Several scholars have argued that Leibniz’s infinite analysis theory of contingency faces the Problem of Lucky Proof. This problem will be discussed here and a solution offered, trying to show that Leibniz’s proof-theory does not generate the alleged paradox. It will be stressed that only the opportunity to be proved by God, and not by us, is relevant to the issue of modality. At the heart of our proposal lies the claim that, on the one hand, Leibniz’s individual concepts are (...) saturated conceptual conjunctions, i.e., infinite conjunctions that contain either the concept itself or its privation for every primitive concept; and that, on the other hand, also certain universal concepts of states and acts are infinite conjunctions of primitive concepts and privations, even if insaturated ones. This will suffice to allow that some truths regarding individuals can’t be demonstrated, although they are included in the concept of their subject. (shrink)