Juliette Kennedy has been a member of the Department of Mathematics and Statistics at the University of Helsinki since 1999. Her work in mathematical logic is focused mainly in the areas of set-theoretic model theory and set theory, but she has also worked in models of arithmetic. In the history, philosophy and foundations of mathematics and logic she has worked extensively on Gödel; but she has also written on Turing, Tarski and Kreisel. In her recent work she has focused on the syntax/semantics distinction; she also works avocationally in the art field as a curator. Sophia Arbeiter is a graduate student in the Department of Philosophy at the University of Pittsburgh. Previously, she has studied Philosophy and Logic at the University of Vienna and Paris Panthéon-Sorbonne. Her current work is focused on the philosophy of logic, such as logical pluralism and the normativity of logic, as well as the History of Analytic Philosophy, most prominently Carnap.

• 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).

Juliette Kennedy has been a member of the Department of Mathematics and Statistics at the University of Helsinki since 1999. Her work in mathematical logic is focused mainly in the areas of set-theoretic model theory and set theory, but she has also worked in models of arithmetic. In the history, philosophy and foundations of mathematics and logic she has worked extensively on Gödel; but she has also written on Turing, Tarski and Kreisel. In her recent work she has focused on the syntax/semantics distinction; she also works avocationally in the art field as a curator. Sophia Arbeiter is a graduate student in the Department of Philosophy at the University of Pittsburgh. Previously, she has studied Philosophy and Logic at the University of Vienna and Paris Panthéon-Sorbonne. Her current work is focused on the philosophy of logic, such as logical pluralism and the normativity of logic, as well as the History of Analytic Philosophy, most prominently Carnap.

• 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).

Juliette Kennedy has been a member of the Department of Mathematics and Statistics at the University of Helsinki since 1999. Her work in mathematical logic is focused mainly in the areas of set-theoretic model theory and set theory, but she has also worked in models of arithmetic. In the history, philosophy and foundations of mathematics and logic she has worked extensively on Gödel; but she has also written on Turing, Tarski and Kreisel. In her recent work she has focused on the syntax/semantics distinction; she also works avocationally in the art field as a curator. Sophia Arbeiter is a graduate student in the Department of Philosophy at the University of Pittsburgh. Previously, she has studied Philosophy and Logic at the University of Vienna and Paris Panthéon-Sorbonne. Her current work is focused on the philosophy of logic, such as logical pluralism and the normativity of logic, as well as the History of Analytic Philosophy, most prominently Carnap.

• 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).