The Palgrave Companion to the Philosophy of Set Theory

This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity.

Key features of this volume: 
•    Explores new and interesting connections between philosophy, set theory, and the study of infinity.
•    Considers questions intended to appeal to a wider audience in both philosophy and mathematical logic.
•    Examines three key areas of study: Epistemology, Formal Theories, and Ontology.

The book provides a key reference text for future debates and is ideal for both newcomers to the philosophy of set theory and established researchers in the field.

Chapter 1. Introduction.- Part I Epistemology.- Chapter 2.The Problem of Existence forDescriptivism About the Reference of Set-Theoretic Expressions.- Chapter 3. Intuition and Observation.- Chapter 4.  Arealism, ThinRealism, and the Problem of Extrinsic Evidence.- Chapter 5. The Hidden Use of New Axioms.- Part II Formal Theories.- Chapter 6. The Iterative Notion of Function and the Iterative Notion of Set.- Chapter 7. What Set Theory Could Not Be About.- Chapter 8. Hamkins’ Analogy Between Set Theory and Geometry: Pluralism by Leveling Up?.- Chapter 9. Basic Mathematics Beyond Classicality.- Part III Ontology.- Chapter 10. Iteration and Dependence Again.- Chapter 11. What Is Forcing Potentialism?.- Chapter 12. On the Consistency of Height and Width Potentialism.- Chapter 13. Higher-Order Platonism and Multiversism.- Chapter 14. Language, Models, and Reality: Weak Existence and a Threefold Correspondence.

Carolin Antos, PhD, is an Assistant Professor for Theoretical Philosophy at the University of Konstanz.

Neil Barton, PhD, is a Lecturer in the Department of Philosophy at the National University of Singapore.

Giorgio Venturi, PhD, is a tenure-track Associate Professor at the Department of Civilization and Forms of Knowledge at the University of Pisa.