Regularity theory (RT) attempts to account for laws in a descriptive manner contra the necessitarian position (NT), which expresses the laws of nature as nomic necessity. According to the RT the fundamental regularities are brute facts; they neither have nor require an explanation. Regularity theorists attempt to formulate laws and theories in a language where the connectives are all truth functional. Thus, each law is expressed with a universal quantifier as in [(x) (Px ⊃ Qx)]. The NT states that there are metaphysical connections of necessity in the world that ground and explain the most fundamental regularities. Necessitarian theorists usually use the word must to express this connection. Thus, NT maintains must-statements are not adequately captured by is-statements (must ≠ is, or certain facts are unaccounted for).
The role of counterfactuals serves to make distinctions in regularities. Concerning the RT and counterfactuals the regularist may claim that laws do not purport what will always occur but what would have occurred if things were different. NT claims that it is difficult for RT to account for certain counterfactual claims because what happens in the actual world do not themselves imply anything about what would have happened had things been different. This is only a mere negative assertion on behalf of NT and carries no positive reason to adopt the NT position. However, RT does have a limited scope in explanation. C.D. Broad argued that the very fact that laws entail counterfactuals is incompatible with regularity theory. He suggests that counterfactuals are either false or trivially true. If it is now true that Q occurs if P causally precedes Q then the regularist may sufficiently account for past counterfactual claims. Given the present antecedent condition of P at tn and P implies Q at tn and it was true that P implied Q at tn-1 then using P as an antecedent for R at hypothetical tn-1’ then R is true if P was a sufficient condition R at tn-1’. Thus, RT accounts for past counterfactuals, but this is trivially true. However, in positive favor of the NT, there is no reason to expect the world to continue to behave in a regular manner as presupposed by the practice of induction. Consider Robin Collins’ illustration of this point: