Lewis dened laws as generalizations in the best
system—the deductive system, cast in a language whose predicates express
natural properties and relations, that best balances the virtues of simplicity
and strength. The restriction on the language of the best system is essential;
otherwise, as Lewis (1983b, p. 367) points out, a simple and maximally strong
theory could be given with a single, simple axiom, ∀xF x, where F is a predicate
true of all and only things in the actual world. All true generalizations would
be counted as laws.
I’d like to get a bit more clear about just why this “simple axiom” would prove illicit by Lewis’s lights. The thought seems to be that this predicate does not express a perfectly natural property or relation. But why should this be? For illustration, assume supersubstantivalism. By assumption, every actual entity is simply a chunk of the spacetime manifold. Thus, F is guaranteed to apply to all actual entities just in case F expresses the property “is a portion of the spacetime manifold”. Doesn’t this seem to be a perfectly natural property?
The point may be more obvious if we ignore the supersubstantivalist assumption and just stipulate that the actual world is composed of all and only the material objects. Thus, so long as F has the value “is material,” it applies to every actual entity. But on superficial examination this seems to me entirely licit: isn’t “is material” a perfectly natural property, or at any rate as good a candidate as any we have?