De Finetti, Countable Additivity, Consistency and Coherence

Datos Bibliográficos

ID8399100
AutoresColin Howson (London School of Economics and Political Science, autor de correspondencia)
Año2008
Volumen59
Número1
Páginas1-23
Fecha de publicación2008-03-01
Peer ReviewedSí
Open AccessNo
TipoARTICLE
RevistaThe British Journal for the Philosophy of Science (JOURNAL)
Identificadores de la revistaISSN: 0007-0882 • E-ISSN: 1464-3537
EditorialOxford University Press (PUBLISHER • GB)
DOI10.1093/bjps/axm042
OpenAlexW2105492369
IdiomaEN
Citas recibidas12
Referencias citadas21

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. Introduction2. Coherence and Consistency3. The Infinite Fair Lottery4. The Puzzle Resolved—But Replaced by Another5. Countable Additivity, Conglomerability and Dutch Books6. The Probability Axioms and Cox's Theorem7. Truth and Probability8. Conclusion: ‘Logical Omniscience’

Additive function · Argument (complex analysis) · Axiom · Coherence (philosophical gambling strategy) · Consistency (knowledge bases) · Countable set · Discrete mathematics · Mathematical economics · Probabilistic logic · Statistics · Epistemology, Ethics, and Metaphysics · Mathematics · Philosophy and History of Science · Philosophy and Theoretical Science