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A probabilistic theory of coherence

Desideratum (1) captures the qualitative features that a probabilistic generalization of logical coherence should satisfy — it requires C to respect the extreme deductive cases, and to be properly sensitive to probabilistic dependence (a general notion of probabilistic dependence will be defined precisely, and in a slightly non-standard way, below). I propose a probabilistic measure of coherence C based on a slight modification of Kemeny and Oppenheim’s (1952) measure of factual support F. The formulation of C is somewhat intricate. We begin with some preliminary definitions. First, we define the two-place function F(X,Y). F(X,Y) may be interpreted as the degree to which one proposition Y supports another proposition X (relative to a finitely additive, regular, Kolmogorov (1956) probability function Pr).