Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman
Wilfried Sieg , Richard Sommer and Carolyn Talcott, Editors
450 pages. Hardcover.
450 pages. Paperback.
Solomon Feferman has shaped the field of foundational research for nearly half a century. These papers, most of which were presented at the symposium honoring him at his 70th birthday, reflect his broad interests as well as his approach to foundational research, which places the solution of mathematical and philosophical problems at the top of his agenda. The contributions range from historical to technical to philosophical topics, with emphasis on proof theory and computational aspects.
Table of Contents
Part I: Proof Theoretic Analysis
- Ordinal analysis without proofs.
- Relating ordinals to proofs in a perspicuous way.
- Internal finite tree embeddings.
Harvey M. Friedman
- Foundational and mathematical uses of higher types.
- The epsilon substitution method and continuity.
- Predicativity: The outer limits.
Stephen G. Simpson
Part II: Logic and Computation
- A pragmatic interpretation of substructural logics.
Gianluigi Bellin and Carlo Dalla Pozza
- Computational complexity and induction for partial computable functions in type theory.
Robert L. Constable and Karl Crary
- Computability theory: structure or algorithms
Jens Erik Fenstad
- Three processes in natural language interpretation.
- Infinitary initial algebra specifications for stream algebras.
J.V. Tucker and J.I. Zucker
Part III: Applicative and Self-Applicative Theories
- On extensionality, uniformity and comprehension in the theories of operations and classes.
- The proof-theoretic analysis of the Suslin operator in applicative theories.
Gehard Jäger and Thomas Strahm
- Feferman-Landin Logic.
Ian A. Mason and Carolyn L. Talcott
- Explicit mathematics with monotone inductive definitions: A survey.
Part IV: Philosophy of Modern Mathematical and Logical Thought
- On the constructivity of proofs. A debate among Behmann, Bernays, Gödel, and Kaufmann.
- Realism and the debate on impredicativity, 1917-1944*.
- Calculations by man and machine: conceptual analysis*.
- Remarks on finitism.
- Logical constants: the variable fortunes of an elusive notion.
Johan van Benthem