One hundred years of Russell's paradox : mathematics, logic, philosophy / edited by Godehard Link.

Format:

Book

Contributor:

Link, Godehard.

Series:

Gruyter series in logic and its applications ; 6.

De Gruyter series in logic and its applications ; 6

Language:

English

Subjects (All):

Paradox.

Liar paradox.

Physical Description:

1 online resource (672 p.)

Other Title:

100 years of Russell's paradox

Place of Publication:

New York : Walter de Gruyter, 2004.

Language Note:

English

Summary:

Die in diesem Band zusammengefassten Beiträge stellen die wesentlichen Forschungsergebnisse der internationalen Münchner Konferenz "100 Jahre Russell-Paradoxon" im Jahr 2001 dar, auf der an die Entdeckung des berühmten Russell Paradoxons vor 100 Jahren erinnert wurde. Die 31 Beiträge und der Einführungsessay des Herausgebers wurden alle - bis auf zwei Ausnahmen - ursprünglich für diesen Band verfasst.

The 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 therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Contents:

Front matter

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 Σ 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

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

ISBN:

9786612194801

9781282194809

1282194801

9783110199680

3110199688

OCLC:

173511912