REGULARITY THEORIES OF LAW

One obvious attraction of regularity theories of laws is the ontological economy that they promise. A Factualist, however, cannot say, as it is tempting to say, that laws will then supervene on first-order states of affairs. For true statements of instantiated law will be true universally quantified propositions, and such truths, according to our argument in chapter 13, demand, over and above first-order states of affairs, the higher-order state of affairs that these are all the relevant first-order states of affairs. Not only do we require a collection of first-order states of affairs where, say, each F is a G, we require the further state of affairs that these are all the Fs. But granted this totality fact, a type of fact required quite independently of the existence of laws, then Humean laws do supervene. What is more, provided it has been conceded that laws are nothing but regularities, the supervenience is a supervenience which can be said fairly uncontroversially to involve no increase of being.

A Regularity theorist will find properties and relations very useful in formulating the theory. What is to be done about the ‘grue’ problem? What are we going to say about predicate expressions in a true unrestricted universally quantified statement that are mere disjunctions of more respectable predicates? Such statements do not really assert regularities. (A ‘disjunctive regularity’ is a falling away from a regularity.