The Ultimate Argument Against Armstrong's Contingent Necessitation View of Laws
Analysis 65 (2005), pp. 147-155.
In this paper I show that Armstrongs view of laws as 2nd 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. Either it does so 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 3rd 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.