Axiomatic Thinking I

Volume 1: History and Philosophy.- Axiomatisches Denken.- Part I: History and Philosophy.- Hilbert's Axiomatisches Denken.- Scope and Limits of Axiomatics.- The Semantic Function of the Axiomatic Method.- Aristotle's Relations: An Interpretation in Combinatory Logic.- The Two Sides of Modern Axiomatics: Dedekind and Peano, Hilbert and Bourbaki.- Notes for a Seminar in Axiomatic Reasoning.- Axiomatic Thinking, Identity of Proofs and the Quest for an Intensional Proof-Theoretic Semantics.- Proofs as Objects.- Where Do Axioms Come From?.- Panel Discussion on the Foundations of Mathematics. 

Fernando Ferreira is Professor of Mathematics at Universidade de Lisboa. He received his Ph.D. at Pennsylvania State University in 1988 under the direction of Stephen Simpson. He was a Fulbright Scholar at Harvard University (Spring 2004) and Tinker Visiting Professor at Stanford University (Fall 2009). He has written papers on weak systems of arithmetic and analysis, proof theory (especially functional interpretations) and the philosophy and foundations of mathematics. He also wrote two papers on the problem of truth in Parmenides and Plato. He is a corresponding member of the Academia das Ciências de Lisboa.
Reinhard Kahle is Carl Friedrich von Weizsäcker Professor of Philosophy and History of Science at the University of Tübingen. Previously he held professorships in Mathematics at the University of Coimbra and at the Universidade Nova in Lisbon, finally becoming full professor in Mathematical Logic. He is a fellow of the Académie Internationale de Philosophie des Sciences. His main research interests are in proof theory and the history and philosophy of modern mathematical logic, in particular, of the Hilbert School. He has (co-)edited more than ten books and special issues such as, for instance, Gentzen's Centenary: The quest for consistency (Springer, 2015) and The Legacy of Kurt Schütte (Springer, 2020), both together with Michael Rathjen.