After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.
Role of discriminantly separable polynomials in integrable dynamical systems
