ABSTRACT
It is helpful in many contemporary discussions involving laws, mechanisms, regularities, and even causation to consider the recent trajectory of these ideas since the mid-twentieth century. After a survey of the discussion around laws and mechanisms, this chapter offers an original argument for two main ways in which laws and mechanisms can relate without either conceptually or ontologically reducing to the other, using Hume to illustrate. The first connection between laws and mechanisms involves the recognition of the "brute" character of laws, such that they can explain but are not themselves further explicable. The second connection between laws and mechanisms involves a unique role for laws via distinctively mathematical explanations, in which laws can provide a further degree of necessity, via mathematics, than can any collection of mechanisms, no matter how comprehensive. Finally, the chapter lays out a schematic argument for Humean roles unique to laws that cannot be assimilated to mechanisms.
