More specifically, for a Jeffrey utility function U defined over a Boolean algebra of propositions, and some propositions a,b, “the sum is greater than its parts” would be expressed as the condition U(a∧b)>U(a)+U(B) (which is, of course, not a theorem). The respective general theorem only states that U(a∧b)=U(a)+U(b∣a), which follows from the definition of conditional utility U(b∣a)=U(a∧b)−U(a).
More specifically, for a Jeffrey utility function U defined over a Boolean algebra of propositions, and some propositions a,b, “the sum is greater than its parts” would be expressed as the condition U(a∧b)>U(a)+U(B) (which is, of course, not a theorem). The respective general theorem only states that U(a∧b)=U(a)+U(b∣a), which follows from the definition of conditional utility U(b∣a)=U(a∧b)−U(a).