The Logic of Explanation by abstract Models

I shall try to answer the question what the logic of explanation by abstract models is. I shall mainly refer to the respective explanatory practice in economics, and my main illustrative example is the Schelling model of (racial) segregation. This model shows that weak racial preferences (in the model) lead to racial segregation (in the model). Clearly, this is only a potential explanation of racial segregation (in the model), because other dynamics may also produce racial segregation (in the model). Therefore, even if the transfer of model results to the real world were without any loss, models by themselves maximally deliver potential explanations for the real world. What is the logic of this transfer? In contrast to most views on this matter, I claim that a robust model makes a mathematical theorem plausible that can be applied immediately both to the model world and the real world.