Symmetry principles

Here is an interesting inductive argument about the restricted Principle of Relativity in Einstein's little popular book on relativity:

But that a principle of such broad generality should hold with such exactness in one domain of phenomena [mechanics], and yet should be invalid for another [electrodynamics], is a priori not very probable.

This is induction across laws: from the laws of mechanics having a property, we infer that the laws of electrodynamics have it as well. If induction is within a natural kind, this induction would require there to be the natural kind law.

One can take the Principle of Relativity to be a second-order law (cf. Earman). That's not the only way to think about it. We could, for instance, imagine the following metaphysics: We are realists about ordinary laws, like those of mechanics and thermodynamics, and we think that God has produced these laws. But in choosing which laws to produce, God followed certain "artistic principles". One of these artistic principles is the Principle of Relativity (and similar symmetry principles). I don't know what advantages of this over a hierarchical view on which there are higher order laws that constrain lower order ones. But it's worth thinking about.