Explanatory schema and the process of model building

In this paper, we argue that rather than exclusively focusing on trying to determine if an idealized model fits a particular account of scientific explanation, philosophers of science should also work on directly analyzing various explanatory schemas that reveal the steps and justification involved in scientists' use of highly idealized models to formulate explanations. We develop our alternative methodology by analyzing historically important cases of idealized statistical modeling that use a three-step explanatory schema involving idealization, mathematical operation, and explanatory interpretation.