We describe incidence calculus, a logic for probabilistic reasoning. In incidence calculus, probabilities are not directly associated with formulae. Rather sets of possible worlds are directly associated with formulae and probabilities are calculated from these. This enables incidence calculus to be truth functional, which a logic based on a purely numeric uncertainty measure cannot be. This, in turn, enables tighter probablity intervals to be calculated for theorems of an incidence calculus theory than is possible in a purely numeric uncertainty theory.