The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. O...

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Bibliographic Details
Published in:International journal of approximate reasoning 2004-08, Vol.37 (1), p.71-85
Main Author: Colyvan, Mark
Format: Article
Language:English
Subjects:
Belief
Cox
Excluded middle
Non-classical logic
Probability
Uncertainty
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Summary:Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2003.11.001