One Hundred Years of Russell´s Paradox

Frontmatter

Table of Contents

Introduction. Bertrand Russell-The Invention of Mathematical Philosophy

Set Theory after Russell: The Journey Back to Eden

A Way Out

Completeness and Iteration in Modern Set Theory

Was sind und was sollen (neue) Axiome?

Iterating S Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo

Typical Ambiguity: Trying to Have Your Cake and Eat It Too

Is ZF Finitistically Reducible?

Inconsistency in the Real World

Predicativity, Circularity, and Anti-Foundation

Russell's Paradox and Diagonalization in a Constructive Context

Constructive Solutions of Continuous Equations

Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik

On a Russellian Paradox about Propositions and Truth

The Consistency of the Naive Theory of Properties

The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes

The Prehistory of Russell's Paradox

Logicism's 'Insolubilia' and Their Solution by Russell's Substitutional Theory

Substitution and Types: Russell's Intermediate Theory

Propositional Ontology and Logical Atomism

Classes of Classes and Classes of Functions in Principia Mathematica

A "Constructive" Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B)

Russell on Method

Paradoxes in Göttingen

David Hilbert and Paul du Bois-Reymond: Limits and Ideals

Russell's Paradox and Hilbert's (much Forgotten) View of Set Theory

Objectivity: The Justification for Extrapolation

Russell's Absolutism vs. (?) Structuralism

Mathematicians and Mathematical Objects

Russell's Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties

The Many Lives of Ebenezer Wilkes Smith

What Makes Expressions Meaningful? A Reflection on Contexts and Actions

Backmatter