According to the Humean Best Systems Account, laws of nature are contingent generalizations in the best systematization of particular matters of fact. Recently, it has become popular to interpret the notion of a best system pragmatically. The best system is sensitive to our interests—that is, to our goals, abilities, and limitations. This account promises a metaphysically minimalistic analysis of laws that fits scientific practice. However, I argue that it is not as minimalistic as it might appear. The concepts of goals, abilities, and limitations that drive the analysis are modally-robust. This leads to a dilemma.

I will use the simple case of a harmonic oscillator to introduce and resolve three novel puzzles about physical symmetries. One puzzle is that the fact that boosts are symmetries of Newtonian mechanics is not particularly important for explaining why a spring inside a ship remains invariant under constant boosts of the ship. A second puzzle is that, in many cases, both the connection between symmetries and representation and the one between symmetries and observations seem trivial. And the third puzzle is that there are symmetries discussed by physicists where the connection between symmetries, representation and observations are broken.

It is commonly believed that symmetry principles explain conservation laws. Since conservation laws can be mathematically derived from symmetries and vice versa, the explanatory asymmetry deserves philosophical justification. Marc Lange (2007) claims that symmetries are meta-laws that govern and hence explain conservation laws. In this paper, I argue that we should not grant symmetry a higher modal status. I present counterexamples to demonstrate that symmetries are neither necessary nor sufficient for conservation laws. Some symmetries are explanatorily prior to laws but not in the way that Lange prescribed. They serve as an epistemic guide rather than a necessary requirement.

A new argument is given for the thesis that only symmetry-invariant physical quantities are real. Non-invariant quantities are dynamically epiphenomenal in that they have no effect on the evolution of invariant quantities, and it is a signifcant theoretical vice to posit epiphenomenal quantities.