Relative Necessity Reformulated

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional necessarily, if C then p where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone (Reports on Mathematical Logic, 31, 33–421, 1981), that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, and offer another considerably simpler solution.