What is the relationship between ontology and modality - between what there is, and what there could be, must be, or might have been? Bob Hale interwove these two strands of metaphysics throughout his long and distinguished career, putting forward his theses in his book, Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them (OUP 2013). Hale addressed questions of ontology and modality on a number of fronts: through the development of a Fregean approach to ontology, an essentialist theory of modality, and in his work on neo-logicism in the philosophy of mathematics. The essays in this volume engage with these themes in Hale's work in order to progress our understanding of ontology, modality, and the relations between them. Some directly address questions in modal metaphysics, drawing on ontological concerns, while others raise questions in modal epistemology and of its links to matters of ontology, such as the challenge to give an epistemology of essence. Several essays also engage with questions of what might be called 'modal ontology': the study of whether and what things exist necessarily or contingently. Such issues have an important bearing on the kinds of semantic commitments engendered in logic and mathematics (to the existence of sets, or numbers, or properties, and so on) and the extent to which one's ontology of necessary beings interacts with other plausible assumptions and commitments.

Ivette Fred-Rivera, Professor of Humanities and Philosophy, University of Puerto Rico,Jessica Leech, Lecturer in Philosophy, King's College London

Ivette Fred-Rivera was born in Bayamon, Puerto Rico, studied in public schools where she discovered Plato's dialogues during high school, and did her Bachelor's and Master's degrees in Philosophy at the University of Puerto Rico, Rio Piedras. She did her PhD in the Department of Philosophy at CUNY Graduate Center, New York. As a postgraduate, Ivette visited the Department of Logic and Metaphysics of the University of St Andrews, Scotland, to work with Professors Bob Hale and Crispin Wright on the problem of a priori knowledge. She has taught at the University of Puerto Rico, Rio Piedras since 1998. Her research areas are epistemology, philosophy of language, and logic, and she also has published works on aesthetics and art.

Jessica Leech first studied philosophy at King's College, Cambridge and took her masters degree at King's College London. She did her doctorate jointly at the University of Sheffield and the University of Geneva (as part of the 'Theory of Essence' research project based at the Eidos Centre for Metaphysics at the University of Geneva) and was supervised by Fabrice Correia and Bob Hale. Jessica's first post-doctoral position was a Junior Research Fellowship at King's College, Cambridge. She then took up a lectureship in philosophy at the University of Sheffield before joining KCL's philosophy department in September 2016. Her research focuses primarily on issues to do with possibility and necessity, both in contemporary debates, and in Kant's work.

1. Introduction, Ivette Fred-Rivera and Jessica Leech
2. On Some Arguments for the Necessity and Irreducibility of Necessity, John Divers
3. The World of Truthmaking, Kit Fine
4. Essentialism and Logical Consequence, Rosanna Keefe and Jessica Leech
5. Radical Contingentism, or: Why not even numbers exist necessarily, Peter Simons
6. Properties and Predicates, Objects and Names: Impredicativity and the Axiom of Choice, Stewart Shapiro
7. Predication, Possibility, and Choice, Roy T Cook
8. Logicism, Ontology, and the Epistemology of Second-order Logic, Richard G Heck Jr
9. On the Permissibility of Impredicative Comprehension, Oystein Linnebo
10. Neo-Fregeanism and the Burali-Forti Paradox, Ian Rumfitt
11. Analytic Essentialist Approaches to the Epistemology of Modality, Anand Jayprakash Vaidya
12. Rethinking the Epistemology of Modality for abstracta, Sonia Roca Royes
13. Counter-Conceivability Again, Crispin Wright