Definition: Regularity theory (RT) attempts to account for natural laws in a descriptive manner contra the necessitarian position (NT), which expresses the laws of nature as nomic necessity.
More about the term: 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:
Suppose that a coin were tossed one thousand times and each time it came up heads. Both [NT and RT proponents] would agree that such an occurrence cries out for explanation, such as that the coin was biased strongly in favor of heads; such an occurrence would constitute too grand of a coincidence to be plausibly ascribed by chance. Moreover, only if we believed that there was some such explanation would we have any reason to believe that the coin would continue to come up heads in the future; if we discovered that it had landed on heads by mere accident, we would have no reason to believe that it would continue to land on heads.
The regularist may point out that generalizations from finite sample sets cannot be warranted unless the appropriate necessary connections are postulated, which is this problem of induction. This is a problem whose examination has often been the occasion for the introduction of NT. Unless a necessitarian is prepared to say that the relation of necessity is actually observed in the instances of some law, the inference to a necessary law creates the problem of induction just as easily.
 Bernard Berofsky, “The Regularity Theory,” Nous Vol. 2 No. 4 (1968): 315.
 Robin Collins, “God and the Laws of Nature,” Philo Vol. 12 No. 2 (2009): 2-3. (Preprint).
 Berofsky, 316.
 Collins, 4.
 C.D. Broad, “Mechanical and Teleological Causation,” Proceedings of the Aristotelian Society: Supplementary Volumes (1935, XIV.
 Berofsky, 325-26.