If there are vague propositions, and the vague supervenes on the precise, then vague propositions cannot be represented by sets of metaphysically possible worlds. According to an alternative, broadly supervaluationist idea, propositions are sets of world-precisification pairs. To interpret this theory non-linguistically, precisifications are understood as assigning an extension to each vague property at each possible world. However, there are many other positions on propositional fineness of grain. The chapter investigates the general logic of propositional individuation. It gives an internal definition of the broadest notion of necessity, and shows that it is at least as broad as any combination of determinacy and necessity operators. It formulates a propositions-first account of vague propositions, in which propositions are taken as primitive and not constructed out of sets of things, and presents a theory of vague propositions in which they are individuated by their role in thought.