Relative Necessity and Propositional Quantification

Abstract

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 necessity. Keywords Relative necessity • Absolute necessity • Logical necessity • Modal logic There are many different notions of necessity. For example, it may well be practically impossible for someone to run from London to Oxford in under three hours, but surely it is physically possible for that person to do so. Similarly, it is physically necessary that nothing goes faster than the speed of light, but many would claim that it is metaphysically possible for something to do so. Although there are various different kinds of necessity, it is commonly assumed that there is an absolute notion of necessity which is broader than all other notions of necessity. Moreover, given this notion of absolute necessity, it is also widely assumed that all other kinds of necessity can be characterised in terms of it. Indeed, since Smiley's [15] influential proposal, it has become standard practice to characterise notions of relative necessity in terms of certain absolutely strict conditionals. According to

Higher‐order metaphysics

“…Thus Dorr (2016, pp. 68–70) considers analysing metaphysical modality in terms of higher‐order identity by understanding a claim of the form ‘□ P ’ as ‘ P ≡⊤’ (see Dunaway, 2013 and Roberts, 2020 for further uses of higher‐order quantification to elucidate the nature of modality). Finally, we are starting to see work incorporating both projects, with Rayo (2020) providing an argument for contingentism, partially based on a higher‐order analysis of modal notions.…”