 One of Lewis’s signature applications of the notion of naturalness is in the analysis of the notion of a law of nature, a notion of great importance for the philosophy of science and for the theory of causation and counterfactuals. In brief, Lewis’s proposal is that it is a law of nature that \(P\) just in case the proposition that \(P\) belongs to every “best system”, where a system is a set of true propositions closed under necessitation, and the “goodness” of a system is a combination of two factors: simplicity and  strength.[43]  The relevant notion of simplicity can, according to Lewis, be understood in terms of  naturalness.[44]  The idea is that the simplicity of a system is a matter of the syntactic simplicity of the its simplest axiomatisation, where an axiomatisation of a system is a set of sentences which express propositions which jointly entail exactly the propositions in the system, on some interpretation where their non-logical constants all stand for perfectly natural  properties.[45] 