When Dependence Disappears: Faithfulness and Effective Independence in Nonlinear Dynamical Systems

This article argues that nonlinear dynamical systems provide a structural mechanism for (near-)unfaithfulness that has received little attention in philosophical discussions of causal discovery. In such systems, observable statistical relations arise from invariant-measure averaging over state-dependent causal effects. Because local causal influences vary across the system’s state space, their contributions may partially cancel, weakening statistical dependence between causally connected variables. The resulting “effective independence” can be empirically indistinguishable from genuine independence, posing challenges for dependence-based causal discovery methods. Unlike classical violations that rely on parameter fine-tuning, this form of (near-)unfaithfulness arises from structural features of system dynamics.