Foundational Theories of Classical and Constructive Mathematics

1. Foundational Frameworks
Geoffrey Hellman*

2. The Problem of Mathematical Objects
Bob Hale

3. Set Theory as a Foundation
Penelope Maddy

4. Foundations: Structures, Sets, and Categories
Stewart Shapiro

5. From Sets to Types, to Categories, to Sets
Steve Awodey

6. Enriched Stratified Systems for the Foundations of Category Theory
Solomon Feferman

7. Recent Debate over Categorical Foundations
Colin McLarty

8. The Axiom of Choice in the Foundations of Mathematics
John L. Bell

9. Reflections on the Categorical Foundations of Mathematics
Joachim Lambek, Philip J. Scott

10. Local Constructive Set Theory and Inductive Definitions
Peter Aczel

11. Proofs and Constructions
Charles McCarty

12. Euclidean Arithmetic: The Finitary Theory of Finite Sets
J.P. Mayberry

13. Intentionality, Intuition, and Proof in Mathematics
Richard Tieszen

14. Foundations for Computable Topology
Paul Taylor

15. Conclusion: A Perspective on Future Research in FOM
Giovanni Sommaruga, John Bell

Nyckelord: Mathematics, Mathematical Logic and Foundations, Philosophy of Science, Logic