Abstract: The revision theory of truth is an influential way to account for the liar paradox and more generally to work with circular definitions. We present a new proposal for what to do at the limit stages in the revision theory. The usual limit criterion is that the limit stage should agree with any definite verdicts that have been brought about. We suggest considering more general properties that are brought about. This more general framework is required if one is interested in considering revision theories for concepts that are concerned with real numbers; such as a revision theory that can account for cases of self-referential probabilities. These are useful for modelling situations where what one believes can affect what happens; for example a case where my confidence that I will be able to jump across a river will affect whether I’ll actually be able to or not. The more general framework also has consequences for the more traditional revision theory of truth.