 So far, we have considered probabilistic arguments which place probabilities over hypotheses in a hypothesis space as well as observations. There is also a tradition of attempts to determine what probability distributions we should have, given certain observations, from the starting point of a joint probability distribution over all the observable variables. One may then postulate axioms directly on this distribution over observables, and examine the consequences for the predictive distribution. Much of the development of inductive logic, including the influential programme by Carnap, proceeded in this manner (Carnap 1950, 1952).