I will try to sum up the main positive theses argued for in this essay.

Laws of nature are dyadic relations of necessitation (or probabilification) holding between universals. They are (higher-order) states of affairs, states of affairs which are simultaneously universals. The instantiations of these universals are the positive instances falling under the law. It is an intelligible notion that a particular first-order state of affairs should necessitate a further first-order state of affairs, yet not in virtue of the universals involved in these states of affairs. But in a law of nature this same relation of necessitation links sorts of states of affairs, that is, universals. Such necessitations ‘might have been other than they are’, that is, they are contingent. Where one sort of state of affairs necessitates another, then it is entailed, in the absence of further interfering factors (which are always at least logically possible), that the first sort of state of affairs is constantly conjoined with the second sort of state of affairs.

All genuine laws are instantiated laws. Statements of uninstantiated law are to be construed as counterfactuals about what laws would hold if certain conditions were realized. Such statements depend for their truth upon the existence of higher-order laws. Given the higher-order law and the contrary-to-fact condition, then the uninstantiated law may be deduced.

Functional laws are higher-order laws governing those lower-order laws which can be deduced from a functional law after substituting particular values for independent variables. Higher-order laws are relations between higher-order universals. These higher-order universals are instantiated by the lower-order universals involved in the lower-order laws. (Mass may be a higher-order universal, instantiated by the determinate mass-values such as one kilogram exact.)

Irreducibly probabilistic laws are also relations between universals. These relations give (are constituted by) a certain objective probability that individual instantiations of the antecedent universal will necessitate instantiation of the consequent universal. They give a probability of a necessitation in the particular case. Like all laws, they must have (positive) instantiations at some time. Deterministic laws are limiting cases of probabilistic laws (probability 1).

It is always logically possible that the antecedent universal of a law of nature should be instantiated, yet that, because of the presence of interfering factors, the consequent universal not be instantiated.