existence, definedness, and the semantics of possibility andnecessity

In this paper, I will address just some of ProfessorWilliamson’s treatment of necessitism in hisModal Logic as Metaphysics [28]. I will give an account of what space might remain for a principled and logically disciplined contingentism. I agree withWilliamson that those interested in the metaphysics of modality would do well to take quantified modal logic—and its semantics—seriously in order to be clear, systematic and precise concerning the commitments we undertake in adopting an account of modality and ontology. Where we differ is in how we present the semantics of that modal logic. I will illustrate how proof theory may play a distinctive role in elaborating a quantified modal logic, and in the development of theories ofmeaning, and in themetaphysics ofmodality.