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Do Renormalization Group Explanations Conform to the Commonality Strategy?

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Abstract

Renormalization group (RG) explanations account for the astonishing phenomenon that microscopically very different physical systems display the same macro-behavior when undergoing phase-transitions. Among philosophers, this explanandum phenomenon is often described as the occurrence of a particular kind of multiply realized macro-behavior. In several recent publications, Robert Batterman denies that RG explanations account for this explanandum phenomenon by following (what I call) the commonality strategy, i.e. by identifying properties that microscopically very different physical systems have in common. Arguing against Batterman’s claim, I defend the view that RG explanations are in accord with the commonality strategy.

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Notes

  1. See Batterman (2000, 2002), Butterfield (2011), Morrison (2012), Norton (2012), Menon and Callender (2013), Hüttemann et al. (2015), and Reutlinger (2014a, b, 2016).

  2. The critical exponent typically figures in an equation describing the order parameter of the physical systems in question (that is, a macroscopic physical quantity such as magnetization), in relation to the so-called reduced temperature.

  3. Alternative theories of explanation will analyze this notion of dependence in different ways. Butterfield (2011) and Norton (2012) are likely to do so in a covering-law framework; the counterfactual theory of explanation I favor interprets dependence in terms of (non-causal) counterfactual dependencies (Reutlinger 2016).

  4. As a referee remarked, the correct interpretation of bridge laws is crucial for deciding whether RG explanations are reductive explanations and, moreover, whether RG explanations support the claim of reductive physicalism (in which Papineau is interested). However, my aim in this paper is not to get involved in debates on reductive explanations and, even less, on reductive physicalism. For this reason, I rely on Dizadji-Bahmani et al.’s (2010, 404) minimalist account of bridge laws according to which bridge laws are interpreted as correlations between macroscopic and microscopic physical quantities. This account of bridge laws has two advantages: (a) the account is neutral with respect to reductive physicalism, and (b) Dizadji-Bahmani et al.’s account of bridge laws is compatible with multiple realization—one of Batterman’s main qualms with respect to bridge laws (Dizadji-Bahmani et al. 2010, 406–407).

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Acknowledgments

I would like to thank Juha Saatsi, Markus Schrenk, and an audience in Leeds for their feedback. I am also grateful for receiving a fellowship from the Durham emergence project.

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Reutlinger, A. Do Renormalization Group Explanations Conform to the Commonality Strategy?. J Gen Philos Sci 48, 143–150 (2017). https://doi.org/10.1007/s10838-016-9339-7

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