There is a venerable tradition of rational reconstruction in philosophy of science, whose objective is to explain the success of scientific practices that we should regard as properly justifiable. This tradition has focused on semantic concepts that unquestionably deserve a central place: logical semantics and probability, as well as useful combinations such as epistemic decision theory. However, this analysis fails to reach a large part of the reasoning deployed in applied mathematics. Indeed, we need a collection of concepts usually associated with perturbation theory---and we should regard those as having a role as fundamental as those of logic and probability theory---to understand how arguments that have approximately true or even false premises but (approximately) true conclusions work. After describing this collection of concepts, I will illustrate the kind of philosophical work it can do by briefly discussing how we ought to think about complexity and success in science.