This volume presents thirteen original essays which explore both traditional and contemporary aspects of the metaphysics of relations. It is uncontroversial that there are true relational predications-'Abelard loves Eloise', 'Simmias is taller than Socrates', 'smoking causes cancer', and so forth. More controversial is whether any true relational predications have irreducibly relational truthmakers. Do any of the statements above involve their subjects jointly instantiating polyadic properties, or can we explain their truths solely in terms of monadic, non-relational properties of the relata? According to a tradition dating back to Plato and Aristotle, and continued by medieval philosophers, polyadic properties are metaphysically dubious. In non-symmetric relations such as the amatory relation, a property would have to inhere in two things at once-lover and beloved-but characterise each differently, and this puzzled the ancients. More recent work on non-symmetric relations highlights difficulties with their directionality. Such problems offer clear motivation for attempting to reduce relations to monadic properties. By contrast, ontic structural realists hold that the nature of physical reality is exhausted by the relational structure expressed in the equations of fundamental physics. On this view, there must be some irreducible relations, for its fundamental ontology is purely relational. The Metaphysics of Relations draws together the work of a team of leading metaphysicians, to address topics as diverse as ancient and medieval reasons for scepticism about polyadic properties; recent attempts to reduce causal and spatiotemporal relations; recent work on the directionality of relational properties; powers ontologies and their associated problems; whether the most promising interpretations of quantum mechanics posit a fundamentally relational world; and whether the very idea of such a world is coherent. From those who question whether there are relational properties at all, to those who hold they are a fundamental part of reality, this book covers a broad spectrum of positions on the nature and ontological status of relations, from antiquity to the present day.

Anna Marmodoro, Corpus Christi College, Oxford,David Yates, University of Lisbon

Anna Marmodoro is an Official Fellow in Philosophy at Corpus Christi College, University of Oxford. She specializes in ancient philosophy and contemporary metaphysics. She has published books and journal articles in both areas; and currently directs two major research projects: one on ancient and contemporary metaphysics of powers funded by the European Research Council, and one on the metaphysics of quantum entanglement, funded by the Templeton World Charity Foundation.

David Yates holds a PhD from King's College London, and is currently a Senior Research Fellow at the University of Lisbon. He specialises in metaphysics (in particular metaphysics of science) with active research interests in the philosophy of mind (in particular neuroscientific approaches to consciousness). He is currently working on a 5-year project investigating the ontological status of spacetime in quantum gravity, funded by the Fundacao para a Ciencia e a Tecnologia (FCT).

1. Introduction: The Metaphysics of Relations, Anna Marmodoro & David Yates
2. Relations as Plural Predications in Plato, Theodore Scaltsas
3. Aristotelian vs. Contemporary Perspectives on Relations, Jeffrey E. Brower
4. Why Do Medieval Philosophers Reject Polyadic Accidents?, Sydney Penner
5. Positionalism Revisited, Maureen Donnelly
6. There Are (Probably) No Relations, E. Jonathan Lowe
7. External Relations, Causal Coincidence, and Contingency, Peter Simons
8. Causal Relations, John Heil
9. Is Powerful Causation an Internal Relation?, David Yates
10. What a Structuralist Theory of Properties Could Not Be, Nora Berenstain
11. The Foundations of Structuralism and the Metaphysics of Relations, James Ladyman
12. Relations All the Way Down? Against Ontic Structural Realism, Sebastian Briceno and Stephen Mumford
13. The Reality of Relations: the Case From Quantum Physics, Michael Esfeld
14. Rovelli's Relational Quantum Mechanics, Anti-Monism and Quantum Becoming, Mauro Dorato
Bibliography
Index