Abstract: Scientists turn to idealized models when the world is too complicated to explain directly. When they do so, they describe these models using statements that are false. I defend a view on which these false statements should be taken seriously. Rather than representing the actual world, I argue that idealizations are simplified versions of the systems they ultimately explain. I argue that idealized models need not represent their explanatory targets, nor even behave similarly to them. Instead, the process of idealized explanation is one of progressive elaboration, adding and correcting details absent in the original model. Because models are simplifications, the same model can idealize a number of dissimilar actual systems, explaining behaviors of each by adding different degrees of freedom as needed. Some explanations in psychology are idealizing explanations. I show that a debate between two models of face recognition phenomena in prosopagnosia is properly understood as a debate between two idealized models. I then generalize this conclusion by arguing that many explanations thought to involve multiply realizable properties are in fact idealizing explanations; unlike multiply realizable properties, idealizing explanations are ontologically respectable and have a clear place in science. I conclude by arguing that the explanatory uses of mental terms are ambiguous: the same term may refer to type-restricted causally effective properties at some times, and at other times refer to non-actual elements of idealizing models. Finally, some preliminary conclusions on the ontological status of the mental are advanced.