Symmetry principles are commonly said to explain conservation laws—and were so employed even by Lagrange and Hamilton, long before Noether's theorem. But within a Hamiltonian framework, the conservation laws likewise entail the symmetries. Why, then, are symmetries explanatorily prior to conservation laws? I explain how the relation between ordinary (i.e., first-order) laws and the facts they govern (a relation involving counterfactuals) may be reproduced one level higher: as a relation between symmetries and the ordinary laws they govern. In that event, (...) symmetries are meta-laws; they are not mere byproducts of the dynamical and force laws. Symmetries then explain conservation laws whereas conservation laws lack the modal status to explain symmetries. I elaborate the variety of natural necessity that meta-laws would possess. Proposed metaphysical accounts of natural law should aim to accommodate the distinction between meta-laws and mere byproducts of the laws just as they must accommodate the distinction between laws and accidents. (shrink)

The Standard Model of elementary particle physics distinguishes between fundamental and accidental symmetries. The distinction is not based on empirical features of the symmetry, nor on a metaphysical notion of necessity. A symmetry is fundamental to the extent that other aspects of nature depend on it, and it is recognized as fundamental by its being theoretically well-connected. This paper clarifies the concept of what it is to be fundamental in this sense, and suggests broader implications for the analysis of scientific (...) knowledge. (shrink)