## One Hundred Years of Russell's Paradox: Mathematics, Logic, PhilosophyThe papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes thereby to the well-established body of mathematical philosophy initiated to a large extent by Russell's work. |

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### Contents

Introduction Bertrand RussellThe Invention of Mathematical Philosophy | 1 |

The Journey Back to Eden | 29 |

AWay Out | 49 |

Completeness and Iteration in Modern Set Theory | 85 |

Iterating | 119 |

Trying to Have Your Cake and Eat It Too | 135 |

Is ZF Finitistically Reducible? | 153 |

Inconsistency in the RealWorld | 181 |

Russells Intermediate Theory | 401 |

Propositional Ontology and Logical Atomism | 417 |

Classes of Classes and Classes of Functions in | 435 |

A Constructive Proper Extension of Ramified Type Theory The Logic of Principia Mathematica Second Edition Appendix B | 449 |

Russell on Method | 481 |

Paradoxes in Göttingen | 501 |

Limits and Ideals | 517 |

Russells Paradox and Hilberts much Forgotten View of Set Theory | 533 |

Predicativity Circularity and AntiFoundation | 191 |

Russells Paradox and Diagonalization in a Constructive Context | 221 |

Constructive Solutions of Continuous Equations | 227 |

Russells Paradox in Consistent Fragments of Freges Grundgesetze der Arithmetik | 247 |

On a Russellian Paradox about Propositions and Truth | 259 |

The Consistency of the Naive Theory of Properties | 285 |

The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes | 311 |

The Prehistory of Russells Paradox | 349 |

Logicisms Insolubilia and Their Solution by Russells Substitutional Theory | 373 |

The Justification for Extrapolation | 549 |

Russells Absolutism vs ? Structuralism | 561 |

Mathematicians and Mathematical Objects | 577 |

Why Semantics Is no Proper Guide to the Nature of Properties | 591 |

The Many Lives of EbenezerWilkes Smith | 611 |

What Makes Expressions Meaningful? A Reflection on Contexts and Actions | 625 |

List of Contributors | 645 |

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One Hundred Years of Russell ́s Paradox: Mathematics, Logic, Philosophy Godehard Link Limited preview - 2004 |