Universality Reduced

Abstract

The universality of critical phenomena is best explained by appeal to the Renormalisation Group (RG). Batterman and Morrison, among others, have claimed that this explanation is irreducible. I argue that the RG account is reducible, but that the higher-level explanation ought not to be eliminated. I demonstrate that the key assumption on which the explanation relies-the scale invariance of critical systems-can be explained in lower-level terms; however, we should not replace the RG explanation with a bottom-up account, rather we should acknowledge that the explanation appeals to dependencies which may be traced down to lower levels.

Can Multiple Realisation be Explained?

“…It's worth emphasising that this example is fairly naturalistic: we needn't think of electrical conductivity in terms of human interactions – it manifests, for example, when lightning strikes. If one still has reservations that the example is unacceptably ad hoc or anthropocentric, Franklin (2019) demonstrates that a similar reductive approach may be applied to the universality of critical phenomena, which, as briefly discussed in §4.2, has been touted by some as a paradigm instance of irreducible MR.…”

“… 23 Although Batterman thinks that universality can be offered an explanation, he contends that this explanation is unavailable from the bottom up due to its appeal to renormalisation group (RG) methods; his technical argument is criticised in e.g. Saatsi and Reutlinger (2018); Franklin (2019). …”

Renormalization group methods: Which kind of explanation?

“…Finally, also Franklin (2018) defends a reductive, though non-eliminativist, account of universality. According to Franklin higher-level explanations are more parsimonious, more robust, and have a broader applicability than lower-level explanations (Franklin, 2018(Franklin, , p. 1295) and should not be replaced by lower-level explanations.…”

“…Finally, also Franklin (2018) defends a reductive, though non-eliminativist, account of universality. According to Franklin higher-level explanations are more parsimonious, more robust, and have a broader applicability than lower-level explanations (Franklin, 2018(Franklin, , p. 1295) and should not be replaced by lower-level explanations. However, higher-level theories can be understood in lower-level terms and are thus reducible where the notion of reducibility here implies two conditions (Franklin, 2018(Franklin, , p. 1296Woodward, 2003, pp.…”