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.

• 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.

• 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.

• 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.