Russell’s Paradox and Diagonalization in a Constructive Context

Chapters in this book

1. Frontmatter i
2. Table of Contents vii
3. Introduction. Bertrand Russell—The Invention of Mathematical Philosophy 1
4. Set Theory after Russell: The Journey Back to Eden 29
5. A Way Out 49
6. Completeness and Iteration in Modern Set Theory 85
7. Was sind und was sollen (neue) Axiome? 93
8. Iterating Σ Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo 119
9. Typical Ambiguity: Trying to Have Your Cake and Eat It Too 135
10. Is ZF Finitistically Reducible? 153
11. Inconsistency in the Real World 181
12. Predicativity, Circularity, and Anti-Foundation 191
13. Russell’s Paradox and Diagonalization in a Constructive Context 221
14. Constructive Solutions of Continuous Equations 227
15. Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik 247
16. On a Russellian Paradox about Propositions and Truth 259
17. The Consistency of the Naive Theory of Properties 285
18. The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes 311
19. The Prehistory of Russell’s Paradox 349
20. Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory 373
21. Substitution and Types: Russell’s Intermediate Theory 401
22. Propositional Ontology and Logical Atomism 417
23. Classes of Classes and Classes of Functions in Principia Mathematica 435
24. A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B) 449
25. Russell on Method 481
26. Paradoxes in Göttingen 501
27. David Hilbert and Paul du Bois-Reymond: Limits and Ideals 517
28. Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory 533
29. Objectivity: The Justification for Extrapolation 549
30. Russell’s Absolutism vs. (?) Structuralism 561
31. Mathematicians and Mathematical Objects 577
32. Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties 591
33. The Many Lives of Ebenezer Wilkes Smith 611
34. What Makes Expressions Meaningful? A Reflection on Contexts and Actions 625
35. Backmatter 645