Reflections on the Foundations of Mathematics Univalent Foundations, Set Theory and General Thoughts /

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Centrone, Stefania (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Kant, Deborah (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Sarikaya, Deniz (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; 407
• Θέματα: Mathematics-Philosophy.; Computer science-Mathematics.; Mathematical logic.; Mathematical physics.; Philosophy of Mathematics.; Mathematics of Computing.; Mathematical Logic and Foundations.; Theoretical, Mathematical and Computational Physics.; Mathematical Logic and Formal Languages.

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover sys...

Πίνακας περιεχομένων:

• Part I: Current Challenges for the Set Theoretic Foundations
• 1. Neil Barton and Sy-David Friedman: Does set theory need an apology?
• 2. Laura Fontanella: The choice of new axioms in set theory
• 3. Michèle Friend: Pluralism in Foundations of Mathematics: Oxymoron, Paradox, Neither or Both?
• 4. Deborah Kant: A distinction between meta set theory and object set theory
• 5. Jan von Plato: The weaknesses of set theory
• 6. Claudio Ternullo: Multiversism and Naturalism
• 7. Philip Welch: Proving Theorems from Reflection: Global Reflection Theorems
• Part II: What are the Univalent Foundations?
• 8. Benedikt Ahrens and Paige North: Univalent foundations and the equivalence principle
• 9. Thorsten Altenkirch: A constructive justification of Homotopy Type Theory
• 10. Ulrik Buchholtz: Title: Higher structures in Homotopy Type Theory
• 11. Andrei Rodin: Models of HoTT and the Semantic View of Theories
• 12. Urs Schreiber: Modern Physics formalized in Modal Homotopy Type Theory
• 13. Vladimir Voevodsky: Multiple Concepts of Equality in the New Foundations of Mathematics
• Part III: Thoughts on the Foundations of Mathematics
• 14. Nathan Bowler: Foundations for the working mathematician, and for their computer
• 15. Merlin Carl: Formal and Natural Proof - A phenomenological approach
• 16. Stefania Centrone and Deniz Sarikaya: Thoughts on the Foundation of Mathematics: Logicism, Intuitionism and Formalism
• 17. Mirna Džamonja: 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 practice
• 20. Roy Wagner: Does mathematics need foundations?.