• 1. Introduction; 2. Why set theory?; 3. The naive conception of set and the classic paradoxes; 4. The logical and combinatorial conceptions of set; 5. Iterative conceptions: first examples; 6. Forcing as a construction method; 7. A 'new' kind of paradox?; 8. Countabilist conceptions of iterative set; 9. Mathematics and philosophy under the different conceptions; 10. Conclusions, open questions, and the future; References.

'This book is a good example of a philosophy of mathematics that is historically and mathematically well informed, rigorous in its treatment of complicated and technical material, and yet still accessible enough for non-experts on the field (like myself). It should be read by any philosopher (of mathematics or otherwise) who is curious about set theory and its philosophy.' Francisco N. Martínez-Aviña, Metascience

• 1. Introduction; 2. Why set theory?; 3. The naive conception of set and the classic paradoxes; 4. The logical and combinatorial conceptions of set; 5. Iterative conceptions: first examples; 6. Forcing as a construction method; 7. A 'new' kind of paradox?; 8. Countabilist conceptions of iterative set; 9. Mathematics and philosophy under the different conceptions; 10. Conclusions, open questions, and the future; References.

'This book is a good example of a philosophy of mathematics that is historically and mathematically well informed, rigorous in its treatment of complicated and technical material, and yet still accessible enough for non-experts on the field (like myself). It should be read by any philosopher (of mathematics or otherwise) who is curious about set theory and its philosophy.' Francisco N. Martínez-Aviña, Metascience

• 1. Introduction; 2. Why set theory?; 3. The naive conception of set and the classic paradoxes; 4. The logical and combinatorial conceptions of set; 5. Iterative conceptions: first examples; 6. Forcing as a construction method; 7. A 'new' kind of paradox?; 8. Countabilist conceptions of iterative set; 9. Mathematics and philosophy under the different conceptions; 10. Conclusions, open questions, and the future; References.

'This book is a good example of a philosophy of mathematics that is historically and mathematically well informed, rigorous in its treatment of complicated and technical material, and yet still accessible enough for non-experts on the field (like myself). It should be read by any philosopher (of mathematics or otherwise) who is curious about set theory and its philosophy.' Francisco N. Martínez-Aviña, Metascience