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.
Highlights
IntroductionMany philosophers argue that there are certain kinds of abstract mathematical explanations that are noncausal (Batterman 2000, 2010; Colyvan 2001; Felline 2018; Jansson and Saatsi 2017; Lange 2013; Lipton 2004; Pincock 2015; Reutlinger 2014; Rice 2015)
I argue that the common example of Renormalization Group (RG) explanations of universality used to motivate the irrelevancy approach deserves more critical attention
He argues that when we move to the transformations of Hamiltonians that exploit mathematical operations, one cannot appeal to accounts of causal explanation that make room for causal abstraction
Summary
Many philosophers argue that there are certain kinds of abstract mathematical explanations that are noncausal (Batterman 2000, 2010; Colyvan 2001; Felline 2018; Jansson and Saatsi 2017; Lange 2013; Lipton 2004; Pincock 2015; Reutlinger 2014; Rice 2015). Proponents of noncausal explanation utilize different approaches to make their case and each approach trades on different scientific examples.1 One such approach is to argue that there are scientific explanations that explain why something is necessary through mathematics or graph theory in a way that fails to be causal (Lange 2013, 2017). Another approach is to argue that abstracting away irrelevant causal
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