 This leads us back to the faithful model assumption  (§1.2.3).  Recall this assumption maintains that our model equations faithfully capture target system behavior and that the model state space faithfully represents the actual possibilities of the target system. Is the sense of faithfulness here that of actual correspondence between mathematical models and features of actual systems? Or can faithfulness be understood in terms of empirical adequacy alone, a primarily instrumentalist construal of faithfulness? Is a realist construal of faithfulness threatened by the mapping between models and systems potentially being one-to-many or many-to-many? 