Universality caused: the case of renormalization group explanation

Abstract

Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group (RG) explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. As a result, the irrelevancy approach and the line between casual and noncausal explanation deserves more scrutiny.

Deep Learning Applied to Scientific Discovery: A Hot Interface with Philosophy of Science

“…Particularly relevant for our discussion are theories of probabilistic causation (Suppes 1970, Hitchcock 2018) and their link with causal modelling/tracking techniques (Spirtes et al 2000, Pearl 2009): we will argue that these theories gain cogency in view of the deep learning results we review. Just a few examples of work from the last three years related to causation in philosophy of science are (Landes et al 2018, Eva et al 2019, Sullivan 2019b, Livengood and Sytsma 2020. This article is organized as follows.…”

Model Explanation Versus Model-Induced Explanation

“…While certain boundary conditions might be necessary for entailing the explanandum, it is not central to the explanatory power of the explanation. For example, Sullivan (2019) argues that in order to delineate a causal explanation from a non-causal explanation, one must identify the 'primary reason' an explanation succeeds, and that boundary conditions are unlikely candidates. This sense of explanatory importance is what we mean by the core.…”

Renormalization group methods: Which kind of explanation?

“…In the last decade, a case for non-causal explanation on which a growing literature has focused is the renormalization group explanation of universality, as has become usual to call it, where the context is that of the physics of critical phenomena in statistical mechanics (SM) and condensed matter physics (CMP) 3 (e.g., Morrison, 2012Morrison, , 2015aMorrison, , 2015bMorrison, , 2018Morrison, , 2019Reutlinger 2014Reutlinger , 2017aReutlinger , 2017bHüttemann, Kühn and Terzidis, 2015;Saatsi and Reutlinger, 2018;Sullivan 2019). 4 1 Unless otherwise necessary, we limit the references to the recent, representative ones.…”

“…For what regards more specically the debate on causal vs non-causal explanation, 27 and the use of RG methods as a paradigm case for non-causal explanation, a recent critical analysis is Sullivan (2019). In a nutshell, Sullivan's argument is based on the claim that simply pointing to the fact that the explanation heavily relies on abstraction procedures, such as RG transformations and Hamiltonian ow, does not preclude a causal interpretation (Sullivan, 2019, p. 17).…”