What is a Law of Nature? Conclusions
Armstrong (David)
Source: Armstrong - What is a Law of Nature?
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  1. I will try to sum up the main positive theses argued for in this essay.
  2. Laws of nature are dyadic relations of necessitation (or probabilification) holding between universals1. They are (higher-order) states of affairs, states of affairs which are simultaneously universals2. The instantiations of these universals3 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 universals4 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, universals5. 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.
  3. 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.
  4. 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 universals6. These higher-order universals7 are instantiated by the lower-order universals8 involved in the lower-order laws. (Mass may be a higher-order universal, instantiated by the determinate mass-values such as one kilogram exact.)
  5. Irreducibly probabilistic laws are also relations between universals9. 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).
  6. 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. (The absence of interfering factors is not a factor.) If this possibility is no more than a logical possibility, then the law may be said to be iron. (A probabilistic law can be an iron law.) If interference sometimes actually occurs, then the law may be said to be oaken.
  7. There are strong, if not conclusive, reasons to reject negative and disjunctive universals10. As a result, there is reason to reject exclusion laws, and laws with disjunctive consequents. However, such laws may be freely admitted as derived laws. Derived laws are no more than the logical consequences of the underived or genuine laws. They involve no further universals11 or relations between universals12.
  8. It appears that all laws link a state of affairs where a particular has a property with a state of affairs where that same particular has a further property. However, the properties involved may be relational properties. The relations involved in these relational properties will regularly involve temporal relations.
  9. The necessitation relation, unlike logical necessitation, is not reflexive, is not transitive, cannot be contraposed, and is not symmetrical.

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