Sieg / Sommer / Talcott Reflections on the Foundations of Mathematics

Essays in Honor of Solomon Feferman
Erscheinungsjahr 2020
ISBN: 978-1-316-99881-6
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 15, 0 Seiten

Reihe: Lecture Notes in Logic

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.

Autoren/Hrsg.

Sieg, Wilfried

Sommer, Richard

Talcott, Carolyn

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

Preface; Part I. Proof Theoretic Analysis: 1. Ordinal analysis without proofs Jeremy Avigad; 2. Relating ordinals to proofs in a perspicuous way Wilfried Buchholz; 3. Internal finite tree embeddings Harvey M. Friedman; 4. Foundational and mathematical uses of higher types Ulrich Kohlenbach; 5. The epsilon substitution method and continuity Grigori Mint; 6. Predicativity: the outer limits Stephen G. Simpson; Part II. Logic and Computation: 7. A pragmatic interpretation of substructural logics Gianluigi Bellin and Carlo Dalla Pozza; 8. Computational complexity and induction for computable functions in type theory Robert L. Constable and Karl Crary; 9. Computability theory: structure or algorithms Jens Erik Fenstad; 10. Three processes in natural language interpretation Tim Fernando; 11. Infinitary initial algebra specifications for stream algebras J. V. Tucker and J. I. Zucker; Part III. Applicative and Self-Applicative Theories: 12. On extensionality, uniformity and comprehension in the theories of operations and classes Andrea Cantini; 13. The proof-theoretic analysis of the Suslin operator in applicative theories Gerhard Jäger and Thomas Strahm; 14. Feferman-Landin logic Ian A. Mason and Carolyn L. Talcott; 15. Explicit mathematics with monotone inductive definitions: a survey Michael Rathjen; Part IV. Philosophy of Modern Mathematical and Logical Thought: 16. On the constructivity of proofs: a debate among Behmann, Bernays, Gödel, and Kaufmann Paolo Mancosu; 17. Realism and the debate on impredicativity, 1917–44 Charles Parsons; 18. Calculations by man and machine: conceptual analysis Wilfried Sieg; 19. Remarks on finitism W. W. Tait; 20. Logical constraints: the variable fortunes of an elusive notion Johan van Benthem; Symposium program.

Über Autor(innen)

Sommer, Richard
Richard Sommer works in the Center for the Study of Language and Information at Stanford University, California.

Sieg, Wilfried
Wilfrid Sieg works in the Department of Philosophy at Carnegie Mellon University, Pennsylvania.

Talcott, Carolyn
Carolyn Talcott works in the Computer Science Department at Stanford University, California.