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.