Existence and Definedness: the semantics of possibility and necessity

October 2016

“Existence and Definedness: the semantics of possibility and necessity,” article in progress.

In this paper, I will address just some of Professor Williamson’s treatment of necessitism in his Modal Logic as Metaphysics. I will give an account of what space might remain for a principled and logically disciplined contingentism. I agree with Williamson 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 of meaning, and in the metaphysics of modality.

The paper was first written for presentation in a workshop on Tim Williamson’s work, at the Asian Workshop in Philosophical Logic and the Taiwan Philosophical Logic Colloquium at the National Taiwan University. The slides from that talk are available here.

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You are welcome to download and read this document. I especially welcome feedback on it. As it is not yet published in final form, if you want to cite the paper, please check with me first. Thanks.


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


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