Cox's theorem [SEP] named after
Cox's theorem
Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This derivation justifies the so-called "logical" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition. Logical (a.k.a. objective Bayesian) probability is a type of Bayesian probability. Other forms of Bayesianism, such as the subjective interpretation, are given other justifications.
Cox's assumptions.
Cox
Tipler.
The original formulation of Cox's theorem is in which is extended with additional results and more discussion in . Jaynes cites Abel for the first known use of the associativity functional equation. Aczél provides a long proof of the "associativity equation" (pages 256-267). Jaynes reproduces the shorter proof by Cox in which differentiability is assumed. A guide to Cox's theorem by Van Horn aims at comprehensively introducing the reader to all these references.
See also.
- Probability axioms
- Probability logic