The most crucial problem for NES concerns the relevant notion of a law of nature. In order to play the explanatory role assigned to them by NES, laws have to be construed not as mere regularities, but as forms of natural necessity. So the law of gravity has to be construed not as the fact that bodies always behave gravitationally, but as the fact that it is, in the relevant nomic way, necessary that they behave in that way. But how are we to understand this nomic necessity? It is not a form of strict, or absolute necessity, since even when it is a law that things behave in a certain way, there are possible worlds in which (with different laws) they do not. But a necessity that is less than strict–which allows for the possibility of things being otherwise–does not seem to be a necessity at all. Unless we can solve this problem, the relevant notion of a law will have to be rejected as incoherent.
Keywords: incoherent, law of nature, natural necessity, NES, nomic necessity, possible worlds, regularities, strict necessity