The ultimate argument against Armstrong's contingent necessitation view of laws

Abstract

I show that Armstrong's view of laws as second-order contingent relations of 'necessitation' among categorical properties faces a dilemma. The necessitation relation confers a relation of extensional inclusion ('constant conjunction') on its relata. It does so either necessarily or contingently. If necessarily, it is not a categorical relation (in the relevant sense). If contingently, then an explanation is required of how it confers extensional inclusion. That explanation will need to appeal to a third-order relation between necessitation and extensional inclusion. The same dilemma reappears at this level. Either Armstrong must concede that some properties are not categorical but have essential powers - or he is faced with a regress.