilism.James M. Joyce - 1998 - Philosophy of Science 65 (4):575-603.

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Citations of this work BETA

Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.James Joyce - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Synthese. pp. 263-297.
Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
Probability and Nonclassical Logic.Robert Williams - 2016 - In Alan Hajek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford university press.

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