What Everyone Should Say About Symmetries (And Why Humeans Get to Say It)

The laws of physics have an interesting internal explanatory structure. Some principles explain others; some constraints fall out of the dynamic equations, and others help determine them. This leads to interesting, and non-trivial, questions for metaphysicians of laws. What sort of explanation is this? Which principles are explananda, and which explanandum? In a recent and insightful series of papers, Marc Lange (2007, 2009, 2011a, 2011b) has discussed these questions in detail, with a focus on the explanatory priority of symmetry principles and their associated conservation laws. Lange argues that symmetry principles are meta-laws: laws governing the laws. The symmetry principles explain the conservation laws by governing them, just as first-order laws explain first-order facts by governing them. He then claims that his metaphysical view of laws can neatly accommodate metalaws but his competitors, namely Humeans and dispositional essentialists, cannot (2009, 2011b). While I agree with Lange that symmetry principles explain conservation laws, I hold that he is wrong on all other counts. Symmetry principles are not meta-laws: they are first-order generalizations. The explanation of conservation laws from symmetry principles is not a covering-law explanation: it has more in common with reductive explanations of higher-order laws from more fundamental principles. And these facts put him at a loss relative to his primary competitor, the Humean view: this correct account of the explanatory power of symmetry principles falls neatly out of Humeanism, but must be added in post hoc to Lange's view