The mathematical field of graph theory has recently been used to provide counterexamples to the Principle of the Identity of Indiscernibles. In response to this, it has been argued that appeal to relations between graphs allows the Principle to survive the counterexamples. In this paper, I aim to show why that proposal does not succeed.

A long-standing charge of circularity against regularity accounts of laws has recently seen a surge of renewed interest. The difficulty is that we appeal to laws to explain their worldly instances, but if these laws are descriptions of regularities in the instances then they are explained by those very instances. By the transitivity of explanation, we reach an absurd conclusion: instances of the laws explain themselves. While drawing a distinction between metaphysical and scientific explanations merely modifies the challenge rather than resolving it, I argue that it does point us towards an attractive solution. According to Humeanism, the most prominent form of the regularity view, laws capture information about important patterns in the phenomena. By invoking laws in scientific explanations, Humeans are showing how a given explanandum is subsumed into a more general pattern. Doing so both undermines a principle of transitivity that plays a crucial role in the circularity argument and draws out a central feature of the Humean approach to scientific explanation.

Symmetry principles are a central part of contemporary physics, yet there has been surprisingly little metaphysical work done on them. This paper develops the Wignerian treatment of symmetries as higher-order laws – metalaws – within a Humean framework of lawhood. Lange has raised two obstacles to Humean metalaws, and the paper shows that the account has the resources available to respond to both. It is argued that this framework for Humean metalaws stands as an example of naturalistic metaphysics, able to bring Humeanism into contact with the practice of actual science without giving up on the central denial of necessary connections.