Chapter 1. Autobiography (Penelope Maddy) -- Part 1: Philosophy of set theory and mathematics -- Chapter 2. Generically invariant set-theory (John Steel) -- Chapter 3. Response to John Steel (Penelope Maddy) -- Chapter 4. Intrinsic and extrinsic evidence in set theory (Donald A. Martin) -- Chapter 5. Response to Tony Martin (Penelope Maddy) -- Chapter 6. Maddy on classes (Øystein Linnebo) -- Chapter 7. Response to Øystein Linnebo (Penelope Maddy) -- Chapter 8. A general framework for a second philosophy analysis of set-theoretic methodology (Carolin Antos and Deborah Kant) -- Chapter 9. Response to Carolin Antos & Deborah Kant (Penelope Maddy) -- Chapter 10. Maddy’s notion of ‘Maximize’ and strong theories of sets (Jeffrey Schatz) -- Chapter 11. Exploring the generous arena (John T. Baldwin) -- Chapter 12. Response to John Baldwin (Penelope Maddy) -- Part 2: Realism, anti-realism and thin realism -- Chapter 13. Second philosophy and realism (Patricia Blanchette) -- Chapter 14. Response to Patricia Blanchette (Penelope Maddy) -- Chapter 15. Meditations on second philosophy: Anti-nominalist reflections on Maddy's semi-nominalism (John P. Burgess) -- Chapter 16. Response to John P. Burgess (Penelope Maddy) -- Chapter 17. Enhanced “If-thenism”, fictionalism, and realist anti-platonism (Mary Leng) -- Chapter 18. Response to Mary Leng (Penelope Maddy) -- Chapter 19. Logical realism –– A tale of two theories (Gila Sher) -- Chapter 20. Response to Gila Sher (Penelope Maddy) -- Chapter 21. Trumping naturalism revisited (A. C. Paseau) -- Chapter 22. Response to Alex Paseau (Penelope Maddy) -- Part 3: History of philosophy -- Chapter 23. What do philosophers do? Maddy, Moore (and Wittgenstein) II (Annalisa Coliva) -- Chapter 24. Response to Annalisa Coliva (Penelope Maddy) -- Chapter 25. A carnapian solution to the puzzle of extrinsic justifications (Zeynep Soysal) -- Chapter 26. Response to Zeynep Soysal (Penelope Maddy) -- Chapter 27. Wittgenstein’s wayward student: The unauthorized autobiography (Curtis Franks) -- Chapter 28. Response to Curtis Franks (Penelope Maddy) -- Part 4: Mathematical practice -- Chapter 29. Realizing infinity (Maryanthe Malliaris and Assaf Peretz) -- Chapter 30. Second philosophy and the depth metaphor (Juliette Kennedy) -- Chapter 31. Response to Juliette Kennedy (Penelope Maddy) -- Chapter 32. The flight from application (Mark Wilson) -- Chapter 33. Response to Mark Wilson (Penelope Maddy) -- Part 5: Conversations on Set Theory -- Chapter 34. A conversation between Penelope Maddy and Menachem Magidor (Jeffrey Schatz) -- Chapter 35. Interview with David Asperó (Corey Switzer) -- Chapter 36. A conversation with Hugh Woodin (Juliette Kennedy and Beau Madison Mount) -- Chapter 37. On multiversism (Penelope Maddy).

This volume features more than 20 essays that explore the work of one of the most important contemporary philosophers of mathematics. It will help readers to better appreciate this significant and prolific philosopher. Within philosophy of mathematics, Penelope Maddy initially advocated realism. She then went on to advance naturalism. Both of her positions became very influential in the field, along with her other work in the philosophy of logic. The contributors comment on and otherwise engage with Maddy’s work. They also weigh in on the state of set theory and its philosophy, the philosophy and history of logic, naturalism, skepticism, and the myriad other areas to which Maddy left her mark. Overall, coverage traces her influence on these various ideas over the years. It will also help readers to better understand how philosophers working at the forefront of these areas see these concepts today. These essays will be essential reading for the wide group of philosophers working in these different areas as well as graduate students studying philosophy of mathematics and logic and the other related issues to which Maddy has contributed. The volume will also appeal to logicians and set theorists in general, as well as to philosophers working in analytic philosophy more widely, as well as to those working in the history of philosophy.