Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thought

Part I: Current Challenges for the Set Theoretic Foundations1. Neil Barton and Sy-David Friedman: Does set theory need an apology?2. Laura Fontanella: The choice of new axioms in set theory3. Michèle Friend: Pluralism in Foundations of Mathematics: Oxymoron, Paradox, Neither or Both?4. Deborah Kant: A distinction between meta set theory and object set theory5. Jan von Plato: The weaknesses of set theory6. Claudio Ternullo: Multiversism and Naturalism7. Philip Welch: Proving Theorems from Reflection: Global Reflection Theorems
Part II: What are the Univalent Foundations? (In Alphabetical order)8. Benedikt Ahrens and Paige North: Univalent foundations and the equivalence principle9. Thorsten Altenkirch: A constructive justification of Homotopy Type Theory10. Ulrik Buchholtz: Title: Higher structures in Homotopy Type Theory11. Andrei Rodin: Models of HoTT and the Semantic View of Theories12. Urs Schreiber: Modern Physics formalized in Modal Homotopy Type Theory13. Vladimir Voevodsky: Multiple Concepts of Equality in the New Foundations of Mathematics
Part III: Thoughts on the Foundations of Mathematics14. Nathan Bowler: Foundations for the working mathematician, and for their computer15. Merlin Carl: Formal and Natural Proof - A phenomenological approach16. Stefania Centrone and Deniz Sarikaya: Thoughts on the Foundation of Mathematics: Logicism, Intuitionism and Formalism17. Mirna Dzamonja: A new foundational crisis in mathematics, is it really happening?18. Penelope Maddy: What foundational jobs do we want done?19. Giovanni Sambin: Dynamics in foundations: what does it mean in practice20. Roy Wagner: Does mathematics need foundations?