Jeffrey's Rule, Passage of Experience, and Neo-Bayesianism

A technically convenient assumption underlying most of probabilistic epistemology is that the state of beliefs of a rational agent can be represented by a coherent probability function P,defined over the sentences in some appropriate language. Curiously, aside from the algebraic requirement of coherence (i.e.,that P be an additive function on a sigma-algebra of sets) very few structural properties were attributed to P. For example, in the algebraic description all propositional formulas are treated on an equal basis and conditional probabilities are defined as ratios of joint probabilities. Thus, the algebraic description of P does not permit us to distinguish the input information P(A | B) = 0 from its logical equivalent P(A, B) = 0, even though the two have different meanings in human discourse. Likewise, judgements about dependencies must be extracted from judgments about probabilities; there is no way to ascertain the independence of A and B unless P also contains the information necessary for computing P(A), A(B) and P(A, B).

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