Relative Necessity and Propositional Quantification

Following Timothy Smiley's (1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Lloyd Humberstone (1981) and others have highlighted various flaws with Smiley's now standard account of relative necessity. In their recent article, Bob Hale and Jessica Leech (2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech's account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessit